# Checkerboard cut-up

From Math Puzzle Wiki

Here is my version of a nice induction problem.

## Puzzle

You have a standard <m>8\times 8</m> checkerboard and a pair of scissors. If you only cut along the lines, you can create 21 L-shaped tiles (each made up of 3 checkerboard squares - no gluing allowed). However, doing so will leave one single square left over. Which of the original 64 squares could the extra, unused square be?

## Extension

For which other sizes of checkerboard will this puzzle work, and which of those will the puzzle work the same way?