a) From a regular 8 by 8 chessboard, the squares c5 and g2 have been cut out. Can the remaining part be tiled with dominoes 1 by 2?
b) The same question, if the squares c6 and g2 have been cut out.
a) Yes, it is possible. It is easy to provide an example of such a tiling.

b) No, it is not possible. Indeed, we have cut out two white cells; but each domino covers one white and one black cell, so if we were to tile the entire board, the number of white and black cells covered would be the same. However, there are 30 white cells left and 32 black cells. Therefore, it is impossible to cover the resulting board with dominoes.

## Answer

a) Yes; b) no.