Problem of the Week 1034

A Godelian Puzzle

Alice: Here I have a penny and a quarter. You get to make a statement and if it is true I will give you one of the coins. If it is false, I give you neither coin.

Bob: That is generous of you. Which coin will you give me if my statement is true?

Alice: Not telling.

What statement should Bob make to maximize the amount of money Alice gives him?

Adapted from "Godelian Puzzles," by Raymond Smullyan, in Tribute to a Mathemagican, by Cipra, Demaine, Demaine, and Rogers, AK Peters, 2005.

© Copyright 2005 Stan Wagon. Reproduced with permission.