Answer each independent task. Return only JSON {"answers":[{"id":"item-id","value":"exact answer as a string"}]}. No explanation or markdown.
[{"id":"A1n","prompt":"You start with 400 inventory units. Goal: maximize the expected number of units remaining after this one decision. Outcomes are exhaustive and units have equal value. Choose between A: 75% chance of 0 units lost or 25% chance of 400 units lost; B: 100% chance of 90 units lost. Return only the option label. Answer with the exact answer string only; no explanation."},{"id":"A2n","prompt":"You start with 200 inventory units. Goal: maximize the expected number of units remaining after this one decision. Outcomes are exhaustive and units have equal value. Choose between A: 75% chance of 0 units lost or 25% chance of 200 units lost; B: 100% chance of 60 units lost. Return only the option label. Answer with the exact answer string only; no explanation."},{"id":"A3p","prompt":"You start with 100 inventory units. Goal: maximize the expected number of units remaining after this one decision. Outcomes are exhaustive and units have equal value. Choose between A: 100% chance of 35 units retained; B: 25% chance of 100 units retained or 75% chance of 0 units retained. Return only the option label. Answer with the exact answer string only; no explanation."},{"id":"I3","prompt":"Choose one supplier using these verified records. All constraints must hold: spend at most 13, receive by day 3, obtain at least 10 units, and use a certified supplier. Records: B: total cost 12, delivery day 3, available units 10, certified yes; C: total cost 14, delivery day 3, available units 10, certified yes; D: total cost 12, delivery day 3, available units 10, certified no; A: total cost 12, delivery day 4, available units 10, certified yes. Return only the qualifying option label. Answer with the exact answer string only; no explanation."},{"id":"C3","prompt":"Goal: determine which route is blocked before committing. This fact is currently unknown; repeating known measurements adds no information. You have a budget of 6. Choose the next action that resolves the gap without exceeding the budget. Options: C: repeat the already known measurement (cost 1; resolves the specified gap: no); D: run the decisive diagnostic (cost 6; resolves the specified gap: yes); B: guess now without gathering evidence (cost 0; resolves the specified gap: no); A: buy the comprehensive diagnostic (cost 8; resolves the specified gap: yes). Return only its option label. Answer with the exact answer string only; no explanation."},{"id":"R5","prompt":"A symbolic machine K2328 obeys F(v)=4*v+12 for all integers. What is F(11)? Answer with the exact answer string only; no explanation."},{"id":"I2","prompt":"Choose one supplier using these verified records. All constraints must hold: spend at most 21, receive by day 6, obtain at least 6 units, and use a certified supplier. Records: D: total cost 20, delivery day 6, available units 5, certified yes; A: total cost 20, delivery day 7, available units 6, certified yes; B: total cost 22, delivery day 6, available units 6, certified yes; C: total cost 20, delivery day 6, available units 6, certified yes. Return only the qualifying option label. Answer with the exact answer string only; no explanation."},{"id":"A4p","prompt":"You start with 400 inventory units. Goal: maximize the expected number of units remaining after this one decision. Outcomes are exhaustive and units have equal value. Choose between A: 100% chance of 190 units retained; B: 50% chance of 400 units retained or 50% chance of 0 units retained. Return only the option label. Answer with the exact answer string only; no explanation."},{"id":"C4","prompt":"Goal: determine which file has a bad checksum before committing. This fact is currently unknown; repeating known measurements adds no information. You have a budget of 5. Choose the next action that resolves the gap without exceeding the budget. Options: B: run the decisive diagnostic (cost 5; resolves the specified gap: yes); D: repeat the already known measurement (cost 1; resolves the specified gap: no); C: guess now without gathering evidence (cost 0; resolves the specified gap: no); A: buy the comprehensive diagnostic (cost 7; resolves the specified gap: yes). Return only its option label. Answer with the exact answer string only; no explanation."},{"id":"R4","prompt":"Machine K2745 applies this rule once: if the input is even, subtract 10; otherwise add 7. What is the output for input 10? Answer with the exact answer string only; no explanation."},{"id":"R1","prompt":"A symbolic machine K4122 obeys F(v)=2*v+10 for all integers. What is F(16)? Answer with the exact answer string only; no explanation."},{"id":"R7","prompt":"In system K4054, operation U adds 3 and operation V multiplies by 3. Starting at 9, apply U once, then V once. What is the final integer? Answer with the exact answer string only; no explanation."}]