task_puzzles__star_battle__remaining_valid_cell_count

Program Contract

Program: count(star_battle.valid_cells, scope=marked_row|marked_column); scene=star_battle; scope=marked_scope_cells

Candidate set: the visible Star Battle grid, regions, clues, placed stars, and highlighted row or column inside the marked_scope_cells objective scope. Operands: visible scene state and prompt-bound operands named by star_battle, valid_cells, marked_row, marked_column, marked_scope_cells. Operation: evaluate count 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 bbox set of counted legal cells only. Query ids: remaining_valid_cells_in_marked_row_count, remaining_valid_cells_in_marked_column_count.

Reasoning Operations

Families: filtering, counting, matching

Behavior

The task renders a partial Star Battle board with visible fixed stars and one highlighted row or column. The prompt names the highlighted row index from the top or column index from the left. The model counts empty cells in that highlighted scope where another star could legally be placed under the Star Battle rules. The annotation is the bbox set of counted legal cells only.