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.