You are given 21 3x1 rectangular pieces to cover an 8x8 chessboard. Since the board has 64 squares, which square on the chessboard must you cut out so that the 21 given pieces exactly cover the remaining 63 squares? Or it is impossible, no matter which square you remove?
Because of both horizontal and vertical Symmetry only need to consider 10 possible sets of answers.
Each square on a long diagonal has 3 images; so 4 solutions cover these 16 squares. Remaining 48 are in sets of 8 so further 6 possible solutions. Is it possible to reduce this further?
early thoughts.
