Can you find 3 similar geometrical figures (common shape but can be different sizes) A, B and C with the following property: If you remove any square from a 8x8 chess board, then the remaining area can be exactly covered with A, B and C.
How do A, B and C look like?
These should do it:
For example, like so:
Just orient the large block so that the missing piece is in the missing corner of the block, then do the same for each successively smaller block.
Just to show another example:
I think this is the answer.
Three L's. Each L is made up of 3 squares. The first L is 3 $4\times 4$ squares, the second is 3 $2 \times 2$, the third is 3 $1\times 1$ squares. Any one square of the chess board is in one of four quadrants, so you align the L so that the empty section matches with that quadrant. Repeat until only the taken square isn't covered.
This is a generalisation:
For any $N \times N$ board with one square missing and $N=2^k$ (some power of two), we can solve the puzzle with $k$ L-shaped pieces as described in the accepted answer. The first piece has width 1, the next has width 2, each piece doubling in width until we reach the largest piece with width $2^{k-1}$.
