You are standing in the very corner of a 10 X 10 grid of dots. How many different ways are there to get to the opposite corner of the grid? You must travel through every node once, and only once. You cannot travel diagonally, and you may not go outside of the overall perimeter.

The answer is zero!  Think of this as a checker-board where each node alternates black and white and because we cannot move diagonally we must always move from black to white and vice versa.  Because there are an even number of rows we must begin and end on the same colored square but because there are an even number of squares we must begin and end on opposite colored squares.  Since this is paradoxiacally impossible, the answer is zero!

I look forward to a solution with a 9x9 grid.

Posted by Eric on 2005-04-06 19:33:19