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.

(In reply to Solution by Jonathan Chang)

I am sorry Jonathan Chang, it is not possible to get to the opposite corner of the grid.
In the postings, people used chess/checkerboard white and black squares to show it was not possible.
Imagine that one point in the grid is one square, then the point next to it  will also be also a square, but from another color.
So if you have a 2x2 grid, you can represent it by a four square grid.  I am sure that you will agree that it is not possible to travel through every square (=grid point) before reaching the top right square.  Suppose now that the left/under square is black, then the up/right will also be black.
If your walk starts on a black and ends on a black, then you will have travelled through an odd number of white squares.
Now, on a 10x10 board there are 50 black and 50 white squares.  This means that if you start and  end on the black, you can not cover the 50 white squares, you can only cover an odd number of white squares.
Conclusion is: you have to travel an even number of squares and you can only do an odd number.  This means it is impossible, there are ZERO ways to solve it.
If you do not believe this, try it on a piece of paper and publish the solution.  If it works out OK, pcbouhid will pay you the $1.000.000 he still ows perplexus.
Please let us know what you think of it.

Posted by Hugo on 2005-04-16 21:01:22