TITLE: $2^n \times 2^n$ chessboard with one square removed - Is the tiling unique?
QUESTION [5 upvotes]: It is well-known that a $2^n \times 2^n$ chessboard with an arbitrary square removed is tilable by an L-shaped tromino (piece composed of three squares). The standard proof is by induction, and is constructive (gives an algorithm for producing such a tiling).
My question is: For a given chessboard with a fixed square removed, is this tiling unique?

REPLY [3 votes]: Here are two explicit tiling of the 8x8 board. I got the second board just by playing around with the tiling.