With a tip of the hat to Gavinksong's that was written by an author that he references, I give one that is of the same type, but simpler. It was included in one of Peter Winkler's books, and it is attributed to Tom Cover in a 1986 publication on open problems in communication and computation. It asks something very similar to choosing apples behind doors, and it may even have inspired that puzzle. Because I have read the solution, I won't contribute anything further in the apples thread.

Paula takes two slips of paper and writes an integer on each. There are no restrictions on the two numbers except that they must be different. She then conceals one slip in each hand. Victor chooses one of Paula's hands, which Paula then opens, allowing Victor to see the number on that slip. Victor must now guess whether that number is the larger or the smaller of Paula's two numbers; if he guesses right, he wins $1, otherwise he loses $1.

Clearly, Victor can achieve equity in this game, for example, by flipping a coin to decide whether to guess "larger" or "smaller." The question is: Not knowing anything about Paula's psychology, is there any way he can do better than break even?

## Question

## bonanova

With a tip of the hat to

Gavinksong's that was written by an author that he references, I give one that is of the same type, but simpler. It was included in one of Peter Winkler's books, and it is attributed to Tom Cover in a 1986 publication on open problems in communication and computation. It asks something very similar to choosing apples behind doors, and it may even have inspired that puzzle. Because I have read the solution, I won't contribute anything further in the apples thread.## Link to comment

## Share on other sites

## 9 answers to this question

## Recommended Posts

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.