> [!NOTE] > For any $n \geq 1,$ a $2^n \times 2^n$ checkerboard with $1\times 1$ corner square removed can be tiled by L-pieces as shown below > > ![[Pasted image 20240709191140.png|100]] ###### Proof Suppose there is a tiling of $2^{k}\times 2^{k}$ chessboard, then we can tile a $2^{k+1}\times 2^{k+1}$ chessboard as follows: ![[Pasted image 20240709195853.png|500]] So the statement holds true by [[Induction Principle|mathematical induction]].