{"runId":"experiment-002-v01","offset":0,"next":20,"sealed":false,"results":[{"id":"gate-actor-0","kind":"actor-check","phase":"gate","index":0,"pass":true,"samples":[{"problem":{"id":"gate-1-011100","split":"gate","initial":1,"operations":[0,1,1,1,0,0],"answer":"Heads","text":"A coin begins on Tails. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Tails. Same → Tails; Different → Heads; Different → Tails; Different → Heads; Same → Heads; Same → Heads.</reasoning><answer>Heads</answer>","reasoning":"Start Tails. Same → Tails; Different → Heads; Different → Tails; Different → Heads; Same → Heads; Same → Heads.","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":111}}]},{"id":"gate-actor-1","kind":"actor-check","phase":"gate","index":1,"pass":true,"samples":[{"problem":{"id":"gate-0-001101","split":"gate","initial":0,"operations":[0,0,1,1,0,1],"answer":"Tails","text":"A coin begins on Heads. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Heads → Heads → Heads → Tails → Heads → Heads → Tails</reasoning><answer>Tails</answer>","reasoning":"Heads → Heads → Heads → Tails → Heads → Heads → Tails","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":53}}]},{"id":"gate-actor-2","kind":"actor-check","phase":"gate","index":2,"pass":true,"samples":[{"problem":{"id":"gate-1-011001","split":"gate","initial":1,"operations":[0,1,1,0,0,1],"answer":"Heads","text":"A coin begins on Tails. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Tails → Same: Tails → Different: Heads → Different: Tails → Same: Tails → Same: Tails → Different: Heads</reasoning><answer>Heads</answer>","reasoning":"Start Tails → Same: Tails → Different: Heads → Different: Tails → Same: Tails → Same: Tails → Different: Heads","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":110}}]},{"id":"gate-actor-3","kind":"actor-check","phase":"gate","index":3,"pass":true,"samples":[{"problem":{"id":"gate-1-110000","split":"gate","initial":1,"operations":[1,1,0,0,0,0],"answer":"Tails","text":"A coin begins on Tails. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Tails → Different: Heads → Different: Tails → Same: Tails → Same: Tails → Same: Tails → Same: Tails</reasoning><answer>Tails</answer>","reasoning":"Tails → Different: Heads → Different: Tails → Same: Tails → Same: Tails → Same: Tails → Same: Tails","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":99}}]},{"id":"gate-actor-4","kind":"actor-check","phase":"gate","index":4,"pass":true,"samples":[{"problem":{"id":"gate-1-000111","split":"gate","initial":1,"operations":[0,0,0,1,1,1],"answer":"Heads","text":"A coin begins on Tails. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Tails → Same: Tails → Same: Tails → Same: Tails → Different: Heads → Different: Tails → Different: Heads</reasoning><answer>Heads</answer>","reasoning":"Start Tails → Same: Tails → Same: Tails → Same: Tails → Different: Heads → Different: Tails → Different: Heads","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":110}}]},{"id":"gate-actor-5","kind":"actor-check","phase":"gate","index":5,"pass":true,"samples":[{"problem":{"id":"gate-0-001011","split":"gate","initial":0,"operations":[0,0,1,0,1,1],"answer":"Tails","text":"A coin begins on Heads. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Heads → Same: Heads → Same: Heads → Different: Tails → Same: Tails → Different: Heads → Different: Tails.</reasoning><answer>Tails</answer>","reasoning":"Start Heads → Same: Heads → Same: Heads → Different: Tails → Same: Tails → Different: Heads → Different: Tails.","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":111}}]},{"id":"gate-actor-6","kind":"actor-check","phase":"gate","index":6,"pass":true,"samples":[{"problem":{"id":"gate-0-000000","split":"gate","initial":0,"operations":[0,0,0,0,0,0],"answer":"Heads","text":"A coin begins on Heads. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Heads. Six consecutive Same operations leave the coin unchanged: Heads → Heads → Heads → Heads → Heads → Heads → Heads.</reasoning><answer>Heads</answer>","reasoning":"Start Heads. Six consecutive Same operations leave the coin unchanged: Heads → Heads → Heads → Heads → Heads → Heads → Heads.","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":125}}]},{"id":"gate-actor-7","kind":"actor-check","phase":"gate","index":7,"pass":true,"samples":[{"problem":{"id":"gate-1-110110","split":"gate","initial":1,"operations":[1,1,0,1,1,0],"answer":"Tails","text":"A coin begins on Tails. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Tails. Different → Heads; Different → Tails; Same → Tails; Different → Heads; Different → Tails; Same → Tails.</reasoning><answer>Tails</answer>","reasoning":"Start Tails. Different → Heads; Different → Tails; Same → Tails; Different → Heads; Different → Tails; Same → Tails.","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":116}}]},{"id":"gate-actor-8","kind":"actor-check","phase":"gate","index":8,"pass":true,"samples":[{"problem":{"id":"gate-0-110000","split":"gate","initial":0,"operations":[1,1,0,0,0,0],"answer":"Heads","text":"A coin begins on Heads. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Heads. Different → Tails. Different → Heads. Same → Heads. Same → Heads. Same → Heads. Same → Heads.</reasoning><answer>Heads</answer>","reasoning":"Start Heads. Different → Tails. Different → Heads. Same → Heads. Same → Heads. Same → Heads. Same → Heads.","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":106}}]},{"id":"gate-actor-9","kind":"actor-check","phase":"gate","index":9,"pass":true,"samples":[{"problem":{"id":"gate-0-010000","split":"gate","initial":0,"operations":[0,1,0,0,0,0],"answer":"Tails","text":"A coin begins on Heads. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Heads. Same → Heads; Different → Tails; Same → Tails; Same → Tails; Same → Tails; Same → Tails.</reasoning><answer>Tails</answer>","reasoning":"Start Heads. Same → Heads; Different → Tails; Same → Tails; Same → Tails; Same → Tails; Same → Tails.","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":101}}]},{"id":"gate-actor-10","kind":"actor-check","phase":"gate","index":10,"pass":true,"samples":[{"problem":{"id":"gate-1-100011","split":"gate","initial":1,"operations":[1,0,0,0,1,1],"answer":"Heads","text":"A coin begins on Tails. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Tails → Different: Heads → Same: Heads → Same: Heads → Same: Heads → Different: Tails → Different: Heads</reasoning><answer>Heads</answer>","reasoning":"Start Tails → Different: Heads → Same: Heads → Same: Heads → Same: Heads → Different: Tails → Different: Heads","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":110}}]},{"id":"gate-actor-11","kind":"actor-check","phase":"gate","index":11,"pass":true,"samples":[{"problem":{"id":"gate-1-100001","split":"gate","initial":1,"operations":[1,0,0,0,0,1],"answer":"Tails","text":"A coin begins on Tails. Two players alternate for 6 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Start Tails. Different → Heads; Same → Heads; Same → Heads; Same → Heads; Same → Heads; Different → Tails.</reasoning><answer>Tails</answer>","reasoning":"Start Tails. Different → Heads; Same → Heads; Same → Heads; Same → Heads; Same → Heads; Different → Tails.","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":106}}]},{"id":"gate-actor-12","kind":"actor-check","phase":"gate","index":12,"pass":true,"samples":[{"problem":{"id":"gate-0-110000011110000110111101001111001110010001","split":"gate","initial":0,"operations":[1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,1,1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1],"answer":"Heads","text":"A coin begins on Heads. Two players alternate for 42 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Different operations: 24, an even number, so the coin returns to its starting side, Heads.</reasoning><answer>Heads</answer>","reasoning":"Different operations: 24, an even number, so the coin returns to its starting side, Heads.","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":90}}]},{"id":"gate-actor-13","kind":"actor-check","phase":"gate","index":13,"pass":true,"samples":[{"problem":{"id":"gate-0-010000001110000100100100100100000100000100","split":"gate","initial":0,"operations":[0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0],"answer":"Tails","text":"A coin begins on Heads. Two players alternate for 42 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Different occurs 11 times, an odd number, so the coin flips from Heads to Tails.</reasoning><answer>Tails</answer>","reasoning":"Different occurs 11 times, an odd number, so the coin flips from Heads to Tails.","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":80}}]},{"id":"gate-actor-14","kind":"actor-check","phase":"gate","index":14,"pass":true,"samples":[{"problem":{"id":"gate-0-001010111100010011000100000110011000011000","split":"gate","initial":0,"operations":[0,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0],"answer":"Heads","text":"A coin begins on Heads. Two players alternate for 42 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>There are 16 Different operations, an even number, so the coin returns to its starting side, Heads.</reasoning><answer>Heads</answer>","reasoning":"There are 16 Different operations, an even number, so the coin returns to its starting side, Heads.","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":99}}]},{"id":"gate-actor-15","kind":"actor-check","phase":"gate","index":15,"pass":true,"samples":[{"problem":{"id":"gate-0-011001101001010011101000101000011001010011","split":"gate","initial":0,"operations":[0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0,0,1,1],"answer":"Tails","text":"A coin begins on Heads. Two players alternate for 42 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Different occurs 19 times, an odd number, so the coin flips from Heads to Tails.</reasoning><answer>Tails</answer>","reasoning":"Different occurs 19 times, an odd number, so the coin flips from Heads to Tails.","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":80}}]},{"id":"gate-actor-16","kind":"actor-check","phase":"gate","index":16,"pass":true,"samples":[{"problem":{"id":"gate-0-101000000001110001000001111110111110000001","split":"gate","initial":0,"operations":[1,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0,0,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1],"answer":"Heads","text":"A coin begins on Heads. Two players alternate for 42 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Different operations: 18, an even number, so the coin ends on its starting side.</reasoning><answer>Heads</answer>","reasoning":"Different operations: 18, an even number, so the coin ends on its starting side.","answer":"Heads"},"score":{"correct":1,"rcot":0,"total":1,"length":80}}]},{"id":"gate-actor-17","kind":"actor-check","phase":"gate","index":17,"pass":true,"samples":[{"problem":{"id":"gate-0-100101001011111011010110100010100111101010","split":"gate","initial":0,"operations":[1,0,0,1,0,1,0,0,1,0,1,1,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0,1,1,1,1,0,1,0,1,0],"answer":"Tails","text":"A coin begins on Heads. Two players alternate for 42 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Different operations: 25, an odd number, so Heads flips to Tails.</reasoning><answer>Tails</answer>","reasoning":"Different operations: 25, an odd number, so Heads flips to Tails.","answer":"Tails"},"score":{"correct":1,"rcot":0,"total":1,"length":65}}]},{"id":"gate-actor-18","kind":"actor-check","phase":"gate","index":18,"pass":false,"samples":[{"problem":{"id":"gate-1-000111011011101001100001001010101001111100","split":"gate","initial":1,"operations":[0,0,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,0],"answer":"Heads","text":"A coin begins on Tails. Two players alternate for 42 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Different occurs 20 times, an even number, so the coin remains on its starting side.</reasoning><answer>Tails</answer>","reasoning":"Different occurs 20 times, an even number, so the coin remains on its starting side.","answer":"Tails"},"score":{"correct":0,"rcot":0,"total":0,"length":84}}]},{"id":"gate-actor-19","kind":"actor-check","phase":"gate","index":19,"pass":false,"samples":[{"problem":{"id":"gate-0-001011011011010000011101101011110000011010","split":"gate","initial":0,"operations":[0,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,1,0,1,0],"answer":"Tails","text":"A coin begins on Heads. Two players alternate for 42 operations. Same leaves the side unchanged; Different flips it.\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Different\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Same\nPlayer 1: Same\nPlayer 2: Different\nPlayer 1: Different\nPlayer 2: Same\nPlayer 1: Different\nPlayer 2: Same\nWhich side is showing after the final operation? Answer Heads or Tails."},"completion":{"raw":"<reasoning>Different operations: 22, an even number, so the coin ends on its starting side, Heads.</reasoning><answer>Heads</answer>","reasoning":"Different operations: 22, an even number, so the coin ends on its starting side, Heads.","answer":"Heads"},"score":{"correct":0,"rcot":0,"total":0,"length":87}}]}]}