predictions.jsonl

{"answer":{"choice":"high","confidence":0.4227,"probabilities":{"high":0.6151,"low":0.104,"medium":0.2809},"type":"choice"},"confidence":0.4227,"correct":true,"dataset":"routing_calibration_en_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"en","latency_ms":2752.326,"pair_id":"architecture_high_001","predicted":"high","prompt":"A payment API is active-active in two regions. During an arbitrary inter-region network partition, each region must complete the payment and return a successful result for the same customer's requests without contacting the other region; rejection, redirection, or deferral until after the partition is not allowed. The payment provider is reachable from both regions but offers no idempotency or deduplication, and the regions have only asynchronously replicated local databases. A client may send the same idempotency key to both regions during the partition. The two required properties are: (1) both regions remain able to complete such a request successfully during the partition, and (2) the system guarantees that at most one provider charge occurs. What is the minimum number of these two properties that must be relaxed to make an implementation possible?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"8eba07cc0f574f4c9b18f0fb0dd618fb"},"task_id":"rc_en_architecture_high_001","usage":{"input_tokens":410,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.2306,"probabilities":{"high":0.394,"low":0.1189,"medium":0.4871},"type":"choice"},"confidence":0.2306,"correct":false,"dataset":"routing_calibration_en_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"en","latency_ms":644.918,"pair_id":"architecture_high_002","predicted":"medium","prompt":"A queue receives 600 logical jobs per second. Exactly 10% fail once and are retried once, so the queue must execute all resulting attempts. A worker executes 50 attempts per second, and surviving active workers may use at most 75% of that rate. Workers are deployed equally across 3 availability zones. After losing any one whole zone, enough workers must remain, and the queue must have at least one partition per active worker; extra deployed workers may remain hot standbys when partitions are fewer. Minimize first the total deployed workers W and then the partition count P. What is 100W+P?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"7d191f9782dc40269ad8b7588190388a"},"task_id":"rc_en_architecture_high_002","usage":{"input_tokens":383,"output_tokens":62}}
{"answer":{"choice":"high","confidence":0.22,"probabilities":{"high":0.48,"low":0.0907,"medium":0.4293},"type":"choice"},"confidence":0.22,"correct":true,"dataset":"routing_calibration_en_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"en","latency_ms":681.821,"pair_id":"architecture_high_003","predicted":"high","prompt":"There is a per-instance L1 cache with TTL 30 seconds and a shared L2 with TTL 100 seconds. A GET checks L1, then L2, then the database, filling every missed level. Database writes immediately refresh existing L2 entries with the new value; listed L1 invalidations occur just before other events at the same time. Initially the database is v1 and caches are empty. Events: t0 GET X; t10 GET Y; t20 write v2 (invalidate X at26,Y at35); t22 GET X; t24 GET Z; t27 GET X; t32 write v3 (invalidate X at50,Y at38,Z at45); t34 GET Y; t39 GET Y; t44 GET Z; t46 GET Z; t49 GET X; t51 GET X. Let O be database-origin GETs and S be GETs returning a version older than the database. What is 100O+S?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"c5778e6914814609bb15fab00a36de65"},"task_id":"rc_en_architecture_high_003","usage":{"input_tokens":468,"output_tokens":59}}
{"answer":{"choice":"medium","confidence":0.3084,"probabilities":{"high":0.324,"low":0.137,"medium":0.539},"type":"choice"},"confidence":0.3084,"correct":false,"dataset":"routing_calibration_en_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"en","latency_ms":577.198,"pair_id":"architecture_high_004","predicted":"medium","prompt":"A rolling column migration assigns codes: 1=drop legacy column; 2=conditionally backfill replacement rows while dual-writes are active; 3=add nullable replacement; 4=deploy compatibility build that reads legacy and dual-writes; 5=verify parity and no null replacements; 6=deploy build that reads replacement with legacy fallback and still dual-writes; 7=wait until all compatibility-build binaries are drained; 8=deploy new-only build that stops legacy writes; 9=complete the rollback observation window. Requirements: dual-writing precedes backfill; verification precedes replacement reads; compatibility binaries are drained before legacy writes stop; and the rollback window completes before the legacy column is dropped. Concatenate all codes in the only safe order.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"451d14ea5b314c9c975b569ee114eb3d"},"task_id":"rc_en_architecture_high_004","usage":{"input_tokens":404,"output_tokens":60}}
{"answer":{"choice":"medium","confidence":0.2027,"probabilities":{"high":0.2746,"low":0.2569,"medium":0.4685},"type":"choice"},"confidence":0.2027,"correct":false,"dataset":"routing_calibration_en_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"en","latency_ms":685.035,"pair_id":"architecture_high_005","predicted":"medium","prompt":"A fulfillment saga starts with 20 available units, $0 held authorization, and 0 active carrier bookings. It reserves 4 units, authorizes $120, and asks a carrier to create a booking. The carrier commits the booking but the reply is lost; retrying the same booking key returns the existing booking. Payment capture then definitively fails before commit. Compensation cancels the booking (the cancel commits, its reply is lost, and the same cancel key is retried), releases inventory (the same event_id is delivered twice to an idempotent consumer), and voids the authorization. Let T be the total number of committed state changes across the inventory, payment-provider, and carrier systems; an idempotent retry that returns existing state and an operation that fails before commit add zero. Let A be final available units, H final held dollars, and B final active bookings. What is 100000T+1000A+10H+B?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"a54ee523d8054fb1b6a7dc6dc381f3f9"},"task_id":"rc_en_architecture_high_005","usage":{"input_tokens":452,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3203,"probabilities":{"high":0.2274,"low":0.2257,"medium":0.5468},"type":"choice"},"confidence":0.3203,"correct":false,"dataset":"routing_calibration_en_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"en","latency_ms":603.558,"pair_id":"architecture_high_006","predicted":"medium","prompt":"A consensus database has exactly 7 voting replicas across US, EU, and AP. Each region needs at least 2 replicas for local read capacity. Losing any whole region must leave the 4-vote majority, so no region may contain more than 3 replicas. The write leader is in US; a 4-ack commit should require as few remote acknowledgements as possible, so subject to the prior constraints maximize replicas in US. Let U,E,A be replica counts. What is 100U+10E+A?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"a9105d6a853c4d30b88cb856482052b9"},"task_id":"rc_en_architecture_high_006","usage":{"input_tokens":358,"output_tokens":63}}
{"answer":{"choice":"high","confidence":0.2489,"probabilities":{"high":0.4992,"low":0.0849,"medium":0.4159},"type":"choice"},"confidence":0.2489,"correct":true,"dataset":"routing_calibration_en_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"en","latency_ms":671.52,"pair_id":"architecture_high_007","predicted":"high","prompt":"Every primary database shard has load capacity 100. Premium tenants A=60 and B=35 each require a dedicated primary shard. Standard tenants C=55,D=45,E=40,F=35,G=30,H=25 may share with at most 3 tenants per shard, but pairs C-D, E-F, and G-H are forbidden from sharing. Every primary shard needs one copy in each of 3 availability zones. A database instance hosts at most 2 shard copies, and copies cannot leave their zone. Minimize primary shards S, then instances I. What is 100S+I?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"ce7e9c8a52f040c7a4132c2d30fa6aa3"},"task_id":"rc_en_architecture_high_007","usage":{"input_tokens":384,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.1933,"probabilities":{"high":0.427,"low":0.1108,"medium":0.4622},"type":"choice"},"confidence":0.1933,"correct":false,"dataset":"routing_calibration_en_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"en","latency_ms":598.653,"pair_id":"architecture_high_008","predicted":"medium","prompt":"A service receives 800 requests per second. At the required utilization, one node safely serves 100 requests per second. It deploys the same integer number of nodes in each of 3 availability zones. During loss of any entire zone plus one additional node drained for deployment, remaining safe capacity must still cover traffic. Separately, the monthly error budget is 1200 full-outage-equivalent seconds; 540 have been consumed and policy reserves 25% of the original budget. A migration causes exactly 20% of requests to fail while it runs. Let N be the minimum deployed nodes and D the maximum whole seconds the migration may run without touching the reserve. What is 10000N+D?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"a945f65fd109411788b4443195467978"},"task_id":"rc_en_architecture_high_008","usage":{"input_tokens":405,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.4481,"probabilities":{"high":0.0738,"low":0.6321,"medium":0.2941},"type":"choice"},"confidence":0.4481,"correct":true,"dataset":"routing_calibration_en_architecture_low","domain":"architecture","error":null,"expected":"low","lang":"en","latency_ms":520.21,"pair_id":"architecture_low_001","predicted":"low","prompt":"A payment API stores the first successful request in a table whose unique key is (tenant_id, idempotency_key). The table is initially empty and no entry expires during this sequence. Requests arrive in order: (Acme,k1), (Acme,k1), (Beta,k1), (Acme,k2), (Acme,k2), (Acme,k2). How many charges are created?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"635c42477d854f2f8051c0a349529e2f"},"task_id":"rc_en_architecture_low_001","usage":{"input_tokens":333,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.7051,"probabilities":{"high":0.0442,"low":0.8034,"medium":0.1524},"type":"choice"},"confidence":0.7051,"correct":true,"dataset":"routing_calibration_en_architecture_low","domain":"architecture","error":null,"expected":"low","lang":"en","latency_ms":510.329,"pair_id":"architecture_low_002","predicted":"low","prompt":"A queue provides at-least-once delivery. In the same database transaction, a worker inserts job_id into a unique processed_jobs table and applies the job's effect; a duplicate job_id applies no effect. The delivered job IDs are 17, 18, 17, 19, 18, 20, 20. How many job effects are applied?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"4670077696fc4fb5a1d756eb5ce337a1"},"task_id":"rc_en_architecture_low_002","usage":{"input_tokens":331,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.252,"probabilities":{"high":0.0892,"low":0.5013,"medium":0.4095},"type":"choice"},"confidence":0.252,"correct":true,"dataset":"routing_calibration_en_architecture_low","domain":"architecture","error":null,"expected":"low","lang":"en","latency_ms":504.743,"pair_id":"architecture_low_003","predicted":"low","prompt":"A read-through cache has a TTL of exactly 60 seconds. A value loaded at time t is fresh for times strictly less than t+60 and expired at t+60. The cache starts empty. Reads occur at seconds 0, 10, 59, 60, 61, 119, and 120; there are no writes or evictions. How many reads go to the origin?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"d3015ab891624c92a65c174472990dcf"},"task_id":"rc_en_architecture_low_003","usage":{"input_tokens":343,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.1886,"probabilities":{"high":0.1301,"low":0.4109,"medium":0.459},"type":"choice"},"confidence":0.1886,"correct":false,"dataset":"routing_calibration_en_architecture_low","domain":"architecture","error":null,"expected":"low","lang":"en","latency_ms":512.926,"pair_id":"architecture_low_004","predicted":"medium","prompt":"A team numbers a zero-downtime column migration as follows: phase 1 add a nullable replacement column; phase 2 deploy code that writes both columns; phase 3 backfill and verify; phase 4 deploy code that reads only the replacement and wait until all old binaries are gone; phase 5 remove the legacy column. In which phase is removing the legacy column first safe?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"174839b26ef7477fa829863515b1a6ec"},"task_id":"rc_en_architecture_low_004","usage":{"input_tokens":327,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.1529,"probabilities":{"high":0.1538,"low":0.4353,"medium":0.4109},"type":"choice"},"confidence":0.1529,"correct":true,"dataset":"routing_calibration_en_architecture_low","domain":"architecture","error":null,"expected":"low","lang":"en","latency_ms":508.38,"pair_id":"architecture_low_005","predicted":"low","prompt":"A replicated store has 5 replicas. A successful write is present on W=3 replicas, and a read contacts R=3 replicas. What is the minimum number of replicas that every such read set is guaranteed to share with the successful write set?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"b090c7631dfe479fa629e22a4f16a258"},"task_id":"rc_en_architecture_low_005","usage":{"input_tokens":299,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.4948,"probabilities":{"high":0.0846,"low":0.6632,"medium":0.2522},"type":"choice"},"confidence":0.4948,"correct":true,"dataset":"routing_calibration_en_architecture_low","domain":"architecture","error":null,"expected":"low","lang":"en","latency_ms":598.99,"pair_id":"architecture_low_006","predicted":"low","prompt":"An order transaction atomically writes an order and one outbox row with a unique event_id. The broker may redeliver events, and the email consumer records event_id before sending, so each event_id can send at most once. Deliveries are E1, E1, E2, E3, E2, E3. How many emails are sent?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"e44c38baad8d4df88bcaaebbb7a8ecd7"},"task_id":"rc_en_architecture_low_006","usage":{"input_tokens":323,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8402,"probabilities":{"high":0.0216,"low":0.8935,"medium":0.0849},"type":"choice"},"confidence":0.8402,"correct":true,"dataset":"routing_calibration_en_architecture_low","domain":"architecture","error":null,"expected":"low","lang":"en","latency_ms":547.489,"pair_id":"architecture_low_007","predicted":"low","prompt":"Database row-level security permits a request to read only rows whose tenant_id equals the authenticated tenant_id. The authenticated tenant is 42. The queried rows have tenant IDs 42, 7, 42, 19, 42, 7, 42. How many rows are visible?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"3fbad50b4a4747fd90395ab4324770e6"},"task_id":"rc_en_architecture_low_007","usage":{"input_tokens":315,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.5881,"probabilities":{"high":0.0457,"low":0.7254,"medium":0.2289},"type":"choice"},"confidence":0.5881,"correct":true,"dataset":"routing_calibration_en_architecture_low","domain":"architecture","error":null,"expected":"low","lang":"en","latency_ms":613.145,"pair_id":"architecture_low_008","predicted":"low","prompt":"A service has a 99.95% monthly success SLO over exactly 100,000 requests. Treat the allowed failures as 0.05% of requests. If 31 requests have already failed, how many additional failures can occur before the error budget is exhausted?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"87e1144409bc4fe0be232e1ef03b1aee"},"task_id":"rc_en_architecture_low_008","usage":{"input_tokens":312,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2493,"probabilities":{"high":0.3297,"low":0.1708,"medium":0.4995},"type":"choice"},"confidence":0.2493,"correct":true,"dataset":"routing_calibration_en_architecture_medium","domain":"architecture","error":null,"expected":"medium","lang":"en","latency_ms":579.355,"pair_id":"architecture_medium_001","predicted":"medium","prompt":"A queue receives exactly 300 new jobs per second. Exactly 10% fail their first attempt and each such job is retried exactly once and then succeeds. A worker handles 30 attempts per second. After any one worker fails, the remaining workers must run at no more than 75% of their attempt capacity. What is the minimum total number of workers?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"6288c5c32af040cc87a682fe2bceada6"},"task_id":"rc_en_architecture_medium_001","usage":{"input_tokens":327,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3322,"probabilities":{"high":0.1548,"low":0.2904,"medium":0.5548},"type":"choice"},"confidence":0.3322,"correct":true,"dataset":"routing_calibration_en_architecture_medium","domain":"architecture","error":null,"expected":"medium","lang":"en","latency_ms":695.072,"pair_id":"architecture_medium_002","predicted":"medium","prompt":"A cache-aside entry has a long TTL. At t=0 a GET misses, reads database value v1, and fills the cache. At t=10 the database changes to v2; its invalidation arrives just before t=30. GETs occur at t=20 and t=30. At t=50 the database changes to v3; its invalidation arrives just before t=55. GETs occur at t=52 and t=56. A GET after an invalidation refills from the database. Let O be the total origin reads and S the GETs that return an older value than the database held at that time. What is 10O+S?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"8e9444a5ab724c42a69f1184e1f237c9"},"task_id":"rc_en_architecture_medium_002","usage":{"input_tokens":397,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3416,"probabilities":{"high":0.2615,"low":0.1774,"medium":0.5611},"type":"choice"},"confidence":0.3416,"correct":true,"dataset":"routing_calibration_en_architecture_medium","domain":"architecture","error":null,"expected":"medium","lang":"en","latency_ms":670.157,"pair_id":"architecture_medium_003","predicted":"medium","prompt":"Five actions in a zero-downtime migration have these codes: 1=drop the legacy column after the rollback window; 2=backfill and verify the replacement; 3=add the nullable replacement column; 4=roll out reads from the replacement and stop legacy writes, then drain older binaries; 5=deploy compatibility code that still reads legacy data but dual-writes both columns. To avoid missing concurrent writes, all writers must dual-write before backfill begins. Concatenate the action codes in their only safe order, with no separators.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"e48e0f14c0774faab73991f7af7cdf01"},"task_id":"rc_en_architecture_medium_003","usage":{"input_tokens":359,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2917,"probabilities":{"high":0.1275,"low":0.3447,"medium":0.5278},"type":"choice"},"confidence":0.2917,"correct":true,"dataset":"routing_calibration_en_architecture_medium","domain":"architecture","error":null,"expected":"medium","lang":"en","latency_ms":625.836,"pair_id":"architecture_medium_004","predicted":"medium","prompt":"A store has 5 replicas and chooses integer write quorum W and read quorum R. It requires W+R>5 so a read intersects the latest acknowledged write; both reads and writes must still complete with any one replica unavailable, so W≤4 and R≤4; and W≥2. Synchronously contacting a write replica costs 1 unit and a read replica costs 2 units, so minimize W+2R. Return 10W+R for the unique minimum-cost pair.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"1c73c316887347b69aead5836779391a"},"task_id":"rc_en_architecture_medium_004","usage":{"input_tokens":351,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2314,"probabilities":{"high":0.2796,"low":0.2328,"medium":0.4876},"type":"choice"},"confidence":0.2314,"correct":true,"dataset":"routing_calibration_en_architecture_medium","domain":"architecture","error":null,"expected":"medium","lang":"en","latency_ms":652.636,"pair_id":"architecture_medium_005","predicted":"medium","prompt":"An order saga starts with 12 available inventory units and a net customer charge of $0. Reserving 3 units succeeds, then charging $75 succeeds, then shipping definitively fails. The saga refunds the charge and releases the reservation. The refund commits but its reply is lost, so it is retried with the same provider idempotency key. The release event is delivered twice to a consumer that deduplicates by event_id. After compensation finishes, let A be available units and C the net charge in dollars. What is 1000A+C?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"8835db4021134a02b1b47b5165ec3540"},"task_id":"rc_en_architecture_medium_005","usage":{"input_tokens":366,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2466,"probabilities":{"high":0.2716,"low":0.2306,"medium":0.4978},"type":"choice"},"confidence":0.2466,"correct":true,"dataset":"routing_calibration_en_architecture_medium","domain":"architecture","error":null,"expected":"medium","lang":"en","latency_ms":663.244,"pair_id":"architecture_medium_006","predicted":"medium","prompt":"An outbox contains E1, E2, E3. Poller P1 leases E1 and E2 until t=30, publishes E1, then crashes before marking either row sent. At t=20, P2 cannot take leased rows, so it leases, publishes, and marks E3. At t=31, P2 leases E1 and E2, publishes both, and marks both. The consumer deduplicates by event_id. Let P be broker publications and X be distinct external effects. What is 10P+X?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"2f5ffd93d70744c29d9512eca5a6ec46"},"task_id":"rc_en_architecture_medium_006","usage":{"input_tokens":365,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3801,"probabilities":{"high":0.1759,"low":0.2374,"medium":0.5867},"type":"choice"},"confidence":0.3801,"correct":true,"dataset":"routing_calibration_en_architecture_medium","domain":"architecture","error":null,"expected":"medium","lang":"en","latency_ms":706.784,"pair_id":"architecture_medium_007","predicted":"medium","prompt":"A database shard has target load capacity 100. Premium tenants must each occupy a dedicated primary shard. Standard tenants may share, but at most two standard tenants may share a shard. Premium tenant loads are 60 and 35. Standard tenant loads are 65, 40, 35, and 25. What is the minimum number of primary shards?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"fb3d2dc67f684681950d52063b6d2c88"},"task_id":"rc_en_architecture_medium_007","usage":{"input_tokens":329,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.5907,"probabilities":{"high":0.048,"low":0.7271,"medium":0.2249},"type":"choice"},"confidence":0.5907,"correct":false,"dataset":"routing_calibration_en_architecture_medium","domain":"architecture","error":null,"expected":"medium","lang":"en","latency_ms":796.639,"pair_id":"architecture_medium_008","predicted":"low","prompt":"A service has a fixed error budget for a 30-day SLO window. At the end of day 10, exactly one half of the entire window's error budget has been consumed. Burn rate is defined as (fraction of error budget consumed)/(fraction of window elapsed). What is 10 times the burn rate?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"e7c9d939f6ac49ab9333f540e461acf7"},"task_id":"rc_en_architecture_medium_008","usage":{"input_tokens":316,"output_tokens":62}}
{"answer":{"choice":"high","confidence":0.2347,"probabilities":{"high":0.4898,"low":0.0556,"medium":0.4546},"type":"choice"},"confidence":0.2347,"correct":true,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":702.484,"pair_id":"high_001","predicted":"high","prompt":"Eight talks A through H occupy slots 1 through 8, one per slot. A is earlier than both D and G. The slot of H equals the slot of C plus 3. E and F are consecutive in either order. B is earlier than D. D is not consecutive with H. Exactly one of B and G is earlier than C. How many schedules satisfy all conditions?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"2242c04fc8d64f55843236a6fdc90002"},"task_id":"rc_en_high_001","usage":{"input_tokens":328,"output_tokens":63}}
{"answer":{"choice":"high","confidence":0.3802,"probabilities":{"high":0.5868,"low":0.0549,"medium":0.3583},"type":"choice"},"confidence":0.3802,"correct":true,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":526.794,"pair_id":"high_002","predicted":"high","prompt":"Consider binary strings on 10 labeled positions arranged in a cycle. How many strings contain exactly five 1s, have no three cyclically consecutive positions all equal to 1, and have different bits at positions 1 and 6? Triples that wrap around positions 10 and 1 count as consecutive.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"bd9830541c4b45fea332cac6a6cf996d"},"task_id":"rc_en_high_002","usage":{"input_tokens":314,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2365,"probabilities":{"high":0.4384,"low":0.0706,"medium":0.491},"type":"choice"},"confidence":0.2365,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":764.882,"pair_id":"high_003","predicted":"medium","prompt":"Two identical workers execute six nonpreemptive tasks. Durations in hours are A=4, B=3, C=5, D=2, E=4, and F=3. C can start only after A; D only after both A and B; E only after B; and F only after C, D, and E. Tasks C and E use the same accelerator and cannot overlap even when assigned to different workers. Both workers are available at time 0. What is the minimum number of hours needed to finish all tasks?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"15f60b9004534d1d8b27f8ef61230eea"},"task_id":"rc_en_high_003","usage":{"input_tokens":361,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.4397,"probabilities":{"high":0.2641,"low":0.1095,"medium":0.6264},"type":"choice"},"confidence":0.4397,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":621.247,"pair_id":"high_004","predicted":"medium","prompt":"A directed graph has these edge costs: S→A=7, S→B=4, A→C=5, A→D=8, B→A=2, B→D=6, B→E=9, C→D=2, C→E=6, D→E=3, D→T=10, E→T=7. Visiting C grants a key that changes the cost of E→T from 7 to 2. At most once, a coupon may replace the cost w of one traversed edge by floor(w/2), after applying any key discount. What is the minimum cost of a path from S to T?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"c6d32e7814af402e941632ea56ad17bb"},"task_id":"rc_en_high_004","usage":{"input_tokens":392,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3154,"probabilities":{"high":0.3703,"low":0.0861,"medium":0.5436},"type":"choice"},"confidence":0.3154,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":776.823,"pair_id":"high_005","predicted":"medium","prompt":"A directed graph has edge costs S→A=4, S→B=2, A→C=4, A→D=7, B→A=1, B→D=4, B→E=8, C→E=2, C→T=9, D→C=1, D→E=3, D→T=8, E→D=1, E→T=5. The first visit to A grants one coupon usable on a later edge; applying it changes cost w to ceil(w/2). The edge E→T may be used only after visiting C. What is the minimum cost from S to T?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"025bf80e02fc4e2991e237ed4eb02637"},"task_id":"rc_en_high_005","usage":{"input_tokens":387,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4487,"probabilities":{"high":0.2434,"low":0.1242,"medium":0.6325},"type":"choice"},"confidence":0.4487,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":695.871,"pair_id":"high_006","predicted":"medium","prompt":"Choose urn U1, U2, or U3 with prior probabilities 1/2, 1/3, and 1/6. Their (red,blue,green) counts are U1=(4,2,1), U2=(2,4,1), and U3=(3,2,2). Draw three balls sequentially without replacement. Given that the first two balls have different colors and at least one of them is red, the conditional probability that the third ball is red is p/q in lowest terms. What is p+q?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"6408b2a6dad34d468c72d61fbcb372dd"},"task_id":"rc_en_high_006","usage":{"input_tokens":364,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2118,"probabilities":{"high":0.4434,"low":0.082,"medium":0.4745},"type":"choice"},"confidence":0.2118,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":891.604,"pair_id":"high_007","predicted":"medium","prompt":"How many binary strings of length 12 satisfy all of these conditions: exactly five bits are 1; no two consecutive positions are both 1; exactly two of the 1s are in odd-numbered positions; and the first and last bits are equal? Adjacency here means consecutive positions only, so positions 1 and 12 are not adjacent.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"4b945dc48fd64833b23068a93b5f61c9"},"task_id":"rc_en_high_007","usage":{"input_tokens":323,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.2343,"probabilities":{"high":0.4404,"low":0.0701,"medium":0.4895},"type":"choice"},"confidence":0.2343,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":851.66,"pair_id":"high_008","predicted":"medium","prompt":"Eight distinct people A through H sit around a circular table. Rotations count as the same seating, but reflections count as different seatings. A and B are not adjacent. C and D sit opposite each other. E is adjacent to exactly one of A and B. How many seatings satisfy all conditions?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"b8dfcaf92d9c472c880e9d28ce0d85f2"},"task_id":"rc_en_high_008","usage":{"input_tokens":311,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4093,"probabilities":{"high":0.2763,"low":0.1175,"medium":0.6062},"type":"choice"},"confidence":0.4093,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":743.562,"pair_id":"high_009","predicted":"medium","prompt":"Eight projects have (cost,value): A=(3,7), B=(4,9), C=(2,4), D=(5,12), E=(3,6), F=(2,5), G=(4,10), H=(1,2). The budget is 11. Selecting D requires A; F requires B; G requires both C and E; A conflicts with B; and D conflicts with H. What is the maximum total value of a valid selection?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"33f88ed90cac4b30adc6f919ad8083a7"},"task_id":"rc_en_high_009","usage":{"input_tokens":352,"output_tokens":63}}
{"answer":{"choice":"high","confidence":0.2738,"probabilities":{"high":0.5159,"low":0.1045,"medium":0.3796},"type":"choice"},"confidence":0.2738,"correct":true,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":750.603,"pair_id":"high_010","predicted":"high","prompt":"A score starts at 0. For each of 6 rounds: if the current score is even, add 1 with probability 1/3 or add 3 with probability 2/3; if the current score is odd, add 1 with probability 3/4 or add 2 with probability 1/4. The probability that the final score is exactly 10 is p/q in lowest terms. What is p+q?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"62f8d0600fa347cfb5d0d20a4edb273c"},"task_id":"rc_en_high_010","usage":{"input_tokens":341,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2938,"probabilities":{"high":0.3908,"low":0.08,"medium":0.5292},"type":"choice"},"confidence":0.2938,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":776.533,"pair_id":"high_011","predicted":"medium","prompt":"Assign nine distinct tasks, numbered 1 through 9, to three labeled servers A, B, and C, with each task assigned to exactly one server. Every server must receive at least one task. Tasks 1 and 2 go to different servers. Tasks 3 and 4 go to the same server. Server A receives exactly three tasks. Task 5 is not on A. Tasks 6 and 7 go to different servers. If task 8 is on B, then task 9 must be on C; this last rule imposes no restriction when task 8 is not on B. How many assignments satisfy all conditions?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"61a3c457e8d34582bcba90db9b5f75d9"},"task_id":"rc_en_high_011","usage":{"input_tokens":378,"output_tokens":61}}
{"answer":{"choice":"medium","confidence":0.3414,"probabilities":{"high":0.3244,"low":0.1146,"medium":0.561},"type":"choice"},"confidence":0.3414,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":1020.553,"pair_id":"high_012","predicted":"medium","prompt":"A token starts at S. Two players alternate moving it along one directed edge; a player with no legal move loses. The edges are S→A,B,C,D; A→E,F; B→F,G; C→G,H; D→I,J; E→I,J; F→J,K; G→I,K; H→K,L; I→M; J→M,N; K→N; L→M. M and N are terminal. Number S's choices A, B, C, D as 1, 2, 3, 4. Under perfect play, what is the number of the unique winning first move?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"504653bf8d3e494fa35d5b89cb0bac5d"},"task_id":"rc_en_high_012","usage":{"input_tokens":385,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.4,"probabilities":{"high":0.3213,"low":0.0786,"medium":0.6},"type":"choice"},"confidence":0.4,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":850.985,"pair_id":"high_013","predicted":"medium","prompt":"A random walk has positions 0 through 6 and starts at 3; positions 0 and 6 are absorbing. At position i, it moves right with probability p_i and left otherwise, where p_1=1/2, p_2=2/3, p_3=1/4, p_4=3/5, and p_5=3/4. The probability of reaching 6 before 0 is a/b in lowest terms. What is a+b?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"603ec0474b1a4af3b27758ac5195a7a6"},"task_id":"rc_en_high_013","usage":{"input_tokens":352,"output_tokens":57}}
{"answer":{"choice":"medium","confidence":0.3652,"probabilities":{"high":0.2582,"low":0.165,"medium":0.5768},"type":"choice"},"confidence":0.3652,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":802.273,"pair_id":"high_014","predicted":"medium","prompt":"Two token piles start with sizes (5,7). A move may choose one pile and remove 1 or 3 tokens if that pile contains enough, or remove 1 token from each pile when both are nonempty. A player wins by making both piles empty, and both players play perfectly. Among the winning first moves, compute the total number of tokens remaining immediately after the move.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"f818f5c951f4412da648fd94e536499d"},"task_id":"rc_en_high_014","usage":{"input_tokens":327,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.4139,"probabilities":{"high":0.2806,"low":0.1101,"medium":0.6093},"type":"choice"},"confidence":0.4139,"correct":false,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":728.411,"pair_id":"high_015","predicted":"medium","prompt":"Seven projects have (cost,value): A=(4,7), B=(5,9), C=(3,5), D=(6,12), E=(2,4), F=(4,8), G=(5,10). Select at most four projects with total cost at most 14. Selecting D requires A; selecting F requires C; B and E cannot both be selected; and D and G cannot both be selected. What is the maximum total value?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"3c15874557274af6b18970d58fd65785"},"task_id":"rc_en_high_015","usage":{"input_tokens":349,"output_tokens":63}}
{"answer":{"choice":"high","confidence":0.2,"probabilities":{"high":0.4666,"low":0.1117,"medium":0.4216},"type":"choice"},"confidence":0.2,"correct":true,"dataset":"routing_calibration_en_high","domain":"reasoning","error":null,"expected":"high","lang":"en","latency_ms":696.75,"pair_id":"high_016","predicted":"high","prompt":"Trace this procedure using a mutable array x=[2,5,1,4,3] and s=0. For i=0,1,2,3,4 in order, run j from 0 through i in order. If (x[j]+i) mod 3 equals 0, set s=s+x[j]×(i-j+1); otherwise set s=s-((x[j]+j) mod 4). After that inner loop, set x[i]=(x[i]+s) mod 7. Every modulo operation uses the least nonnegative residue. After all iterations, what is s plus the sum of the entries of x?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"d91c5d69cdb646e29c2504f51d8189cf"},"task_id":"rc_en_high_016","usage":{"input_tokens":384,"output_tokens":60}}
{"answer":{"choice":"low","confidence":0.9546,"probabilities":{"high":0.0038,"low":0.9697,"medium":0.0265},"type":"choice"},"confidence":0.9546,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":605.451,"pair_id":"low_001","predicted":"low","prompt":"What is 27 + 15?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"cb895bba5c6f4b4dba73835ee4bdb58e"},"task_id":"rc_en_low_001","usage":{"input_tokens":259,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.9431,"probabilities":{"high":0.0043,"low":0.9621,"medium":0.0336},"type":"choice"},"confidence":0.9431,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":479.062,"pair_id":"low_002","predicted":"low","prompt":"What is 84 - 37?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"5768504e7c0e4e8497b3650ec12a4131"},"task_id":"rc_en_low_002","usage":{"input_tokens":259,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.9603,"probabilities":{"high":0.0046,"low":0.9736,"medium":0.0218},"type":"choice"},"confidence":0.9603,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":470.63,"pair_id":"low_003","predicted":"low","prompt":"What is 8 multiplied by 7?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"2d66896914cc4303b384c99129e29b33"},"task_id":"rc_en_low_003","usage":{"input_tokens":258,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.9469,"probabilities":{"high":0.0062,"low":0.9646,"medium":0.0292},"type":"choice"},"confidence":0.9469,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":486.594,"pair_id":"low_004","predicted":"low","prompt":"What is half of 96?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"93c4236aedab4331b3eec8e825d452df"},"task_id":"rc_en_low_004","usage":{"input_tokens":257,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.9064,"probabilities":{"high":0.0066,"low":0.9376,"medium":0.0559},"type":"choice"},"confidence":0.9064,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":476.476,"pair_id":"low_005","predicted":"low","prompt":"What is 25% of 80?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"fce7087e406d4aaa91875ee98c9b63ac"},"task_id":"rc_en_low_005","usage":{"input_tokens":260,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.6698,"probabilities":{"high":0.0147,"low":0.7799,"medium":0.2055},"type":"choice"},"confidence":0.6698,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":585.632,"pair_id":"low_006","predicted":"low","prompt":"Maya has 12 apples, buys 5 more, and then gives 4 to a friend. How many apples does she have now?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"a432882a5ab04b7abc600b008ec2c586"},"task_id":"rc_en_low_006","usage":{"input_tokens":279,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8101,"probabilities":{"high":0.0132,"low":0.8734,"medium":0.1134},"type":"choice"},"confidence":0.8101,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":571.538,"pair_id":"low_007","predicted":"low","prompt":"A meeting starts at 14:15 and lasts 45 minutes. At what hour from 0 through 23 does it end?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"de6873300a374a1e8f995b4fe2def2bf"},"task_id":"rc_en_low_007","usage":{"input_tokens":280,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.7278,"probabilities":{"high":0.0165,"low":0.8185,"medium":0.165},"type":"choice"},"confidence":0.7278,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":481.42,"pair_id":"low_008","predicted":"low","prompt":"Find the smallest of 0.8, 0.08, 0.18, and 0.81, then multiply it by 100. What is the result?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"f97b2ebbfa12459ba79ff1ea5764d7e3"},"task_id":"rc_en_low_008","usage":{"input_tokens":291,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.8869,"probabilities":{"high":0.0116,"low":0.9246,"medium":0.0638},"type":"choice"},"confidence":0.8869,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":576.399,"pair_id":"low_009","predicted":"low","prompt":"What number comes next in the sequence 3, 6, 9, 12, ...?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"8828970045784737aad358a69b90679d"},"task_id":"rc_en_low_009","usage":{"input_tokens":271,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8558,"probabilities":{"high":0.0197,"low":0.9039,"medium":0.0764},"type":"choice"},"confidence":0.8558,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":501.781,"pair_id":"low_010","predicted":"low","prompt":"Every tulip is a flower. This plant is a tulip. Must this plant be a flower? Use 1 for yes and 0 for no.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"eab324830cf14ac981863b3f86acede8"},"task_id":"rc_en_low_010","usage":{"input_tokens":281,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8763,"probabilities":{"high":0.0152,"low":0.9175,"medium":0.0673},"type":"choice"},"confidence":0.8763,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":495.749,"pair_id":"low_011","predicted":"low","prompt":"How many vowels are in the uppercase word BALLOON?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"bb77561568824af7b856aef1c48de8b3"},"task_id":"rc_en_low_011","usage":{"input_tokens":261,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.7152,"probabilities":{"high":0.0186,"low":0.8101,"medium":0.1713},"type":"choice"},"confidence":0.7152,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":488.76,"pair_id":"low_012","predicted":"low","prompt":"How many centimeters are in 3 meters and 40 centimeters?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"69ac315d148a44a3bb31b6ced655e8ed"},"task_id":"rc_en_low_012","usage":{"input_tokens":265,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8782,"probabilities":{"high":0.0072,"low":0.9188,"medium":0.074},"type":"choice"},"confidence":0.8782,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":511.653,"pair_id":"low_013","predicted":"low","prompt":"What is the arithmetic mean of 6, 8, and 10?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"319090cb56c84ac2befcf6e71c0e2e03"},"task_id":"rc_en_low_013","usage":{"input_tokens":266,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.8565,"probabilities":{"high":0.0071,"low":0.9044,"medium":0.0885},"type":"choice"},"confidence":0.8565,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":487.483,"pair_id":"low_014","predicted":"low","prompt":"A rectangle has length 9 and width 4. What is its perimeter?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"02612d4e22e94cdbbb5ac479a15b3643"},"task_id":"rc_en_low_014","usage":{"input_tokens":265,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.9371,"probabilities":{"high":0.0059,"low":0.9581,"medium":0.036},"type":"choice"},"confidence":0.9371,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":533.456,"pair_id":"low_015","predicted":"low","prompt":"An item costs $18. You pay with $20. How many dollars of change should you receive?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"789c407871854547ad2ed17d8c398014"},"task_id":"rc_en_low_015","usage":{"input_tokens":272,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.9035,"probabilities":{"high":0.0101,"low":0.9357,"medium":0.0542},"type":"choice"},"confidence":0.9035,"correct":true,"dataset":"routing_calibration_en_low","domain":"reasoning","error":null,"expected":"low","lang":"en","latency_ms":680.975,"pair_id":"low_016","predicted":"low","prompt":"How many even numbers are in this list: 27, 35, 42, 51?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"81569475a02b406fbef9cc76bd9a083f"},"task_id":"rc_en_low_016","usage":{"input_tokens":274,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.391,"probabilities":{"high":0.2768,"low":0.1292,"medium":0.594},"type":"choice"},"confidence":0.391,"correct":false,"dataset":"routing_calibration_en_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"en","latency_ms":967.886,"pair_id":"marketing_high_001","predicted":"medium","prompt":"A company has three funnels. Enterprise: 2,000 visitors with lead, demo, and close rates of 30%, 40%, and 25%. SMB: 5,000 visitors with rates 20%, 30%, and 20%. Self-serve: 8,000 visitors with rates 15%, 25%, and 16%. Choose any interventions within 7 budget units: A costs 4 and adds 5 percentage points to Enterprise lead rate and 2 points to SMB lead rate; B costs 3 and adds 5 points to every demo rate; C costs 5 and adds 3 points to Enterprise close rate and 4 points to both other close rates; D costs 2 and adds 1,000 Self-serve visitors at the unchanged Self-serve rates. Effects of selected interventions combine, and expected closes equal visitors times all three stage rates. What is 100 times the maximum expected total closes?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"7770eab2264b4b82991b1b62812c544d"},"task_id":"rc_en_marketing_high_001","usage":{"input_tokens":460,"output_tokens":61}}
{"answer":{"choice":"medium","confidence":0.3218,"probabilities":{"high":0.1621,"low":0.2901,"medium":0.5479},"type":"choice"},"confidence":0.3218,"correct":false,"dataset":"routing_calibration_en_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"en","latency_ms":856.52,"pair_id":"marketing_high_002","predicted":"medium","prompt":"An experiment has three preregistered strata with population weights 50%, 30%, and 20%. In New customers, control-assigned conversion is 4%, treatment-assigned conversion is 5.2%, treatment take-up is 80% among treatment-assigned and 20% among control-assigned. In Returning, the four figures are 10%, 11.5%, 75%, and 25%. In Enterprise, they are 20%, 21%, 60%, and 10%. Within each stratum, estimate the local average treatment effect for compliers using the Wald adjustment: divide the treatment-minus-control conversion-rate difference by the treatment-minus-control take-up difference. Then population-weight the three effects. How many incremental conversions does the result imply per 10,000 customers?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"ce0d41bd1eb64e67860d723ff9d64814"},"task_id":"rc_en_marketing_high_002","usage":{"input_tokens":428,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3061,"probabilities":{"high":0.2726,"low":0.1899,"medium":0.5374},"type":"choice"},"confidence":0.3061,"correct":false,"dataset":"routing_calibration_en_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"en","latency_ms":697.132,"pair_id":"marketing_high_003","predicted":"medium","prompt":"A campaign market had 1,000 pre-period sales and 1,450 post-period sales. A synthetic control uses donor growth-factor weights 50%, 30%, and 20%; the donors' observed post/pre growth factors are 1.10, 1.20, and 0.95. Campaign spillover reduced every donor's observed growth factor by exactly 0.02, so correct each donor factor upward by 0.02 before combining them. Only 80% of eligible customers in the campaign market were actually reached. Assuming unreached customers had zero effect and effect scales linearly with reach, what is the implied incremental sales at 100% reach?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"d4b3146aaec74742a0942cb6a29b0ab1"},"task_id":"rc_en_marketing_high_003","usage":{"input_tokens":402,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4666,"probabilities":{"high":0.1617,"low":0.1939,"medium":0.6444},"type":"choice"},"confidence":0.4666,"correct":false,"dataset":"routing_calibration_en_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"en","latency_ms":729.106,"pair_id":"marketing_high_004","predicted":"medium","prompt":"Four channels A, B, C, and D have coalition conversion values v: v(∅)=0; v(A)=18, v(B)=12, v(C)=9, v(D)=5; v(AB)=38, v(AC)=31, v(AD)=25, v(BC)=26, v(BD)=19, v(CD)=20; v(ABC)=60, v(ABD)=51, v(ACD)=46, v(BCD)=42; v(ABCD)=80. Compute channel B's four-player Shapley value, using every ordering of the channels as equally likely. What is six times B's Shapley value?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"3a7aebe7e72e45b79148b2c51b178cab"},"task_id":"rc_en_marketing_high_004","usage":{"input_tokens":407,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3784,"probabilities":{"high":0.2701,"low":0.1443,"medium":0.5856},"type":"choice"},"confidence":0.3784,"correct":false,"dataset":"routing_calibration_en_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"en","latency_ms":920.164,"pair_id":"marketing_high_005","predicted":"medium","prompt":"Choose Basic price b from {40,50,60} dollars and Pro price p from {100,120,140} dollars, subject to p being at least twice b. Demand is D_B=2600−30b+3(p−100) Basic units and D_P=1300−8p+3(b−40) Pro units. Unit costs are $20 for Basic and $60 for Pro. There are no fixed costs. What is the maximum contribution profit (b−20)D_B+(p−60)D_P in dollars?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"3773dc9e177648b89d9ccb6cd998038e"},"task_id":"rc_en_marketing_high_005","usage":{"input_tokens":384,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.365,"probabilities":{"high":0.3088,"low":0.1145,"medium":0.5767},"type":"choice"},"confidence":0.365,"correct":false,"dataset":"routing_calibration_en_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"en","latency_ms":927.998,"pair_id":"marketing_high_006","predicted":"medium","prompt":"Audience weights are Enterprise 50, SMB 30, and Developer 20. Six claims have (Enterprise,SMB,Developer) scores and production costs: A=(9,5,4), cost 4; B=(7,9,5), cost 3; C=(5,7,10), cost 3; D=(3,9,8), cost 2; E=(10,4,6), cost 4; F=(6,6,9), cost 2. A claim's base impact is 50×Enterprise score+30×SMB score+20×Developer score. Select exactly three claims with total cost at most 9. A and E cannot both be selected; D requires B. Pair B+C incurs an 80-point overlap penalty; C+F adds a 90-point synergy; A+F adds a 50-point synergy; all other pair adjustments are zero. What is the maximum total impact?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"b2d0c7c4fdaf4048bfe1be04f4ad66ad"},"task_id":"rc_en_marketing_high_006","usage":{"input_tokens":455,"output_tokens":62}}
{"answer":{"choice":"high","confidence":0.3271,"probabilities":{"high":0.5514,"low":0.0576,"medium":0.391},"type":"choice"},"confidence":0.3271,"correct":true,"dataset":"routing_calibration_en_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"en","latency_ms":989.742,"pair_id":"marketing_high_007","predicted":"high","prompt":"A budget has 10 units. Successive blocks in each channel must be bought in order. Search blocks cost 2 each and yield 90, 70, and 50 conversions; Social blocks cost 2 each and yield 75, 60, and 40; Email blocks cost 1 each and yield 45 and 35; Video blocks cost 3 each and yield 100 and 75; Affiliate blocks cost 1 each and yield 40 and 30. Buying any Video block requires at least one Social block. Buying the second Affiliate block requires at least one Search block. Having at least one Search and one Email block adds 20 conversions; having at least one Social and one Video block adds 30. What is the maximum total conversions within budget?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"87b16d73004544a2bf4a435e342e9e0c"},"task_id":"rc_en_marketing_high_007","usage":{"input_tokens":422,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.3103,"probabilities":{"high":0.3408,"low":0.119,"medium":0.5402},"type":"choice"},"confidence":0.3103,"correct":false,"dataset":"routing_calibration_en_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"en","latency_ms":939.51,"pair_id":"marketing_high_008","predicted":"medium","prompt":"Choose at most one localization level per market. Each option lists engineering units, translation units, and monthly incremental contribution in local currency: Taiwan Basic=(1,2,NT$90,000), Full=(2,4,NT$156,000); Japan Basic=(1,3,¥375,000), Full=(3,5,¥825,000); Germany Basic=(2,2,€3,360), Full=(4,3,€5,760); Brazil Basic=(1,2,R$14,000), Full=(2,4,R$25,000). Budgets are 6 engineering and 9 translation units, and at most three markets may be selected. Select at least one of Taiwan/Japan and at least one of Germany/Brazil. Japan Full requires at least Taiwan Basic. Germany Full and Brazil Full cannot both be selected. Use US$1=NT$30=¥150, US$1=€0.80, and US$1=R$5. What is the maximum monthly incremental contribution in US dollars?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"d83de6dffbe349ec8e38f51a1dcfef6b"},"task_id":"rc_en_marketing_high_008","usage":{"input_tokens":494,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.5848,"probabilities":{"high":0.0362,"low":0.7232,"medium":0.2406},"type":"choice"},"confidence":0.5848,"correct":true,"dataset":"routing_calibration_en_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"en","latency_ms":662.448,"pair_id":"marketing_low_001","predicted":"low","prompt":"A campaign served 12,000 impressions and received 360 clicks. What was its click-through rate in basis points? One percentage point equals 100 basis points.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"f46ed84b808941e293620416d1717b09"},"task_id":"rc_en_marketing_low_001","usage":{"input_tokens":289,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8854,"probabilities":{"high":0.0094,"low":0.9236,"medium":0.067},"type":"choice"},"confidence":0.8854,"correct":true,"dataset":"routing_calibration_en_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"en","latency_ms":590.088,"pair_id":"marketing_low_002","predicted":"low","prompt":"A landing page received 1,000 visits and produced 80 purchases. What was the visit-to-purchase conversion rate as a percentage?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"b33ad014643449faa2e3a483bdedb6a1"},"task_id":"rc_en_marketing_low_002","usage":{"input_tokens":280,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.5952,"probabilities":{"high":0.0317,"low":0.7301,"medium":0.2382},"type":"choice"},"confidence":0.5952,"correct":true,"dataset":"routing_calibration_en_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"en","latency_ms":736.622,"pair_id":"marketing_low_003","predicted":"low","prompt":"In an A/B test, control had 40 sign-ups from 400 visitors and treatment had 75 sign-ups from 500 visitors. By how many percentage points did treatment's sign-up rate exceed control's?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"2f748abfbf804f2d8f9810fb569a68f2"},"task_id":"rc_en_marketing_low_003","usage":{"input_tokens":298,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.788,"probabilities":{"high":0.0258,"low":0.8587,"medium":0.1155},"type":"choice"},"confidence":0.788,"correct":true,"dataset":"routing_calibration_en_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"en","latency_ms":718.322,"pair_id":"marketing_low_004","predicted":"low","prompt":"Two equally sized matched customer groups were used for a campaign holdout. The campaign group made 130 purchases and the untreated holdout made 90 purchases during the same period. How many incremental purchases are attributed to the campaign?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"3adc078a038f4a45bae858c45ec8695d"},"task_id":"rc_en_marketing_low_004","usage":{"input_tokens":297,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.7991,"probabilities":{"high":0.0178,"low":0.866,"medium":0.1161},"type":"choice"},"confidence":0.7991,"correct":true,"dataset":"routing_calibration_en_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"en","latency_ms":601.694,"pair_id":"marketing_low_005","predicted":"low","prompt":"A $240 conversion is attributed 50% to paid search, 30% to email, and 20% to direct. How many dollars are attributed to email?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"0663ce615ff6443f849e79456e2afcf4"},"task_id":"rc_en_marketing_low_005","usage":{"input_tokens":288,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.4661,"probabilities":{"high":0.0268,"low":0.6441,"medium":0.3291},"type":"choice"},"confidence":0.4661,"correct":true,"dataset":"routing_calibration_en_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"en","latency_ms":653.114,"pair_id":"marketing_low_006","predicted":"low","prompt":"A product has an $80 list price and is sold at a 25% discount. Its unit cost is $35. What is the gross profit in dollars on one discounted sale?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"e5269969901d4280a62695977d5d59fe"},"task_id":"rc_en_marketing_low_006","usage":{"input_tokens":289,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.4875,"probabilities":{"high":0.0493,"low":0.6583,"medium":0.2923},"type":"choice"},"confidence":0.4875,"correct":true,"dataset":"routing_calibration_en_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"en","latency_ms":795.875,"pair_id":"marketing_low_007","predicted":"low","prompt":"An English landing page had 900 visits and 90 orders. Its Traditional Chinese version had 600 visits and 72 orders. By how many percentage points was the higher conversion rate above the lower one?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"7e30c54ae4684be1afa45f89e540fe0d"},"task_id":"rc_en_marketing_low_007","usage":{"input_tokens":296,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.6011,"probabilities":{"high":0.0285,"low":0.7341,"medium":0.2374},"type":"choice"},"confidence":0.6011,"correct":true,"dataset":"routing_calibration_en_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"en","latency_ms":742.98,"pair_id":"marketing_low_008","predicted":"low","prompt":"A team spends $3,000 on social ads at a cost per acquisition of $30 and $2,000 on search ads at a cost per acquisition of $20. Assuming those rates hold, how many acquisitions are produced in total?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"0b6e4e3394d640888922c25ab1e4f6af"},"task_id":"rc_en_marketing_low_008","usage":{"input_tokens":303,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4112,"probabilities":{"high":0.096,"low":0.2965,"medium":0.6075},"type":"choice"},"confidence":0.4112,"correct":true,"dataset":"routing_calibration_en_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"en","latency_ms":776.853,"pair_id":"marketing_medium_001","predicted":"medium","prompt":"A funnel has two segments. New visitors: 2,000 visitors, 40% sign up, 25% of sign-ups start a trial, and currently 20% of trials become paid. Returning visitors: 1,000 visitors, 60% sign up, 50% of sign-ups start a trial, and currently 25% of trials become paid. A checkout fix raises the trial-to-paid rate by 5 percentage points in both segments, with all other rates unchanged. How many paid customers are expected after the fix?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"d0d5a0589db247049aba372faa3ba485"},"task_id":"rc_en_marketing_medium_001","usage":{"input_tokens":369,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.254,"probabilities":{"high":0.0935,"low":0.4038,"medium":0.5027},"type":"choice"},"confidence":0.254,"correct":true,"dataset":"routing_calibration_en_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"en","latency_ms":697.715,"pair_id":"marketing_medium_002","predicted":"medium","prompt":"For each 10,000 visitors, control converts 8% at an average order value of $50. Treatment converts 10% at an average order value of $48, incurs an additional $2 of fulfillment cost per treatment order, and costs $1,000 to operate per 10,000 visitors. Ignore all other costs. What is treatment's incremental contribution profit in dollars versus control per 10,000 visitors?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"a1edb268994749ec8117b5ee834dc6c1"},"task_id":"rc_en_marketing_medium_002","usage":{"input_tokens":350,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.2718,"probabilities":{"high":0.0879,"low":0.5145,"medium":0.3976},"type":"choice"},"confidence":0.2718,"correct":false,"dataset":"routing_calibration_en_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"en","latency_ms":804.395,"pair_id":"marketing_medium_003","predicted":"low","prompt":"A test market had 1,000 sales before a campaign and 1,400 after it. Donor market C1 rose from 800 to 960 sales, and donor market C2 rose from 1,200 to 1,320. Build the counterfactual growth factor as 25% of C1's growth factor plus 75% of C2's growth factor, then apply it to the test market's pre-period sales. How many incremental sales did the campaign generate?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"a23e575b27624d20aab1dc7f0f059aa4"},"task_id":"rc_en_marketing_medium_003","usage":{"input_tokens":363,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2021,"probabilities":{"high":0.0785,"low":0.4534,"medium":0.468},"type":"choice"},"confidence":0.2021,"correct":true,"dataset":"routing_calibration_en_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"en","latency_ms":637.778,"pair_id":"marketing_medium_004","predicted":"medium","prompt":"Use a position-based attribution rule: the first touch gets 40% of revenue, the last touch gets 40%, and all middle touches split the remaining 20% equally. There are three conversions: Search > Email > Direct worth $100; Email > Social > Direct worth $200; and Search > Email > Referral > Direct worth $300. How many dollars are attributed to Email in total?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"e0f9b22fc108421ab2c6fee938bb612b"},"task_id":"rc_en_marketing_medium_004","usage":{"input_tokens":340,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.4063,"probabilities":{"high":0.106,"low":0.2898,"medium":0.6042},"type":"choice"},"confidence":0.4063,"correct":true,"dataset":"routing_calibration_en_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"en","latency_ms":777.354,"pair_id":"marketing_medium_005","predicted":"medium","prompt":"A seller is choosing among three prices. At $40 it expects 1,500 orders with a 10% return rate; at $45, 1,350 orders with an 8% return rate; at $50, 1,200 orders with a 5% return rate. A returned order produces no revenue, incurs exactly $6 processing cost, and recovers its product cost in full. Each non-returned order incurs $20 net product cost. What is the maximum expected contribution profit in dollars?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"8fd9442ff1214356888f7ad7e726be7c"},"task_id":"rc_en_marketing_medium_005","usage":{"input_tokens":367,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.4659,"probabilities":{"high":0.035,"low":0.6439,"medium":0.3211},"type":"choice"},"confidence":0.4659,"correct":false,"dataset":"routing_calibration_en_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"en","latency_ms":684.398,"pair_id":"marketing_medium_006","predicted":"low","prompt":"Three customer segments have weights Enterprise 40%, SMB 35%, and Creator 25%. Message A scores 8, 6, and 4 in those segments; message B scores 6, 7, and 8; message C scores 7, 5, and 9. Compute each message's weighted-average score, choose the highest, and multiply that winning score by 100. What is the result?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"40c8270c2112417ba5af7281573b4493"},"task_id":"rc_en_marketing_medium_006","usage":{"input_tokens":340,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.42,"probabilities":{"high":0.2117,"low":0.175,"medium":0.6133},"type":"choice"},"confidence":0.42,"correct":true,"dataset":"routing_calibration_en_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"en","latency_ms":757.119,"pair_id":"marketing_medium_007","predicted":"medium","prompt":"A $12,000 budget can be allocated only in $2,000 blocks. Incremental conversions from successive blocks are: Search 80, 60, 40; Social 70, 50, 30; CRM 65, 55, 45. Within a channel, a later block may be allocated only after all earlier blocks. At most three blocks may be allocated per channel. What is the maximum number of incremental conversions?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"83ab4a1fbd0449748cdae63b623e599e"},"task_id":"rc_en_marketing_medium_007","usage":{"input_tokens":353,"output_tokens":60}}
{"answer":{"choice":"medium","confidence":0.4266,"probabilities":{"high":0.1382,"low":0.2441,"medium":0.6178},"type":"choice"},"confidence":0.4266,"correct":true,"dataset":"routing_calibration_en_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"en","latency_ms":773.569,"pair_id":"marketing_medium_008","predicted":"medium","prompt":"Three localized stores have these monthly results. US: 10,000 visits, 5% conversion, $60 average order value, 5% payment fee. Taiwan: 8,000 visits, 4% conversion, NT$1,500 average order value, 10% payment fee. Japan: 6,000 visits, 3% conversion, ¥6,000 average order value, 8% payment fee. Use US$1=NT$30 and US$1=¥150. Fees are percentages of revenue. What is total revenue after payment fees, in US dollars?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"112c3d81a4da48849030ca9e19aa36dc"},"task_id":"rc_en_marketing_medium_008","usage":{"input_tokens":387,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4628,"probabilities":{"high":0.2491,"low":0.1091,"medium":0.6418},"type":"choice"},"confidence":0.4628,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":698.789,"pair_id":"medium_001","predicted":"medium","prompt":"Seven talks—Aurora, Beacon, Cedar, Drift, Ember, Fjord, and Grove—occupy slots 1 through 7, one talk per slot. Cedar is immediately after Aurora. Ember is before Aurora. Exactly two talks are between Ember and Fjord. Fjord is before Drift, which is before Grove. Beacon is neither first nor last and is before Drift. Grove is after Cedar. Aurora is before Drift. What slot is Beacon in?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"9a98ae014c4340b09079b648f5f6fd7c"},"task_id":"rc_en_medium_001","usage":{"input_tokens":347,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4794,"probabilities":{"high":0.241,"low":0.1061,"medium":0.6529},"type":"choice"},"confidence":0.4794,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":823.997,"pair_id":"medium_002","predicted":"medium","prompt":"Monday through Friday each has exactly one presenter and one topic. The five presenters are Imani, Jorge, Keira, Leo, and Mina; the five topics are Atlas, Birch, Comet, Delta, and Ember. Each presenter and topic is used exactly once. Atlas is on Monday. Leo is immediately before Imani. Keira is exactly two days after Leo. Mina is before Leo. Jorge is after Keira. Imani presents Ember. Birch is immediately before Ember. Comet is after Ember but before Delta. Number Monday as 1 through Friday as 5. Compute 10 times Keira's day number plus Delta's day number.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"1897264005284cc28926a508afee8bbd"},"task_id":"rc_en_medium_002","usage":{"input_tokens":381,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.5868,"probabilities":{"high":0.163,"low":0.1124,"medium":0.7245},"type":"choice"},"confidence":0.5868,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":777.002,"pair_id":"medium_003","predicted":"medium","prompt":"Choose urn U1, U2, or U3 with probabilities 1/2, 1/3, and 1/6. U1 contains 4 red and 2 blue balls; U2 contains 3 red and 3 blue; U3 contains 1 red and 5 blue. Two balls are drawn without replacement, and exactly one is observed to be red. The posterior probability that U2 was chosen is p/q in lowest terms. What is p+q?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"05fd4af9655a4f4c978e38b44b2e39e8"},"task_id":"rc_en_medium_003","usage":{"input_tokens":349,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.4345,"probabilities":{"high":0.218,"low":0.159,"medium":0.623},"type":"choice"},"confidence":0.4345,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":566.957,"pair_id":"medium_004","predicted":"medium","prompt":"Find the smallest integer n greater than 600 such that n leaves remainder 3 when divided by 7, remainder 5 when divided by 8, and remainder 4 when divided by 9.\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"a3f138d9df4d4fd1b12e0cdaaa823555"},"task_id":"rc_en_medium_004","usage":{"input_tokens":292,"output_tokens":60}}
{"answer":{"choice":"medium","confidence":0.3142,"probabilities":{"high":0.3224,"low":0.1348,"medium":0.5428},"type":"choice"},"confidence":0.3142,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":699.649,"pair_id":"medium_005","predicted":"medium","prompt":"A, B, C, and D are distinct decimal digits. A, C, and D are nonzero; A<C; and B>C. The two-digit number AB multiplied by C equals the three-digit number DDD. What is A+B+C+D?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"110840f5369e4e11ae5a187641928de1"},"task_id":"rc_en_medium_005","usage":{"input_tokens":302,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3353,"probabilities":{"high":0.1456,"low":0.2975,"medium":0.5568},"type":"choice"},"confidence":0.3353,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":699.257,"pair_id":"medium_006","predicted":"medium","prompt":"Let a[0]=2 and a[1]=5. For n=2,3,...,12, define a[n]=(3a[n-1]+2a[n-2]+n) mod 17, taking the least nonnegative residue each time. What is a[12]?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"0320727eeb5342c7b3a3f8a883f4378a"},"task_id":"rc_en_medium_006","usage":{"input_tokens":312,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3427,"probabilities":{"high":0.3445,"low":0.0937,"medium":0.5618},"type":"choice"},"confidence":0.3427,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":816.841,"pair_id":"medium_007","predicted":"medium","prompt":"Exactly one of Ari, Bo, Cy, Di, Eli, and Fay caused an incident, and exactly three statements are true. Ari: \"The culprit is Bo or Cy.\" Bo: \"Di is not the culprit.\" Cy: \"Ari is the culprit if and only if Eli is not the culprit.\" Di: \"Neither Bo nor Fay is the culprit.\" Eli: \"Cy is the culprit.\" Fay: \"Exactly one of Ari and Di is the culprit.\" Number the people in the listed order from 1 to 6. What is the culprit's number?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"3db2b2d62d50417189ec934796a1da6e"},"task_id":"rc_en_medium_007","usage":{"input_tokens":365,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4784,"probabilities":{"high":0.1922,"low":0.1555,"medium":0.6523},"type":"choice"},"confidence":0.4784,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":710.775,"pair_id":"medium_008","predicted":"medium","prompt":"A directed graph has edges S→A=4, S→B=2, A→C=5, A→D=2, B→A=1, B→C=7, B→D=6, C→T=3, D→C=1, and D→T=8. What is the minimum cost of a path from S to T that visits both A and D?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"1dc7a4cce5ce448ab7bd5c80d6480947"},"task_id":"rc_en_medium_008","usage":{"input_tokens":334,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4297,"probabilities":{"high":0.042,"low":0.3382,"medium":0.6198},"type":"choice"},"confidence":0.4297,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":649.598,"pair_id":"medium_009","predicted":"medium","prompt":"An item costs $250. Apply a 20% discount, then a $15 coupon, then 8% sales tax on the reduced price, and finally add $12 shipping. What is the final price in dollars?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"4fe960490e7747a597a6e7ab98ae11cf"},"task_id":"rc_en_medium_009","usage":{"input_tokens":299,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.5447,"probabilities":{"high":0.0868,"low":0.2167,"medium":0.6965},"type":"choice"},"confidence":0.5447,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":673.725,"pair_id":"medium_010","predicted":"medium","prompt":"Machine A makes 5 parts every 4 minutes, and machine B makes 7 parts every 6 minutes. During a 120-minute shift, A is stopped for 16 minutes and B is stopped for 18 minutes. Each machine produces at its stated constant rate whenever running. How many parts do they produce in total?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"07a1cb676d3143b19fb4d042a1e58303"},"task_id":"rc_en_medium_010","usage":{"input_tokens":319,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5024,"probabilities":{"high":0.1051,"low":0.2266,"medium":0.6683},"type":"choice"},"confidence":0.5024,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":664.045,"pair_id":"medium_011","predicted":"medium","prompt":"Among 80 employees, 42 took course A, 38 took B, and 30 took C. The pairwise overlaps are |A∩B|=18, |A∩C|=12, and |B∩C|=10, while 5 employees took all three. How many employees took exactly one of the three courses?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"d56d7e4b2caf44dd8d566a1c81e403f7"},"task_id":"rc_en_medium_011","usage":{"input_tokens":326,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5288,"probabilities":{"high":0.0974,"low":0.2168,"medium":0.6858},"type":"choice"},"confidence":0.5288,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":546.766,"pair_id":"medium_012","predicted":"medium","prompt":"Starting at (0,0), move only one unit right or one unit up until reaching (5,4). How many shortest paths avoid the point (2,2)?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"9b13e6ef763541afaf056a19bf04b0a4"},"task_id":"rc_en_medium_012","usage":{"input_tokens":284,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3994,"probabilities":{"high":0.0761,"low":0.3243,"medium":0.5996},"type":"choice"},"confidence":0.3994,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":677.575,"pair_id":"medium_013","predicted":"medium","prompt":"Two fair six-sided dice are rolled. Given that their sum is even, the probability that their sum is greater than 8 is p/q in lowest terms. What is p+q?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"d760f863f3ba47eaaf1f101d86a1a30e"},"task_id":"rc_en_medium_013","usage":{"input_tokens":287,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4069,"probabilities":{"high":0.3086,"low":0.0868,"medium":0.6046},"type":"choice"},"confidence":0.4069,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":720.425,"pair_id":"medium_014","predicted":"medium","prompt":"Six distinct tasks A, B, C, D, E, and F are arranged in a line. A and B must each be before D. C must be immediately before E. F is neither first nor last. A and B are not adjacent. How many arrangements satisfy all conditions?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"6126d4f6bebe48c2bdad4cc233415b84"},"task_id":"rc_en_medium_014","usage":{"input_tokens":307,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5846,"probabilities":{"high":0.0857,"low":0.1912,"medium":0.7231},"type":"choice"},"confidence":0.5846,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":758.748,"pair_id":"medium_015","predicted":"medium","prompt":"A tank holds 20 liters of a well-mixed solution that is 30% salt. Remove 5 liters and replace them with 5 liters of pure water. Mix thoroughly, then remove 4 liters and replace them with 4 liters of pure water. What percentage of the final solution is salt?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"33e7f8cb71c2450fb9402a75040af29a"},"task_id":"rc_en_medium_015","usage":{"input_tokens":313,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2562,"probabilities":{"high":0.1044,"low":0.3915,"medium":0.5041},"type":"choice"},"confidence":0.2562,"correct":true,"dataset":"routing_calibration_en_medium","domain":"reasoning","error":null,"expected":"medium","lang":"en","latency_ms":897.978,"pair_id":"medium_016","predicted":"medium","prompt":"Start with the ordered pair (a,b)=(2,3). Repeat this update 6 times, replacing the pair simultaneously by (b,(a+2b) mod 11), where mod uses the least nonnegative residue. After the sixth update, what is 10a+b?\n\nSolve the problem. End your response with a final line containing only the numeric answer.","request_ids":{"x-typesafe-request-id":"504d11f9b9b9479cb9774ba4c9b93730"},"task_id":"rc_en_medium_016","usage":{"input_tokens":309,"output_tokens":63}}
{"answer":{"choice":"high","confidence":0.4515,"probabilities":{"high":0.6344,"low":0.1081,"medium":0.2575},"type":"choice"},"confidence":0.4515,"correct":true,"dataset":"routing_calibration_zh_hant_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"zh-Hant","latency_ms":898.479,"pair_id":"architecture_high_001","predicted":"high","prompt":"某付款 API 在兩個區域採 active-active 架構。任意區域間網路分割期間，每個區域都必須完成同一客戶的付款請求並回傳成功結果，且不能聯絡另一區域；不得拒絕、重新導向，也不得延後到分割結束後才處理。付款供應商可從兩區域連線，但不提供冪等或去重功能；兩區域只有非同步複寫的本機資料庫。客戶可能在分割期間，以相同冪等鍵向兩區域送出請求。兩項必要屬性為：(1) 分割期間兩區域仍能成功完成這類請求；(2) 系統保證供應商最多只產生一筆扣款。若要讓實作成為可能，至少必須放寬這兩項屬性中的幾項？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"58564a23ee454bb899baf869f168fa35"},"task_id":"rc_zh_hant_architecture_high_001","usage":{"input_tokens":403,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2377,"probabilities":{"high":0.414,"low":0.0942,"medium":0.4918},"type":"choice"},"confidence":0.2377,"correct":false,"dataset":"routing_calibration_zh_hant_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"zh-Hant","latency_ms":768.339,"pair_id":"architecture_high_002","predicted":"medium","prompt":"某佇列每秒收到 600 個邏輯工作。恰有 10% 會失敗一次並重試一次，因此佇列必須執行所有產生的嘗試。每個 worker 每秒執行 50 次嘗試，存活且作用中的 worker 最多只能使用此速率的 75%。worker 平均部署於 3 個可用區。失去任一整個可用區後，仍須有足夠 worker；佇列也必須為每個作用中 worker 提供至少一個分割區。當分割區較少時，多出的已部署 worker 可作為熱備援。先最小化已部署 worker 總數 W，再最小化分割區數 P。100W+P 等於多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"436b2e25b40740e587096491b2966be2"},"task_id":"rc_zh_hant_architecture_high_002","usage":{"input_tokens":401,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.2087,"probabilities":{"high":0.4265,"low":0.101,"medium":0.4725},"type":"choice"},"confidence":0.2087,"correct":false,"dataset":"routing_calibration_zh_hant_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"zh-Hant","latency_ms":987.477,"pair_id":"architecture_high_003","predicted":"medium","prompt":"系統有每個執行個體各自擁有、TTL 為 30 秒的 L1 快取，以及共享、TTL 為 100 秒的 L2 快取。GET 依序檢查 L1、L2、資料庫，並填入每一層未命中的快取。資料庫寫入會立即以新值更新 L2 既有項目；下列 L1 失效通知若與其他事件同時，會在該事件前一刻發生。起初資料庫為 v1，所有快取皆空。事件依序為：t0 GET X；t10 GET Y；t20 寫入 v2（X 在 t26 失效、Y 在 t35 失效）；t22 GET X；t24 GET Z；t27 GET X；t32 寫入 v3（X 在 t50 失效、Y 在 t38 失效、Z 在 t45 失效）；t34 GET Y；t39 GET Y；t44 GET Z；t46 GET Z；t49 GET X；t51 GET X。令 O 為存取資料庫來源的 GET 次數，S 為回傳版本比資料庫舊的 GET 次數。100O+S 等於多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"25cc8c4028cc41afa1ac87690e975824"},"task_id":"rc_zh_hant_architecture_high_003","usage":{"input_tokens":528,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.2911,"probabilities":{"high":0.309,"low":0.1635,"medium":0.5274},"type":"choice"},"confidence":0.2911,"correct":false,"dataset":"routing_calibration_zh_hant_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"zh-Hant","latency_ms":925.198,"pair_id":"architecture_high_004","predicted":"medium","prompt":"某滾動式欄位遷移的動作代碼如下：1=刪除舊欄位；2=同時寫入兩欄位期間，以條件式更新回填替代欄位；3=新增可為 null 的替代欄位；4=部署讀取舊欄位並同時寫入兩欄位的相容版本；5=驗證資料一致且替代欄位沒有 null；6=部署優先讀取替代欄位、以舊欄位作為後備，並繼續同時寫入兩欄位的版本；7=等待所有相容版本執行檔退出；8=部署只使用新欄位並停止寫入舊欄位的版本；9=完成回滾觀察期。要求：開始回填前必須先同時寫入兩欄位；開始讀取替代欄位前必須完成驗證；停止寫入舊欄位前必須讓相容版本執行檔全數退出；刪除舊欄位前必須完成回滾觀察期。請依唯一安全順序串接所有代碼。\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"ff2761122081498abac270f30a6a3b22"},"task_id":"rc_zh_hant_architecture_high_004","usage":{"input_tokens":455,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.2538,"probabilities":{"high":0.2697,"low":0.2278,"medium":0.5025},"type":"choice"},"confidence":0.2538,"correct":false,"dataset":"routing_calibration_zh_hant_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"zh-Hant","latency_ms":852.09,"pair_id":"architecture_high_005","predicted":"medium","prompt":"某履約 saga 起初有 20 個可用庫存單位、0 美元的保留授權金額，以及 0 筆有效貨運預約。它預留 4 個單位、授權 120 美元，並要求貨運業者建立預約。業者已提交預約但回覆遺失；使用同一個預約鍵重試時會回傳既有預約。接著付款請款在提交前確定失敗。補償流程會取消預約（取消已提交但回覆遺失，並以同一取消鍵重試）、釋放庫存（同一 event_id 被傳遞兩次給冪等消費者），以及撤銷授權。令 T 為庫存、付款供應商與貨運系統中已提交狀態變更的總次數；只回傳既有狀態的冪等重試，以及提交前失敗的操作，都不增加 T。另令 A 為最終可用庫存單位數，H 為最終保留美元數，B 為最終有效預約數。100000T+1000A+10H+B 等於多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"bbebc4c35e87490d82106ece0fd76d2b"},"task_id":"rc_zh_hant_architecture_high_005","usage":{"input_tokens":471,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3861,"probabilities":{"high":0.2154,"low":0.1939,"medium":0.5907},"type":"choice"},"confidence":0.3861,"correct":false,"dataset":"routing_calibration_zh_hant_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"zh-Hant","latency_ms":708.121,"pair_id":"architecture_high_006","predicted":"medium","prompt":"某共識資料庫在 US、EU、AP 三個區域共有恰好 7 個投票副本。每個區域至少需要 2 個副本來提供本機讀取容量。失去任一整個區域後，必須仍保有 4 票多數，因此任何區域都不能有超過 3 個副本。寫入 leader 位於 US；需要 4 個確認的提交應使用盡量少的遠端確認，因此在符合前述限制下，要讓 US 的副本數最大。令 U、E、A 分別為 US、EU、AP 的副本數。100U+10E+A 等於多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"08f09241993749a8866a8f43eeaab110"},"task_id":"rc_zh_hant_architecture_high_006","usage":{"input_tokens":380,"output_tokens":63}}
{"answer":{"choice":"high","confidence":0.2146,"probabilities":{"high":0.4764,"low":0.0717,"medium":0.452},"type":"choice"},"confidence":0.2146,"correct":true,"dataset":"routing_calibration_zh_hant_architecture_high","domain":"architecture","error":null,"expected":"high","lang":"zh-Hant","latency_ms":853.756,"pair_id":"architecture_high_007","predicted":"high","prompt":"每個主要資料庫分片的負載容量為 100。高階租戶 A=60 與 B=35 各自需要獨占一個主要分片。標準租戶 C=55、D=45、E=40、F=35、G=30、H=25 可以共用，每個分片最多容納 3 個租戶，但 C-D、E-F、G-H 這三組都禁止共用。每個主要分片都需要在 3 個可用區各放一份副本。每個資料庫執行個體最多可容納 2 份分片副本，而且副本不能離開所屬可用區。先最小化主要分片數 S，再最小化執行個體數 I。100S+I 等於多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"49489220b81746d0a9569be3cfff92c5"},"task_id":"rc_zh_hant_architecture_high_007","usage":{"input_tokens":420,"output_tokens":62}}
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{"answer":{"choice":"high","confidence":0.2944,"probabilities":{"high":0.5296,"low":0.0766,"medium":0.3938},"type":"choice"},"confidence":0.2944,"correct":true,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":619.71,"pair_id":"high_002","predicted":"high","prompt":"把 10 個有編號的位置排成一圈，並在每個位置放一個二進位位元。共有多少個字串同時滿足：恰有五個 1；循環方向上不會有三個連續位置全為 1；位置 1 與位置 6 的位元不同？跨越位置 10 與位置 1 的三連續位置也要計入。\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"47c7e97076d34dccbe2a6f1449b8b475"},"task_id":"rc_zh_hant_high_002","usage":{"input_tokens":329,"output_tokens":63}}
{"answer":{"choice":"high","confidence":0.2412,"probabilities":{"high":0.4941,"low":0.0573,"medium":0.4486},"type":"choice"},"confidence":0.2412,"correct":true,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":899.259,"pair_id":"high_003","predicted":"high","prompt":"兩位能力相同的工作者要執行六項不可中斷的工作。工時為 A=4、B=3、C=5、D=2、E=4、F=3 小時。C 必須等 A 完成；D 必須等 A 與 B 都完成；E 必須等 B 完成；F 必須等 C、D、E 都完成。C 與 E 共用同一個加速器，即使分配給不同工作者也不能同時執行。兩位工作者都可在時間 0 開始。完成所有工作最少需要幾小時？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"a87c0fdac67a4a769691a90e3bd1959d"},"task_id":"rc_zh_hant_high_003","usage":{"input_tokens":366,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2863,"probabilities":{"high":0.4084,"low":0.0674,"medium":0.5242},"type":"choice"},"confidence":0.2863,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":916.863,"pair_id":"high_004","predicted":"medium","prompt":"一張有向圖的邊成本如下：S→A=7、S→B=4、A→C=5、A→D=8、B→A=2、B→D=6、B→E=9、C→D=2、C→E=6、D→E=3、D→T=10、E→T=7。經過節點 C 會取得鑰匙，使 E→T 的成本從 7 降為 2。另有一張最多使用一次的折價券，可將所走某一條邊的成本 w 改為 ⌊w/2⌋，也就是將 w/2 向下取整；若鑰匙折扣適用，先套用鑰匙折扣再計算折價券。從 S 到 T 的最低成本是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"2154f1e4035a461a8de197ffd06dc7b1"},"task_id":"rc_zh_hant_high_004","usage":{"input_tokens":424,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3152,"probabilities":{"high":0.3854,"low":0.0711,"medium":0.5435},"type":"choice"},"confidence":0.3152,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":702.181,"pair_id":"high_005","predicted":"medium","prompt":"一張有向圖的邊成本如下：S→A=4、S→B=2、A→C=4、A→D=7、B→A=1、B→D=4、B→E=8、C→E=2、C→T=9、D→C=1、D→E=3、D→T=8、E→D=1、E→T=5。第一次經過 A 時會取得一張折價券，可用在之後的一條邊，把成本 w 改為 ⌈w/2⌉，也就是將 w/2 向上取整。只有曾經過 C 之後才能走 E→T。從 S 到 T 的最低成本是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"f1e1feb2e88d401690cf276937e79746"},"task_id":"rc_zh_hant_high_005","usage":{"input_tokens":405,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3452,"probabilities":{"high":0.3437,"low":0.0929,"medium":0.5634},"type":"choice"},"confidence":0.3452,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":655.611,"pair_id":"high_006","predicted":"medium","prompt":"分別以先驗機率 1/2、1/3、1/6 選到罐子 U1、U2、U3。三個罐子的（紅球，藍球，綠球）數量分別為 U1=(4,2,1)、U2=(2,4,1)、U3=(3,2,2)。依序不放回地抽出三顆球。已知前兩顆顏色不同，且其中至少一顆是紅球，第三顆是紅球的條件機率化為最簡分數 p/q。p+q 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"2f07c4552fbb4354bd7164c5d3f1ae73"},"task_id":"rc_zh_hant_high_006","usage":{"input_tokens":365,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.213,"probabilities":{"high":0.4226,"low":0.1021,"medium":0.4754},"type":"choice"},"confidence":0.213,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":768.933,"pair_id":"high_007","predicted":"medium","prompt":"長度為 12 的二進位字串中，有多少個同時滿足以下條件：恰有五個位元是 1；任兩個連續位置不會同為 1；奇數編號位置中恰有兩個 1；第一個與最後一個位元相同？此處相鄰只指編號連續的位置，因此位置 1 與位置 12 不視為相鄰。\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"7af79d3a54f8477aa593efcdd35a72ed"},"task_id":"rc_zh_hant_high_007","usage":{"input_tokens":329,"output_tokens":62}}
{"answer":{"choice":"high","confidence":0.2531,"probabilities":{"high":0.502,"low":0.0598,"medium":0.4382},"type":"choice"},"confidence":0.2531,"correct":true,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":668.01,"pair_id":"high_008","predicted":"high","prompt":"八位不同的人 A 至 H 圍坐圓桌。旋轉後相同的排法視為同一種，但鏡射後的排法視為不同。A 與 B 不相鄰。C 與 D 相對而坐。E 與 A、B 兩人中的恰好一人相鄰。共有多少種符合條件的座位排法？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"5cc727a893484c78aede4ea76856cff0"},"task_id":"rc_zh_hant_high_008","usage":{"input_tokens":316,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.4125,"probabilities":{"high":0.308,"low":0.0837,"medium":0.6083},"type":"choice"},"confidence":0.4125,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":829.109,"pair_id":"high_009","predicted":"medium","prompt":"八個專案的（成本，價值）如下：A=(3,7)、B=(4,9)、C=(2,4)、D=(5,12)、E=(3,6)、F=(2,5)、G=(4,10)、H=(1,2)，預算為 11。選 D 必須也選 A；選 F 必須也選 B；選 G 必須同時選 C 與 E；A 與 B 不能同時選；D 與 H 不能同時選。有效選擇可得到的最大總價值是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"26172c3544f04e96977d9a1fc6df3789"},"task_id":"rc_zh_hant_high_009","usage":{"input_tokens":366,"output_tokens":62}}
{"answer":{"choice":"high","confidence":0.1868,"probabilities":{"high":0.4579,"low":0.0863,"medium":0.4559},"type":"choice"},"confidence":0.1868,"correct":true,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":760.737,"pair_id":"high_010","predicted":"high","prompt":"分數從 0 開始，共進行 6 回合。每一回合中，若目前分數是偶數，則以機率 1/3 加 1、以機率 2/3 加 3；若目前分數是奇數，則以機率 3/4 加 1、以機率 1/4 加 2。最後分數恰為 10 的機率化為最簡分數 p/q。p+q 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"8490fb6c1ac74a80b8f0a278e6dbeb68"},"task_id":"rc_zh_hant_high_010","usage":{"input_tokens":351,"output_tokens":63}}
{"answer":{"choice":"high","confidence":0.2724,"probabilities":{"high":0.5149,"low":0.0527,"medium":0.4324},"type":"choice"},"confidence":0.2724,"correct":true,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":777.208,"pair_id":"high_011","predicted":"high","prompt":"將編號 1 至 9 的九項不同工作分配給三臺有標籤的伺服器 A、B、C，每項工作恰好分配給一臺。每臺伺服器至少要有一項工作。工作 1 與 2 分配到不同伺服器。工作 3 與 4 分配到同一臺。伺服器 A 恰好分配三項工作。工作 5 不在 A。工作 6 與 7 分配到不同伺服器。若工作 8 分配到 B，則工作 9 必須分配到 C；當工作 8 不在 B 時，最後這條規則不加任何限制。共有多少種符合所有條件的分配方式？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"c531d7ea34ca4174af7582607a0fc824"},"task_id":"rc_zh_hant_high_011","usage":{"input_tokens":386,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2752,"probabilities":{"high":0.3925,"low":0.0907,"medium":0.5168},"type":"choice"},"confidence":0.2752,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":777.801,"pair_id":"high_012","predicted":"medium","prompt":"一枚棋子從 S 開始，兩位玩家輪流沿一條有向邊移動棋子；無合法移動者落敗。邊如下：S→A,B,C,D；A→E,F；B→F,G；C→G,H；D→I,J；E→I,J；F→J,K；G→I,K；H→K,L；I→M；J→M,N；K→N；L→M。M 與 N 是終點。把 S 的四個選擇 A、B、C、D 依序編為 1、2、3、4。雙方採最佳策略時，唯一必勝的第一步編號是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"cf880bd4d701433fad85922fbb9da0cd"},"task_id":"rc_zh_hant_high_012","usage":{"input_tokens":387,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4602,"probabilities":{"high":0.2818,"low":0.0781,"medium":0.6402},"type":"choice"},"confidence":0.4602,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":770.567,"pair_id":"high_013","predicted":"medium","prompt":"一個隨機漫步有位置 0 至 6，從位置 3 開始，位置 0 與 6 為吸收狀態。在位置 i 時，以機率 p_i 向右移一步，否則向左移一步，其中 p_1=1/2、p_2=2/3、p_3=1/4、p_4=3/5、p_5=3/4。先到達 6 而非 0 的機率化為最簡分數 a/b。a+b 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"83af6737116b4e38afcbfd2b89df722d"},"task_id":"rc_zh_hant_high_013","usage":{"input_tokens":361,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2371,"probabilities":{"high":0.3879,"low":0.1206,"medium":0.4914},"type":"choice"},"confidence":0.2371,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":717.785,"pair_id":"high_014","predicted":"medium","prompt":"兩堆代幣起始數量為 (5,7)。每一步可以選擇其中一堆，在該堆有足夠代幣時拿走 1 枚或 3 枚；或者，在兩堆都非空時，從兩堆各拿走 1 枚。若一步後兩堆皆空，走這一步的玩家獲勝。雙方都採最佳策略。在所有必勝的第一步中，完成該步後剩餘代幣總數是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"ff13687aba534162877e5ade307c6935"},"task_id":"rc_zh_hant_high_014","usage":{"input_tokens":340,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4469,"probabilities":{"high":0.2607,"low":0.108,"medium":0.6313},"type":"choice"},"confidence":0.4469,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":638.977,"pair_id":"high_015","predicted":"medium","prompt":"七個專案的（成本，價值）如下：A=(4,7)、B=(5,9)、C=(3,5)、D=(6,12)、E=(2,4)、F=(4,8)、G=(5,10)。最多選四個專案，總成本不得超過 14。選 D 必須也選 A；選 F 必須也選 C；B 與 E 不能同時選；D 與 G 不能同時選。可得到的最大總價值是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"9302e8545a5c4549be87731727bd00e6"},"task_id":"rc_zh_hant_high_015","usage":{"input_tokens":354,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.2342,"probabilities":{"high":0.3916,"low":0.1189,"medium":0.4895},"type":"choice"},"confidence":0.2342,"correct":false,"dataset":"routing_calibration_zh_hant_high","domain":"reasoning","error":null,"expected":"high","lang":"zh-Hant","latency_ms":879.3,"pair_id":"high_016","predicted":"medium","prompt":"追蹤下列程序，其中可變陣列 x=[2,5,1,4,3]，s=0。依序令 i=0、1、2、3、4；每次再依序令 j 從 0 到 i。若 (x[j]+i) mod 3 等於 0，令 s=s+x[j]×(i-j+1)；否則令 s=s-((x[j]+j) mod 4)。每次內層迴圈結束後，令 x[i]=(x[i]+s) mod 7。所有 mod 都取最小非負餘數。全部執行完後，s 加上 x 各元素總和是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"a1784ed5f50f4d6297ed9ed87cdfab1a"},"task_id":"rc_zh_hant_high_016","usage":{"input_tokens":391,"output_tokens":63}}
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{"answer":{"choice":"low","confidence":0.954,"probabilities":{"high":0.0046,"low":0.9693,"medium":0.0261},"type":"choice"},"confidence":0.954,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":625.37,"pair_id":"low_002","predicted":"low","prompt":"84 減 37 等於多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"ec02ca5a54754562951901b41eeff4b7"},"task_id":"rc_zh_hant_low_002","usage":{"input_tokens":256,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.9496,"probabilities":{"high":0.0056,"low":0.9664,"medium":0.028},"type":"choice"},"confidence":0.9496,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":534.076,"pair_id":"low_003","predicted":"low","prompt":"8 乘以 7 等於多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"cc1ba8a451584296a643e29ebe78fb0b"},"task_id":"rc_zh_hant_low_003","usage":{"input_tokens":254,"output_tokens":62}}
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{"answer":{"choice":"low","confidence":0.884,"probabilities":{"high":0.0077,"low":0.9227,"medium":0.0697},"type":"choice"},"confidence":0.884,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":589.64,"pair_id":"low_005","predicted":"low","prompt":"80 的 25% 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"e1f7a053875a418dad4d36f626ee3603"},"task_id":"rc_zh_hant_low_005","usage":{"input_tokens":256,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.6187,"probabilities":{"high":0.0126,"low":0.7458,"medium":0.2416},"type":"choice"},"confidence":0.6187,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":584.884,"pair_id":"low_006","predicted":"low","prompt":"美玲原本有 12 顆蘋果，又買了 5 顆，接著送給朋友 4 顆。她現在有幾顆蘋果？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"9e6a331194da4f7682cf8189b16e68ae"},"task_id":"rc_zh_hant_low_006","usage":{"input_tokens":279,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.7662,"probabilities":{"high":0.0186,"low":0.8441,"medium":0.1373},"type":"choice"},"confidence":0.7662,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":617.764,"pair_id":"low_007","predicted":"low","prompt":"一場會議在 14:15 開始，持續 45 分鐘。會議結束時的 24 小時制小時數（0 至 23）是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"f5b03b99cd6d4bc1be204db543fff5f6"},"task_id":"rc_zh_hant_low_007","usage":{"input_tokens":285,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.6497,"probabilities":{"high":0.0206,"low":0.7665,"medium":0.2129},"type":"choice"},"confidence":0.6497,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":557.812,"pair_id":"low_008","predicted":"low","prompt":"先找出 0.8、0.08、0.18、0.81 中最小的數，再將它乘以 100。結果是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"00023d53b91c444b9182439e8c5371b3"},"task_id":"rc_zh_hant_low_008","usage":{"input_tokens":283,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.861,"probabilities":{"high":0.0148,"low":0.9073,"medium":0.0779},"type":"choice"},"confidence":0.861,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":490.427,"pair_id":"low_009","predicted":"low","prompt":"數列 3、6、9、12、…… 的下一個數是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"c81113d1aad34ca1b7537d66d6626649"},"task_id":"rc_zh_hant_low_009","usage":{"input_tokens":264,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.6708,"probabilities":{"high":0.0506,"low":0.7805,"medium":0.1689},"type":"choice"},"confidence":0.6708,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":590.873,"pair_id":"low_010","predicted":"low","prompt":"每一株鬱金香都是花。這株植物是鬱金香。這株植物必然是花嗎？若答案為「是」請輸出 1，否則輸出 0。\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"0fd64720e008461f9d0e33b9ada5b30c"},"task_id":"rc_zh_hant_low_010","usage":{"input_tokens":282,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8779,"probabilities":{"high":0.0163,"low":0.9186,"medium":0.065},"type":"choice"},"confidence":0.8779,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":697.503,"pair_id":"low_011","predicted":"low","prompt":"大寫英文單字 BALLOON 中有幾個母音字母？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"5bb66cccf4724991a4a8a692a1fa3bba"},"task_id":"rc_zh_hant_low_011","usage":{"input_tokens":260,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.8072,"probabilities":{"high":0.0157,"low":0.8715,"medium":0.1128},"type":"choice"},"confidence":0.8072,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":596.07,"pair_id":"low_012","predicted":"low","prompt":"3 公尺 40 公分等於多少公分？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"63a2944a58124032bec612c89fea98dd"},"task_id":"rc_zh_hant_low_012","usage":{"input_tokens":257,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8839,"probabilities":{"high":0.0081,"low":0.9226,"medium":0.0693},"type":"choice"},"confidence":0.8839,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":458.063,"pair_id":"low_013","predicted":"low","prompt":"6、8、10 的算術平均數是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"d4411f887e9b4a90b5dcce578389dd12"},"task_id":"rc_zh_hant_low_013","usage":{"input_tokens":259,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8399,"probabilities":{"high":0.0087,"low":0.8932,"medium":0.0981},"type":"choice"},"confidence":0.8399,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":507.455,"pair_id":"low_014","predicted":"low","prompt":"一個長方形的長為 9、寬為 4。它的周長是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"aea574853a5c4aa2aec1133d4b125270"},"task_id":"rc_zh_hant_low_014","usage":{"input_tokens":264,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.9219,"probabilities":{"high":0.0069,"low":0.9479,"medium":0.0452},"type":"choice"},"confidence":0.9219,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":505.455,"pair_id":"low_015","predicted":"low","prompt":"一件商品售價 18 元，你付了 20 元。應找回多少元？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"a8ec2dcfaf3849598278f67f4f43df4a"},"task_id":"rc_zh_hant_low_015","usage":{"input_tokens":268,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.9104,"probabilities":{"high":0.0079,"low":0.9402,"medium":0.0519},"type":"choice"},"confidence":0.9104,"correct":true,"dataset":"routing_calibration_zh_hant_low","domain":"reasoning","error":null,"expected":"low","lang":"zh-Hant","latency_ms":587.135,"pair_id":"low_016","predicted":"low","prompt":"下列數字中有幾個偶數：27、35、42、51？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"54443159d6854cdab99b6712276f9ab2"},"task_id":"rc_zh_hant_low_016","usage":{"input_tokens":264,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4108,"probabilities":{"high":0.3025,"low":0.0903,"medium":0.6072},"type":"choice"},"confidence":0.4108,"correct":false,"dataset":"routing_calibration_zh_hant_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"zh-Hant","latency_ms":875.795,"pair_id":"marketing_high_001","predicted":"medium","prompt":"某公司有三個行銷漏斗。企業客戶：2,000 位訪客，成為潛在客戶、預約產品展示、成交三個階段的轉換率依序為 30%、40%、25%。中小企業：5,000 位訪客，三階段轉換率依序為 20%、30%、20%。自助服務：8,000 位訪客，三階段轉換率依序為 15%、25%、16%。可在 7 個預算單位內任選下列措施：A 成本為 4，將企業客戶成為潛在客戶的轉換率提高 5 個百分點，並將中小企業的同一轉換率提高 2 個百分點；B 成本為 3，將所有客群預約產品展示的轉換率提高 5 個百分點；C 成本為 5，將企業客戶成交率提高 3 個百分點，並將另外兩個客群的成交率各提高 4 個百分點；D 成本為 2，以原有自助服務轉換率增加 1,000 位自助服務訪客。所選措施的效果會合併，而預期成交數等於訪客數乘以全部三個階段的轉換率。最高預期總成交數的 100 倍是多少？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"cf37f12bc12f4606b239e88c73fc3518"},"task_id":"rc_zh_hant_marketing_high_001","usage":{"input_tokens":536,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3751,"probabilities":{"high":0.1791,"low":0.2375,"medium":0.5834},"type":"choice"},"confidence":0.3751,"correct":false,"dataset":"routing_calibration_zh_hant_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"zh-Hant","latency_ms":924.08,"pair_id":"marketing_high_002","predicted":"medium","prompt":"某實驗預先登錄了三個分層，其母體權重分別為 50%、30%、20%。在新客戶層中，分派至控制組者的轉換率為 4%，分派至實驗組者的轉換率為 5.2%；實驗組分派者的處置接受率為 80%，控制組分派者則為 20%。在回訪客戶層中，上述四個數字依序為 10%、11.5%、75%、25%。在企業客戶層中，則依序為 20%、21%、60%、10%。在每個分層內，以 Wald 調整估計遵從者的局部平均處置效果：用實驗組減控制組的轉換率差，除以實驗組減控制組的處置接受率差。接著依母體權重加總三個效果。所得結果代表每 10,000 位客戶有多少筆增量轉換？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"5116e0180c914fa4a1b373e9b0958f2a"},"task_id":"rc_zh_hant_marketing_high_002","usage":{"input_tokens":466,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3988,"probabilities":{"high":0.2353,"low":0.1655,"medium":0.5992},"type":"choice"},"confidence":0.3988,"correct":false,"dataset":"routing_calibration_zh_hant_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"zh-Hant","latency_ms":1040.623,"pair_id":"marketing_high_003","predicted":"medium","prompt":"某廣告活動市場在活動前有 1,000 筆銷售，活動後有 1,450 筆。合成控制法使用三個供體市場，其成長倍數權重分別為 50%、30%、20%；這些供體觀察到的活動後／活動前成長倍數依序為 1.10、1.20、0.95。廣告活動的外溢效應使每個供體觀察到的成長倍數恰好減少 0.02，因此在合併前，須將每個供體的成長倍數向上修正 0.02。廣告活動市場中只有 80% 的合格客戶實際接觸到廣告。假設未接觸者的效果為零，且效果與觸及率呈線性關係，則觸及率為 100% 時的推算增量銷售是多少？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"f31b7db26203492293a01ce7254e26de"},"task_id":"rc_zh_hant_marketing_high_003","usage":{"input_tokens":433,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5006,"probabilities":{"high":0.1709,"low":0.162,"medium":0.6671},"type":"choice"},"confidence":0.5006,"correct":false,"dataset":"routing_calibration_zh_hant_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"zh-Hant","latency_ms":1047.522,"pair_id":"marketing_high_004","predicted":"medium","prompt":"四個管道 A、B、C、D 的聯盟轉換價值 v 如下：v(∅)=0；v(A)=18、v(B)=12、v(C)=9、v(D)=5；v(AB)=38、v(AC)=31、v(AD)=25、v(BC)=26、v(BD)=19、v(CD)=20；v(ABC)=60、v(ABD)=51、v(ACD)=46、v(BCD)=42；v(ABCD)=80。將管道的每一種排列視為等可能，計算管道 B 在四個管道情況下的 Shapley 值。B 的 Shapley 值乘以 6 是多少？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"36f75cb23f954f8a9872bfd97a45e40b"},"task_id":"rc_zh_hant_marketing_high_004","usage":{"input_tokens":411,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.3854,"probabilities":{"high":0.2874,"low":0.1223,"medium":0.5903},"type":"choice"},"confidence":0.3854,"correct":false,"dataset":"routing_calibration_zh_hant_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"zh-Hant","latency_ms":1093.082,"pair_id":"marketing_high_005","predicted":"medium","prompt":"從 {40,50,60} 美元中選擇 Basic 方案價格 b，並從 {100,120,140} 美元中選擇 Pro 方案價格 p，限制為 p 至少是 b 的兩倍。Basic 需求量為 D_B=2600−30b+3(p−100)，Pro 需求量為 D_P=1300−8p+3(b−40)。Basic 的單位成本為 20 美元，Pro 為 60 美元，沒有固定成本。貢獻利潤 (b−20)D_B+(p−60)D_P 的最大值是多少美元？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"c33b6dce1a7b48efa89c37090f0a60c1"},"task_id":"rc_zh_hant_marketing_high_005","usage":{"input_tokens":396,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.236,"probabilities":{"high":0.4216,"low":0.0877,"medium":0.4907},"type":"choice"},"confidence":0.236,"correct":false,"dataset":"routing_calibration_zh_hant_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"zh-Hant","latency_ms":1114.16,"pair_id":"marketing_high_006","predicted":"medium","prompt":"企業客戶、中小企業、開發者三個受眾的權重依序為 50、30、20。六項訴求的（企業客戶、中小企業、開發者）分數與製作成本如下：A=(9,5,4)，成本 4；B=(7,9,5)，成本 3；C=(5,7,10)，成本 3；D=(3,9,8)，成本 2；E=(10,4,6)，成本 4；F=(6,6,9)，成本 2。每項訴求的基礎影響分數為 50×企業客戶分數+30×中小企業分數+20×開發者分數。恰好選擇三項訴求，總成本不得超過 9。A 與 E 不得同時選擇；選擇 D 必須同時選擇 B。B+C 會產生 80 分的重疊扣分；C+F 會增加 90 分的綜效；A+F 會增加 50 分的綜效；其他配對調整皆為零。總影響分數的最大值是多少？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"d5799d7fee784925b67b650d83b28a7b"},"task_id":"rc_zh_hant_marketing_high_006","usage":{"input_tokens":490,"output_tokens":62}}
{"answer":{"choice":"high","confidence":0.3396,"probabilities":{"high":0.5598,"low":0.0576,"medium":0.3826},"type":"choice"},"confidence":0.3396,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"zh-Hant","latency_ms":1106.2,"pair_id":"marketing_high_007","predicted":"high","prompt":"共有 10 個預算單位。每個管道的預算區塊都必須依序購買。搜尋區塊每個成本為 2，依序帶來 90、70、50 筆轉換；社群區塊每個成本為 2，依序帶來 75、60、40 筆；電子郵件區塊每個成本為 1，依序帶來 45、35 筆；影音區塊每個成本為 3，依序帶來 100、75 筆；聯盟行銷區塊每個成本為 1，依序帶來 40、30 筆。購買任何影音區塊都必須至少購買一個社群區塊。購買第二個聯盟行銷區塊必須至少購買一個搜尋區塊。同時至少有一個搜尋與一個電子郵件區塊時，額外增加 20 筆轉換；同時至少有一個社群與一個影音區塊時，額外增加 30 筆。在預算內可獲得的總轉換數最大為多少？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"3c9c850cc0a64affa711d08f4f0143b9"},"task_id":"rc_zh_hant_marketing_high_007","usage":{"input_tokens":448,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.2531,"probabilities":{"high":0.4081,"low":0.0899,"medium":0.5021},"type":"choice"},"confidence":0.2531,"correct":false,"dataset":"routing_calibration_zh_hant_marketing_high","domain":"marketing","error":null,"expected":"high","lang":"zh-Hant","latency_ms":1295.328,"pair_id":"marketing_high_008","predicted":"medium","prompt":"每個市場最多選擇一種在地化層級。各選項依序列出工程單位、翻譯單位、以當地貨幣計算的每月增量貢獻：台灣 Basic=(1,2,NT$90,000)、Full=(2,4,NT$156,000)；日本 Basic=(1,3,¥375,000)、Full=(3,5,¥825,000)；德國 Basic=(2,2,€3,360)、Full=(4,3,€5,760)；巴西 Basic=(1,2,R$14,000)、Full=(2,4,R$25,000)。工程與翻譯預算分別為 6 與 9 個單位，最多可選擇三個市場。台灣／日本中至少選一個，德國／巴西中也至少選一個。選擇日本 Full 時，台灣至少必須選擇 Basic。德國 Full 與巴西 Full 不得同時選擇。匯率使用 1 美元=30 新台幣=150 日圓、1 美元=0.80 歐元，以及 1 美元=5 巴西雷亞爾。每月增量貢獻的最大值是多少美元？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"2507e6441b724899bed89498ff27ba5c"},"task_id":"rc_zh_hant_marketing_high_008","usage":{"input_tokens":510,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.6208,"probabilities":{"high":0.0285,"low":0.7472,"medium":0.2243},"type":"choice"},"confidence":0.6208,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"zh-Hant","latency_ms":762.994,"pair_id":"marketing_low_001","predicted":"low","prompt":"某廣告活動獲得 12,000 次曝光與 360 次點擊。其點擊率是多少個基點？一個百分點等於 100 個基點。\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"35dadf6cff6c449c863493057fa33d3a"},"task_id":"rc_zh_hant_marketing_low_001","usage":{"input_tokens":289,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.842,"probabilities":{"high":0.0105,"low":0.8947,"medium":0.0948},"type":"choice"},"confidence":0.842,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"zh-Hant","latency_ms":731.299,"pair_id":"marketing_low_002","predicted":"low","prompt":"某登陸頁獲得 1,000 次造訪並帶來 80 筆購買。從造訪到購買的轉換率是多少百分比？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"ff53be0925a3429d9273c6a9d68053d1"},"task_id":"rc_zh_hant_marketing_low_002","usage":{"input_tokens":280,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.677,"probabilities":{"high":0.0181,"low":0.7847,"medium":0.1972},"type":"choice"},"confidence":0.677,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"zh-Hant","latency_ms":820.945,"pair_id":"marketing_low_003","predicted":"low","prompt":"在一項 A/B 測試中，控制組的 400 位訪客中有 40 人註冊，實驗組的 500 位訪客中有 75 人註冊。實驗組的註冊率比控制組高出多少個百分點？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"0c19b0150bf04ab2ac7142c685b5c821"},"task_id":"rc_zh_hant_marketing_low_003","usage":{"input_tokens":305,"output_tokens":62}}
{"answer":{"choice":"low","confidence":0.7542,"probabilities":{"high":0.0304,"low":0.8361,"medium":0.1335},"type":"choice"},"confidence":0.7542,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"zh-Hant","latency_ms":834.67,"pair_id":"marketing_low_004","predicted":"low","prompt":"某廣告活動以兩個人數相同、條件相符的客群進行保留組測試。在同一期間，廣告活動組完成 130 筆購買，未接受廣告的保留組完成 90 筆購買。可歸因於此廣告活動的增量購買有幾筆？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"1ff408774be24260880e8f48de6d6771"},"task_id":"rc_zh_hant_marketing_low_004","usage":{"input_tokens":306,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.8099,"probabilities":{"high":0.0132,"low":0.8733,"medium":0.1135},"type":"choice"},"confidence":0.8099,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"zh-Hant","latency_ms":854.3,"pair_id":"marketing_low_005","predicted":"low","prompt":"某筆價值 240 美元的轉換，將 50% 歸因於付費搜尋、30% 歸因於電子郵件、20% 歸因於直接流量。歸因於電子郵件的金額是多少美元？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"a5d630c4a60648baae1dcdef312a812a"},"task_id":"rc_zh_hant_marketing_low_005","usage":{"input_tokens":296,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.6602,"probabilities":{"high":0.0171,"low":0.7735,"medium":0.2094},"type":"choice"},"confidence":0.6602,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"zh-Hant","latency_ms":650.298,"pair_id":"marketing_low_006","predicted":"low","prompt":"某產品定價 80 美元，以七五折出售，單位成本為 35 美元。每賣出一件折扣商品的毛利是多少美元？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"fb31a758a2f5487f88ce839e080cec72"},"task_id":"rc_zh_hant_marketing_low_006","usage":{"input_tokens":279,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.3258,"probabilities":{"high":0.0761,"low":0.5505,"medium":0.3734},"type":"choice"},"confidence":0.3258,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"zh-Hant","latency_ms":689.611,"pair_id":"marketing_low_007","predicted":"low","prompt":"英文登陸頁有 900 次造訪與 90 筆訂單，繁體中文版本有 600 次造訪與 72 筆訂單。較高的轉換率比另一個轉換率高出多少個百分點？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"a1b52aa96aea473d8586e5dc8dd0609a"},"task_id":"rc_zh_hant_marketing_low_007","usage":{"input_tokens":300,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.6279,"probabilities":{"high":0.0207,"low":0.752,"medium":0.2273},"type":"choice"},"confidence":0.6279,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_low","domain":"marketing","error":null,"expected":"low","lang":"zh-Hant","latency_ms":771.655,"pair_id":"marketing_low_008","predicted":"low","prompt":"某團隊在社群廣告投入 3,000 美元，每次獲客成本為 30 美元；並在搜尋廣告投入 2,000 美元，每次獲客成本為 20 美元。假設上述每次獲客成本維持不變，總共可獲得多少位新客戶？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"b1d620d982484115a0271bc338a87c67"},"task_id":"rc_zh_hant_marketing_low_008","usage":{"input_tokens":314,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.3831,"probabilities":{"high":0.0782,"low":0.3331,"medium":0.5887},"type":"choice"},"confidence":0.3831,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":1000.413,"pair_id":"marketing_medium_001","predicted":"medium","prompt":"某行銷漏斗有兩個客群。新訪客：共 2,000 人，其中 40% 註冊，25% 的註冊者開始試用，目前有 20% 的試用者成為付費客戶。回訪者：共 1,000 人，其中 60% 註冊，50% 的註冊者開始試用，目前有 25% 的試用者成為付費客戶。結帳流程修正後，兩個客群從試用到付費的轉換率都提高 5 個百分點，其他比例不變。修正後預期共有多少位付費客戶？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"5ea078782f42455aa1547452d0666436"},"task_id":"rc_zh_hant_marketing_medium_001","usage":{"input_tokens":381,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4068,"probabilities":{"high":0.099,"low":0.2964,"medium":0.6045},"type":"choice"},"confidence":0.4068,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":877.305,"pair_id":"marketing_medium_002","predicted":"medium","prompt":"每 10,000 位訪客中，控制組的轉換率為 8%，平均訂單金額為 50 美元。實驗組的轉換率為 10%，平均訂單金額為 48 美元；每筆實驗組訂單另產生 2 美元履約成本，而且每 10,000 位訪客需支付 1,000 美元營運成本。忽略其他所有成本。每 10,000 位訪客中，實驗組相較控制組增加多少美元的貢獻利潤？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"dd2ce4c568a64156bd21b1e3487bc870"},"task_id":"rc_zh_hant_marketing_medium_002","usage":{"input_tokens":369,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.221,"probabilities":{"high":0.0934,"low":0.426,"medium":0.4807},"type":"choice"},"confidence":0.221,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":770.078,"pair_id":"marketing_medium_003","predicted":"medium","prompt":"某測試市場在廣告活動前有 1,000 筆銷售，活動後有 1,400 筆。供體市場 C1 的銷售從 800 筆增至 960 筆，供體市場 C2 則從 1,200 筆增至 1,320 筆。以 C1 成長倍數的 25% 加上 C2 成長倍數的 75%，建立反事實成長倍數，再套用到測試市場活動前的銷售量。此廣告活動產生多少筆增量銷售？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"c3cf786fae494fad9d950a0b6e795a0b"},"task_id":"rc_zh_hant_marketing_medium_003","usage":{"input_tokens":374,"output_tokens":61}}
{"answer":{"choice":"medium","confidence":0.2207,"probabilities":{"high":0.0631,"low":0.4565,"medium":0.4805},"type":"choice"},"confidence":0.2207,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":740.56,"pair_id":"marketing_medium_004","predicted":"medium","prompt":"採用以接觸位置為基礎的歸因規則：首次接觸分配 40% 營收，末次接觸分配 40%，所有中間接觸平均分配剩餘的 20%。共有三筆轉換：搜尋 > 電子郵件 > 直接流量，價值 100 美元；電子郵件 > 社群 > 直接流量，價值 200 美元；搜尋 > 電子郵件 > 推薦 > 直接流量，價值 300 美元。總共應將多少美元歸因於電子郵件？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"ff897a08d6d14a2ca3caf50c1ebc8917"},"task_id":"rc_zh_hant_marketing_medium_004","usage":{"input_tokens":357,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4876,"probabilities":{"high":0.1224,"low":0.2192,"medium":0.6584},"type":"choice"},"confidence":0.4876,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":786.644,"pair_id":"marketing_medium_005","predicted":"medium","prompt":"某賣家要從三種價格中做選擇。定價 40 美元時，預期有 1,500 筆訂單，退貨率為 10%；定價 45 美元時，預期有 1,350 筆訂單，退貨率為 8%；定價 50 美元時，預期有 1,200 筆訂單，退貨率為 5%。退貨訂單不產生營收，恰好會產生 6 美元處理成本，且產品成本可全額回收。每筆未退貨訂單會產生 20 美元淨產品成本。最高的預期貢獻利潤是多少美元？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"52feeb3a9cb34692aba206421f3c5645"},"task_id":"rc_zh_hant_marketing_medium_005","usage":{"input_tokens":385,"output_tokens":63}}
{"answer":{"choice":"low","confidence":0.5249,"probabilities":{"high":0.0273,"low":0.6833,"medium":0.2894},"type":"choice"},"confidence":0.5249,"correct":false,"dataset":"routing_calibration_zh_hant_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":804.598,"pair_id":"marketing_medium_006","predicted":"low","prompt":"三個客群的權重分別為：企業客戶 40%、中小企業 35%、創作者 25%。訊息 A 在這三個客群的分數依序為 8、6、4；訊息 B 為 6、7、8；訊息 C 為 7、5、9。計算每則訊息的加權平均分數，選出最高者，再將該分數乘以 100。結果是多少？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"e4d4387048174817ae53dc443962d84a"},"task_id":"rc_zh_hant_marketing_medium_006","usage":{"input_tokens":344,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5013,"probabilities":{"high":0.1918,"low":0.1406,"medium":0.6676},"type":"choice"},"confidence":0.5013,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":990.533,"pair_id":"marketing_medium_007","predicted":"medium","prompt":"一筆 12,000 美元的預算只能以每 2,000 美元為一個配置單位。各管道依序投入每個配置單位所帶來的增量轉換數如下：搜尋為 80、60、40；社群為 70、50、30；CRM 為 65、55、45。在同一管道中，必須先配置所有較前面的單位，才能配置後面的單位；每個管道最多可配置三個單位。可取得的增量轉換數最大為多少？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"3f9d787f67f1421682b9aef3f3cf8523"},"task_id":"rc_zh_hant_marketing_medium_007","usage":{"input_tokens":360,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5232,"probabilities":{"high":0.1341,"low":0.1838,"medium":0.6821},"type":"choice"},"confidence":0.5232,"correct":true,"dataset":"routing_calibration_zh_hant_marketing_medium","domain":"marketing","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":862.364,"pair_id":"marketing_medium_008","predicted":"medium","prompt":"三個在地化商店的每月數據如下。美國：10,000 次造訪、5% 轉換率、60 美元平均訂單金額、5% 支付手續費。台灣：8,000 次造訪、4% 轉換率、1,500 新台幣平均訂單金額、10% 支付手續費。日本：6,000 次造訪、3% 轉換率、6,000 日圓平均訂單金額、8% 支付手續費。匯率使用 1 美元兌 30 新台幣，以及 1 美元兌 150 日圓。手續費皆按營收比例計算。扣除支付手續費後的總營收為多少美元？\n\n請解題，並在回覆的最後一行只填寫數字答案。","request_ids":{"x-typesafe-request-id":"d5b5e7361d8a469a8da0b27f79909beb"},"task_id":"rc_zh_hant_marketing_medium_008","usage":{"input_tokens":409,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.428,"probabilities":{"high":0.3033,"low":0.078,"medium":0.6187},"type":"choice"},"confidence":0.428,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":932.236,"pair_id":"medium_001","predicted":"medium","prompt":"七場簡報 Aurora、Beacon、Cedar、Drift、Ember、Fjord、Grove 分別安排在第 1 至第 7 時段，每個時段恰有一場。Cedar 緊接在 Aurora 之後。Ember 在 Aurora 之前。Ember 與 Fjord 之間恰有兩場簡報。Fjord 在 Drift 之前，Drift 又在 Grove 之前。Beacon 不在第一或最後一個時段，且在 Drift 之前。Grove 在 Cedar 之後。Aurora 在 Drift 之前。Beacon 位於第幾個時段？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"0462892a0ff04ea9b414367de3e93712"},"task_id":"rc_zh_hant_medium_001","usage":{"input_tokens":380,"output_tokens":61}}
{"answer":{"choice":"medium","confidence":0.4484,"probabilities":{"high":0.2985,"low":0.0692,"medium":0.6323},"type":"choice"},"confidence":0.4484,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":977.522,"pair_id":"medium_002","predicted":"medium","prompt":"星期一至星期五每天各安排一位簡報者與一個主題。五位簡報者為 Imani、Jorge、Keira、Leo、Mina，五個主題為 Atlas、Birch、Comet、Delta、Ember；每位簡報者與每個主題都恰好安排一次。Atlas 在星期一。Leo 緊接在 Imani 的前一天。Keira 恰好比 Leo 晚兩天。Mina 在 Leo 之前。Jorge 在 Keira 之後。Imani 的主題是 Ember。Birch 緊接在 Ember 的前一天。Comet 在 Ember 之後、Delta 之前。將星期一編為 1，依序到星期五編為 5。計算 Keira 的日期編號乘以 10，再加上 Delta 的日期編號。\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"74e56dcf61a7421a9accd3a279754713"},"task_id":"rc_zh_hant_medium_002","usage":{"input_tokens":416,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.6405,"probabilities":{"high":0.1225,"low":0.1172,"medium":0.7603},"type":"choice"},"confidence":0.6405,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":694.525,"pair_id":"medium_003","predicted":"medium","prompt":"分別以機率 1/2、1/3、1/6 選到罐子 U1、U2、U3。U1 有 4 顆紅球與 2 顆藍球；U2 有 3 顆紅球與 3 顆藍球；U3 有 1 顆紅球與 5 顆藍球。不放回地抽出兩顆，觀察到恰有一顆紅球。已知此觀察結果，選到 U2 的後驗機率化為最簡分數 p/q。p+q 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"b0f49f58f31b4257a6597cca816d494e"},"task_id":"rc_zh_hant_medium_003","usage":{"input_tokens":371,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4024,"probabilities":{"high":0.1936,"low":0.2048,"medium":0.6016},"type":"choice"},"confidence":0.4024,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":577.354,"pair_id":"medium_004","predicted":"medium","prompt":"找出大於 600 的最小整數 n，使 n 除以 7 餘 3、除以 8 餘 5、除以 9 餘 4。\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"5feb1fa89ac44bce802efa29cb588c0d"},"task_id":"rc_zh_hant_medium_004","usage":{"input_tokens":285,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3615,"probabilities":{"high":0.3134,"low":0.1123,"medium":0.5744},"type":"choice"},"confidence":0.3615,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":712.463,"pair_id":"medium_005","predicted":"medium","prompt":"A、B、C、D 是互不相同的十進位數字。A、C、D 都不為 0，且 A<C、B>C。兩位數 AB 乘以 C，等於三位數 DDD。A+B+C+D 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"f54688cd2eae4ad095d059db1d1fa6ce"},"task_id":"rc_zh_hant_medium_005","usage":{"input_tokens":301,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.3881,"probabilities":{"high":0.1359,"low":0.272,"medium":0.5921},"type":"choice"},"confidence":0.3881,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":773.11,"pair_id":"medium_006","predicted":"medium","prompt":"令 a[0]=2、a[1]=5。對 n=2、3、……、12，定義 a[n]=(3a[n-1]+2a[n-2]+n) mod 17，且每次均取最小非負餘數。a[12] 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"257d4a336e094061bb279ac566ff0e09"},"task_id":"rc_zh_hant_medium_006","usage":{"input_tokens":311,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.4723,"probabilities":{"high":0.2464,"low":0.1053,"medium":0.6482},"type":"choice"},"confidence":0.4723,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":917.131,"pair_id":"medium_007","predicted":"medium","prompt":"Ari、Bo、Cy、Di、Eli、Fay 中恰有一人造成事故，且以下敘述恰有三句為真。Ari：「肇事者是 Bo 或 Cy。」Bo：「Di 不是肇事者。」Cy：「Ari 是肇事者，若且唯若 Eli 不是肇事者。」Di：「Bo 與 Fay 都不是肇事者。」Eli：「Cy 是肇事者。」Fay：「Ari 與 Di 中恰有一人是肇事者。」依上述姓名順序把六人編為 1 到 6。肇事者的編號是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"352178b6a96f4d4cbe6dce6feefbd72f"},"task_id":"rc_zh_hant_medium_007","usage":{"input_tokens":377,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5063,"probabilities":{"high":0.1509,"low":0.1782,"medium":0.6709},"type":"choice"},"confidence":0.5063,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":697.391,"pair_id":"medium_008","predicted":"medium","prompt":"一張有向圖的邊成本如下：S→A=4、S→B=2、A→C=5、A→D=2、B→A=1、B→C=7、B→D=6、C→T=3、D→C=1、D→T=8。從 S 到 T 且同時經過 A 與 D 的路徑，最低成本是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"36ea8cd06b1c416b86f518cf4eaea15d"},"task_id":"rc_zh_hant_medium_008","usage":{"input_tokens":335,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.419,"probabilities":{"high":0.0428,"low":0.3446,"medium":0.6127},"type":"choice"},"confidence":0.419,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":547.24,"pair_id":"medium_009","predicted":"medium","prompt":"一件商品售價 250 元。依序先降價 20%，再使用 15 元折價券，接著以折後價格加收 8% 的營業稅，最後加上 12 元運費。最終價格是多少元？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"8beabea154e94cbb9dc462ad87ca9012"},"task_id":"rc_zh_hant_medium_009","usage":{"input_tokens":303,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.5317,"probabilities":{"high":0.0726,"low":0.2396,"medium":0.6878},"type":"choice"},"confidence":0.5317,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":719.568,"pair_id":"medium_010","predicted":"medium","prompt":"機器 A 每 4 分鐘製造 5 個零件，機器 B 每 6 分鐘製造 7 個零件。在 120 分鐘的班次中，A 停機 16 分鐘，B 停機 18 分鐘；運轉時都維持各自的固定速率。兩臺機器總共製造多少個零件？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"c7c8c1ef605546adb94a8bf68eb23aca"},"task_id":"rc_zh_hant_medium_010","usage":{"input_tokens":325,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4869,"probabilities":{"high":0.1007,"low":0.2414,"medium":0.6579},"type":"choice"},"confidence":0.4869,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":763.692,"pair_id":"medium_011","predicted":"medium","prompt":"80 位員工中，42 位修過課程 A、38 位修過 B、30 位修過 C。兩兩重疊人數為 |A∩B|=18、|A∩C|=12、|B∩C|=10，三門都修過的有 5 位。恰好只修過其中一門課程的共有多少位？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"1b8066148e3945fea300dba931f1fd6e"},"task_id":"rc_zh_hant_medium_011","usage":{"input_tokens":334,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5595,"probabilities":{"high":0.0906,"low":0.2031,"medium":0.7063},"type":"choice"},"confidence":0.5595,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":813.538,"pair_id":"medium_012","predicted":"medium","prompt":"從 (0,0) 出發，每一步只能向右或向上移動一個單位，直到 (5,4)。避開 (2,2) 的最短路徑共有多少條？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"ad4c1d835bb745bcb764d51ea4f20123"},"task_id":"rc_zh_hant_medium_012","usage":{"input_tokens":284,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5278,"probabilities":{"high":0.1295,"low":0.1853,"medium":0.6852},"type":"choice"},"confidence":0.5278,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":725.151,"pair_id":"medium_013","predicted":"medium","prompt":"擲兩顆公平的六面骰子。已知點數和為偶數，點數和大於 8 的條件機率化為最簡分數 p/q。p+q 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"050d9ca17fb94e8285d933b2d2e3cc35"},"task_id":"rc_zh_hant_medium_013","usage":{"input_tokens":288,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.4007,"probabilities":{"high":0.3218,"low":0.0777,"medium":0.6005},"type":"choice"},"confidence":0.4007,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":691.112,"pair_id":"medium_014","predicted":"medium","prompt":"將六項不同的工作 A、B、C、D、E、F 排成一列。A 與 B 都必須在 D 之前。C 必須緊接在 E 之前。F 不在第一或最後一個位置。A 與 B 不相鄰。共有多少種符合所有條件的排列？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"05b2f3042acf4676bcb15f4be644fbc0"},"task_id":"rc_zh_hant_medium_014","usage":{"input_tokens":314,"output_tokens":63}}
{"answer":{"choice":"medium","confidence":0.5929,"probabilities":{"high":0.087,"low":0.1844,"medium":0.7286},"type":"choice"},"confidence":0.5929,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":669.989,"pair_id":"medium_015","predicted":"medium","prompt":"水槽中有 20 公升充分混合、含鹽 30% 的溶液。先取出 5 公升，再補入 5 公升純水；充分混合後，再取出 4 公升並補入 4 公升純水。最終溶液的含鹽百分比是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"eb88813158df4607a5e3ec8233f51705"},"task_id":"rc_zh_hant_medium_015","usage":{"input_tokens":314,"output_tokens":62}}
{"answer":{"choice":"medium","confidence":0.3683,"probabilities":{"high":0.1042,"low":0.3169,"medium":0.5789},"type":"choice"},"confidence":0.3683,"correct":true,"dataset":"routing_calibration_zh_hant_medium","domain":"reasoning","error":null,"expected":"medium","lang":"zh-Hant","latency_ms":834.961,"pair_id":"medium_016","predicted":"medium","prompt":"起始有序數對為 (a,b)=(2,3)。重複更新 6 次，每次同時把數對替換為 (b,(a+2b) mod 11)，其中 mod 取最小非負餘數。第六次更新後，10a+b 是多少？\n\n請解出問題，並在回覆最後一行只寫數字答案。","request_ids":{"x-typesafe-request-id":"9b13142b2c254b5ebd5b244bbd1fb0f4"},"task_id":"rc_zh_hant_medium_016","usage":{"input_tokens":308,"output_tokens":63}}