On a giant tape measure sits an N-frog: that is, a frog with a special preference for the number N. The frog's location at the beginning of each of its jumps is called M. The frog moves on the tape measure according to the following rules:

Whenever M>N, then the N-frog makes an N-jump to the left and lands on the number M-N.

Whenever M<N, then the N-frog makes an N-jump to the right and lands on number M+N; during landing it also changes its preference and becomes an M-frog.

Whenever M=N then the frog is happy and stays on that number.

Where will a 851-frog that sits on 1517 be happy?
Where will an N-frog that sits on M be happy?

A negative-frog that starts on a regular tape measure unhappily hops off the the positive end of the tape measure.  This is the same fate as a positive frog that starts at a negative location.

And a 0-frog is eternally frustrated and unhappy (and immobile), unless he has the great fortune to start at 0.

Edited on July 12, 2005, 2:44 pm

Posted by Steve Herman on 2005-07-09 11:57:53