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(3): General formula by Steve Herman)

I think the inconsistency arises again from definitions.  The new formula I wrote, is equivalent to the first, but it uses a different definition of "round."

According to my first formula, the 6th response is a yes, meaning there are 5 no's before it.

According to the second formula, Bert responds yes the 3rd time.  This means that before he said yes, Arthur said no 3 times and Bert said no 2 times.

I think our methods are consistent with each other.

Posted by Tristan on 2005-11-01 00:22:24