Here’s a puzzle I hadn’t seen before. I’m concealing the source to discourage Googling, but will give credit where it’s due in a couple of days.
Alice, Betty and Carol each has a positive integer stamped on her forehead. They know that one of their numbers is equal to the sum of the other two. They proceed alphabetically around the table, each one either announcing her own number (if she’s managed to figure it out) or announcing that she doesn’t know it.
The game proceeds as follows:
Alice: “I don’t know my number”.
Betty: “I don’t know my number”.
Carol: “I don’t know my number”.
Alice: “My number is 25″.
What are the other two numbers?