Imagery and Puzzles

More of my brother's jazz:

Just to reinforce this importance of using the right "setting/imagery" in a
puzzle:

A) There is a 2n*2n grid of squares. One of the pair of diagonally opposite
squares is removed from the grid.
You have (2*n^2-1) dominoes, each of which can cover 2 adjacent squares. Can you
cover the remaining grid (whole - one pair of corner squares) with the
dominoes?

Setting: Now rephrase the problem. Instead of 2n*2n grid, consider a chess
board. So you have 31 dominoes each
of which can cover two squares. Now can you cover the board - one pair of
diagonally opposite squares with the dominoes?