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.

There are too many ways to procced with the joining from one dot to another. One could move from the left dot to right dot & move vertically upward & turn to the left dot & then move upward to turn to the right. As there are many ways of movement from one dot to another, there should be more than 500 ways of movements for this solution.