# Inspired by AOTM: Day 1

**Discrete Mathematics**Level 5

"An 8x8 chessboard has two of its opposite corners removed. For example, A1 and H8. Can this board be tiled completely by a sufficient number of 2x1 rectangles with no overlap?"

The answer turned out to be no. So I decided to give the problem some actual thought and I came up with an over complicated proof using modular arithmetic.

This inspired me to make a new problem:

How many ways can you remove two tiles from an 8x8 chess board such that the board cannot be completely tiled by 31, 2x1 rectangles without overlap?