# 6.3. Dominos

> There is an 8x8 chessboard in which two diagonally opposite corners have been cut off. You are given 31 dominos, and a single domino can cover exactly two squares. Can you use the 31 dominos to cover the entire board? Prove your answer (by providing an example or showing why it's impossible).

With the opposite corners left, it'd take 8/2 * 8 = 36 dominos to cover it.

With the two diagonally opposite corners cut off, we can traversely cross each cell diagonally from one cutoff to another in an L. This takes 13 dominos. Keep doing diagonals in the center, we'll have to do some verticals/horizontals on the edges. The smaller pieces atke 18 dominoes. Up to a total of 31 dominos.

## Solution

The dominos are supposed to cover the whole cell so diagonals aren't allowed. So it's impossible to cover it with 31 dominos.