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.

Zero! Coloring dots alternately black and white shows the reason: opposite corners have the same color, but as the grid is 10x10, there are 50 black and 50 white dots... so any trip through all dots must end at a different color than it started.

Posted by e.g. on 2005-04-06 21:06:48