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task_puzzles__matchstick__max_square_count_after_additions_value

Program Contract

Program: count_max(matchstick_lattice.complete_unit_squares_after_k_edge_additions, add_count=k, source=visible_incomplete_square_lattice); scene=matchstick; scope=square_lattice_missing_edges

Candidate set: the visible matchstick segments, digit/equation/lattice structure, segment labels, and labeled candidate options when present inside the square_lattice_missing_edges objective scope. Operands: visible scene state and prompt-bound operands named by matchstick_lattice, complete_unit_squares_after_k_edge_additions, add_count, k, source, visible_incomplete_square_lattice, matchstick, square_lattice_missing_edges. Operation: evaluate count_max 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 integer schema; generation binds a unique final answer. Annotation witnesses: annotation uses the bbox_set schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: counting, ranking, state_update

Answer And Annotation

  • Answer type: integer.
  • Annotation type: bbox_set.
  • Annotation schema: bbox_set.
  • Annotation value: an unordered list of image-pixel unit-square bounding boxes [x0, y0, x1, y1], one for each complete unit square counted in the final optimal board.
  • The answer and annotation are bound from the same sampled trace. The sampler rejects instances unless the maximum answer and final counted square-bbox set are unique.

Rendering And Prompt

The matchstick scene renders one incomplete matchstick lattice on a square grid using wooden-match, colored-rod, chalk-stick, neon-rod, or metal-rod visual styles. Existing sticks are rendered as matchsticks, and empty grid edge positions are indicated by the lattice vertices. Prompt prose comes from src/trace_tasks/resources/prompts/puzzles/matchstick/puzzles_matchstick_v1.json.