Edmund's Brainteasers
Problem 21
Problem 21: Another hat problem
Here is another All Saints' Annual Party hat game. Jonathan has 100 paper hats and he writes the numbers from 1 to 100 on the hats. Phil and Jane play the game, each sitting on a chair facing the other. Jonathan takes a hat at random and places it on Phil's head, and another chosen at random on Jane's head. Each can see the number of the other's hat but not of course the number on their own. Jonathan tells them that the two numbers differ by three. He then rings a bell every minute and says that once they have worked out the number on their hat they must stand up after the next ring of the bell and will win. Jane sees that the number written on Phil's hat is 25. What will happen? Will Phil win? Will Jane win?