Medium | Discrete Maths |

An 8x8 chessboard can be entirely covered by 32 dominoes of size 2x1. Suppose we cut off two opposite corners of chess (i.e. two white blocks or two black blocks). Prove that now it is impossible to cover the remaining chessboard with 31 dominoes.

Hint

The two diagonally opposite corners are of the same color.

Solution

The two diagonally opposite corners are of the same color. A domino covers adjacent faces & hence a domino always covers 1 black and 1 white square. The 31 dominoes will cover 31 blacks and 31 whites. The chess has 30 & 32 square instead. Hence this can't be done.

Source: Martin Gardner

Enable Like and Comment Latest solved Puzzles

Color Switches Weird Sequences Intersecting Pillars Consecutive sums Scaling a Square Difficulty Level

© BRAINSTELLAR |