task_games__pool__blocking_ball_count

Program Contract

Program: count(filter(pool_balls, intersects_marked_shot_segment)); scene=pool; scope=blocking_ball_count

Candidate set: the visible game board, pieces, tokens, cards, tiles, marked state, legal-move cues, result panels, and labeled options inside the blocking_ball_count objective scope. Operands: visible scene state and prompt-bound operands named by filter, pool_balls, intersects_marked_shot_segment, pool, blocking_ball_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 bbox_set schema; it contains the visible blocking balls that intersect the marked shot segments. Query ids: single.

Reasoning Operations

Families: filtering, counting, spatial_relations

Generation Notes

• The shown shot has two straight segments: cue ball to the marked target ball, then the marked target ball to the marked pocket.
• Annotation is a bbox_set projected around the blocking balls from the same generated pool state used for answer verification.