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!"):

121231231212312312*121231231212312312*121231....etc.

How far apart, in inches, were the cracks in the sidewalk?

(In reply to Solution by SilverKnight)

I think this sounds too easy. Do you account for the 9 inches of the sole?
I agree that the person taking the steps must have stood on a crack, but I'm not sure that you can say that the cracks are exactly 95 inches away from each other.
Count the steps like this, with each crack in brackets:

0 -> 35 -> 70 -> (95) 105 -> 140 -> 175 -> (190) 210 -> 245 -> 280 -> (285) 315 -> 350 -> (380) 385 -> 420 -> 455 -> (475) 490 -> 525 -> 560 -> (570) 595 -> 630 -> (665) 665

With a 9-inch-long sole it's possible that he stepped on the crack 380 inches away from the start. It's only 5 inches less than his 11th step took him. He could have touched it with the lower part of his sole.

Perhaps I missed something, but I think we must be more precise.

Posted by abc on 2003-09-17 14:31:17