For new problems look again at a chessboard. Suppose a
chess piece can move only one square horizontally
or vertically
at a time, i.e. a king that cannot move diagonally. It is not
too difficult to see how this king could
move about the board in
such a way that every square is covered exactly once and return
to the square on
which he started. Suppose now that two squares
at opposite ends of the same diagonal are deleted from the
board.
Is it possible now for the king to visit every square and return
to his starting point? If so, give the path.
If not, explain
why not. Many variations of this puzzle are possible. Could
this be done on a 5x7 board
(no deleted squares)? On a 7x6
board? On a 13x17 board? In general, for what values of m and n
is it
possible on an mxn board (and why)?