I once knew a fellow who was a bit long of leg and short of foot.
The soles of his shoes were, in fact, exactly 9 inches long and his stride was exactly 35 inches. He had a habit of counting his steps when they were all on the same slab of the sidewalk and saying "Boing!" every time he stepped on a crack. If he stepped over a crack his counting started again at one, and of course his counting started at one after each "Boing!"
In his neighborhood there was a sidewalk with perfectly regular slabs all the same size. He noticed that when he walked along this sidewalk he always got the following repeating pattern (where "*" stands for "Boing!"):
How far apart, in inches, were the cracks in the sidewalk?