{"id":"odd-cells-xor-parity-formula","text":"A cell (r,c) has an odd value iff exactly one of `row_count[r]` and `col_count[c]` is odd; the return formula `odd_rows*(n-odd_cols) + (m-odd_rows)*odd_cols` computes this via two disjoint terms with no overlap.","truth_value":"IN","source":"entries/2026/06/06/cells-with-odd-values-in-a-matrix-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"odd-cells-xor-parity-formula","truth_value":"IN","reason":"premise"}]}}