Suppose a grid with 2m rows and 2n columns is given, where m and n are positive integers. You may place one pawn on any square of this grid, except the bottom left one or the top right one. After placing the pawn, a snail wants to undertake a journey on the grid. Starting from the bottom left square, it wants to visit every square exactly once, except the one with the pawn on it, which the snail wants to avoid. Moreover, it wants to finish in the top right square. It can only move horizontally or vertically on the grid.

On which squares can you put the pawn for the snail to be able to finish its journey?

Assuming the start and end squares are black, at the very least, the pawn would have to be on a white square.

Posted by Larry on 2020-12-12 10:43:56