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.
- Adam: n years ago, you two together were as old as I will be m years from now.
- Beth: m years ago, you two together were as old as I will be n years from now.
- Cleo: In m years, you two together will be as old as I am today.
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