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 re(2): Solution by SilverKnight)

All.... I submit to you that this problem ISN'T possible if the fellow wasn't quite so short in foot. If his foot is even an inch longer (at least 10 inches), then this problem is impossible.

Since, I am proposing this, I will refrain from attempting to prove/show this. ;-)

Anyone else wish to step up?
Edited on September 17, 2003, 3:38 pm

Posted by SilverKnight on 2003-09-17 15:38:01