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 almost a proof by pcbouhid)

In the example of  A = 4, B = 9, X = 13 and Y = 16, A knows from the beginning that B has either 9 or 12--nothing in between. Likewise B knows that A has either 4 or 7--nothing in between.

When each professes ignorance, no new knowledge is imparted to either one--they new from the beginning that either of the possibilities for the other would result in that person not being able to identify which of the two was the case.

Posted by Charlie on 2005-10-30 12:57:55