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task_puzzles__matchstick__equation_repair_stick_label

Program Contract

Program: select_option(matchstick_equation.remove_one_stick_repair, source=false_visible_equation, candidates=labeled_digit_sticks); scene=matchstick; scope=false_equation_labeled_digit_sticks

Candidate set: the visible matchstick segments, digit/equation/lattice structure, segment labels, and labeled candidate options when present inside the false_equation_labeled_digit_sticks objective scope. Operands: visible scene state and prompt-bound operands named by matchstick_equation, remove_one_stick_repair, source, false_visible_equation, candidates, labeled_digit_sticks, matchstick, false_equation_labeled_digit_sticks. Operation: evaluate select_option over the candidate set using the visible states, constraints, transforms, comparisons, counts, paths, or option-selection rules encoded in the program expression; generation enforces a unique final answer. Output binding: answer uses the option_letter schema; generation binds a unique final answer. Annotation witnesses: annotation uses the segment schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: state_update, formula_evaluation, matching

Answer And Annotation

  • Answer type: option_letter.
  • Annotation type: segment.
  • Annotation schema: segment.
  • Annotation value: [[x1, y1], [x2, y2]], the image-pixel centerline endpoints of the selected labeled stick.
  • The answer and annotation are bound from the same sampled trace. The trace records every possible digit-stick removal and guarantees exactly one removal repairs the equation.

Rendering And Prompt

The matchstick scene renders a single false matchstick equation in one panel. Four or six candidate digit sticks are labeled directly on the equation. Prompt prose comes from src/trace_tasks/resources/prompts/puzzles/matchstick/puzzles_matchstick_v1.json.