Arthur and Bert each writes down a positive integer on a piece of paper and then shows it to Charles. Charles then writes two numbers on a blackboard, visible to Arthur and Bert: one of them is the sum of Arthur's and Bert's numbers, and the other is a random number.

After this Charles asks Arthur if he knows Bert's number. If Arthur says he doesn't know, then he asks Bert if he knows Arthur's number. If Bert says he doesn't know, Charles continues with Arthur, then if necessary with Bert and so on... until he gets a positive answer.

When will Charles get a positive answer?

(In reply to re: General formula by Mindrod)

Yes, that's correct.  When it says it takes 5 rounds, that means that Arthur has already answered negative twice and Bert has already answered negative twice, before Arthur finally answers positive on the fifth round.

The formula is not proven, but it describes the observations that I took for cases with lower x-y.

Posted by Tristan on 2005-11-05 01:56:04