task_games__tower_defense__covered_path_segment_count

Contract

1. Domain: games
2. Scene: tower_defense
3. Scene id: tower_defense
4. Public task id: task_games__tower_defense__covered_path_segment_count
5. Supported query_id values: single
6. Answer schema: integer_count
7. Annotation schema: point_set

Program Contract

Program: count(path_enemy for path_enemy in path_enemies if any(path_enemy_center inside tower_range_circle for tower in towers)); scene=tower_defense; scope=covered_path_segment_count

Candidate set: the visible game board, pieces, tokens, cards, tiles, marked state, legal-move cues, result panels, and labeled options inside the covered_path_segment_count objective scope. Operands: visible scene state and prompt-bound operands named by path_enemy, path_enemies, if, any, path_enemy_center, inside, tower_range_circle, tower, towers, tower_defense, covered_path_segment_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: counting, spatial_relations, topology

Generation Notes

1. The path is drawn with small visible enemy markers along a winding or switchback route.
2. Towers are placed off the path and display circular range rings.
3. A path enemy is covered when its center lies inside at least one tower range ring.
4. Annotation contains one point at the center of every covered path enemy.