Three friends, Adam, Beth, and Cleo, are sitting together and talking. Together they are 150 years old.
Adam: In 9 years, you two together will be as old as we three together are right now.
Beth: Ten years ago, the sum of your both ages was my age right now.
Cleo: Beth, 10 years ago I was twice your age.
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?
Erich Prisner, August 2003