Franklin College
Erich Prisner

Writing Project 31:

The old liar II

For all integers n and m we have the following problem P(n,m): 

Three friends, Adam, Beth, and Cleo, are sitting together and talking. Together they are 150 years old. 

If we know that the oldest, and only the oldest of the three is a liar, can you tell the ages of the three persons?

a) For which combination of n and m is there a solution to the problem P(n,m)?

b) For which combination of n and m are there more than one solutions?

c) Show that A is never the oldest of the three.

Erich Prisner, September 2003