task_games__hex__candidate_neighbor_count

Contract

1. Domain: games
2. Scene: hex
3. Scene id: hex
4. Public task id: task_games__hex__candidate_neighbor_count
5. Supported query_id values: single
6. Answer schema: integer_count
7. Annotation schema: point_set
8. Program schema: count(filter(adjacent_cells(reference_cell), state=neighbor_target_state)); scene=hex; scope=candidate_neighbor_count

Program Contract

Program: count(filter(adjacent_cells(reference_cell), state=neighbor_target_state)); scene=hex; scope=candidate_neighbor_count

Candidate set: the visible game board, pieces, tokens, cards, tiles, marked state, legal-move cues, result panels, and labeled options inside the candidate_neighbor_count objective scope. Operands: visible scene state and prompt-bound operands named by filter, adjacent_cells, reference_cell, state, neighbor_target_state, hex, candidate_neighbor_count. Operation: evaluate count over the candidate set using the visible game state, rules, legal moves, comparisons, counts, simulations, or option-selection constraints 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 point_set schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: filtering, counting, topology

Generation Notes

1. The reference cell is filled green in the rendered board and is not counted.
2. The target neighbor state is sampled with neighbor_target_state (red, blue, or empty).
3. The generator samples an interior reference cell so each instance has exactly six adjacent cells.
4. Annotation is the set of pixel-space centers for neighboring cells that match the requested state; an empty annotation list is valid when the answer is 0.