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task_puzzles__cell_board__reachable_region_size

Program Contract

Program: count_reachable_cells(cell_board, start=green_S_cell, passable=non_wall_cells, adjacency=orthogonal_4_neighbor); scene=cell_board; scope=reachable_region_size

Candidate set: the visible grid cells, cell colors/states, labels, walls, start/goal markers, and mirror or connectivity cues inside the reachable_region_size objective scope. Operands: visible scene state and prompt-bound operands named by cell_board, start, green_S_cell, passable, non_wall_cells, adjacency, orthogonal_4_neighbor, reachable_region_size. Operation: evaluate count_reachable_cells 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; one image-pixel cell bbox for every reachable light passable cell, including the start cell. Query ids: single.

Reasoning Operations

Families: filtering, counting, topology

2) Scene + task contract

  1. Entities/relations: A rectangular board with dark wall cells, light passable cells, disconnected light distractor regions, and a green start cell marked S.
  2. Supported query_id values: single
  3. answer_gt.type: integer
  4. Annotation schema: bbox_set
  5. Alternate annotation forms: none
  6. Annotation witness policy: one image-pixel cell bbox for every reachable light passable cell, including the start cell.
  7. Overlap/touch policy: dark walls block movement; diagonal/corner touching between light cells does not connect regions.

3) Prompt contract

  1. prompt_bundle_id: puzzles_cell_board_v1
  2. scene_key: cell_board
  3. task_key: cell_board_topology_query
  4. Prompt query key: reachable_region_size
  5. Required slots: output-mode slots from the prompt bundle.
  6. JSON example validity rule: bbox-set cardinality equals the integer answer.
  7. Output modes: answer_only, answer_and_annotation

4) Determinism + constraints

  1. Seed namespaces used: task-local region namespaces plus shared cell-board layout/style/font/noise namespaces.
  2. Unique-answer policy: construction creates and verifies an exact reachable region size in answer range 1..8.
  3. Reject/resample conditions: reachable-region size mismatch or insufficient disconnected passable distractors raises and retries.
  4. No-auto-relaxation guarantee: semantic constraints are not relaxed.