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?

I think that there are only two possibilities.

#1

Arthur says he doesn't know.

Bert says he doesn't know.

Arthur guesses Bert's number correctly by substracting his number from the first number on the blackboard.

OR

#2

Arthur says he doesn't know.

Bert says he doesn't know.

Arthur guesses Bert's number incorrectly by substracting his number from the first number on the blackboard.

Bert guesses Arthur's number correctly by substracting his number from the second number, since if he is smart enough he will know Arthur worked with the first number.

Sorry if this sounds a little too simple, but the truth is there isn't a feasible way to know without knowing if one of your guesses is right or wrong.  HOWEVER, it would be too simple for Arthur to figure Bert's number byu the third time he's asked, so Bert figures it out before him.  Something like that.

Posted by Alexis on 2005-10-30 08:17:55