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: Solution by abc)

Actually, it *is* this easy. You bring up a good point, though.

If we assume there is a solution, then what I described earlier suffices. However, as we are trained to be skeptical (as you are), we should assume that perhaps what DJ is looking for is "it's not possible!".

Fair enough... no one suggested that we must start at 0 (as you did in the example). So, let's start at a "convenient location". After doing a little analysis, you may come up with beginning at 30... so... to continue with your description (where the cracks are described in parenthesis).
30 -> 65 -> (95) 100 -> 135 -> 170 -> (190) 205 -> 240 -> 275 -> (285) 310 -> 345 -> (380) 380 -> 415 -> 450 -> (475) 485 -> 520 -> 555 -> (570) 590 -> 625 -> *BOING*

Now, if you are troubled by the 380 (as you may be), then simply add 0.5 inches to every number not in parenthesis, and we have a clear solution.

--- SK

Posted by SilverKnight on 2003-09-17 15:21:00