via-color-counting Color-counting argument

COMPLETE route · research/via-color-counting.md

Target

• mutilated-board-untileable ESTABLISHED The mutilated chessboard admits no domino tiling

Requires

• domino-color-balance ESTABLISHED Every domino covers one dark and one light square
• mutilated-board-color-count ESTABLISHED Opposite corners share a color, leaving a 32–30 imbalance

Statement

A tiling by 31 dominoes would cover 31 dark and 31 light squares (domino-color-balance), but the region has 32 and 30 (mutilated-board-color-count). Contradiction.