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(2): almost a proof by pcbouhid)

To quote pc:

Re-reasoning: A = 4, B = 9, X = 13 and Y = 16.

After Arthurīs "NO", Bert(9) thinks:"Arthur, that have a 4 or a 7, knows that I have a 9 or a 12, and concluded nothing after my first "NO". But if Arthur had a 7, (13-7=6 and 16-7=9) he would know that I couldnīt have a 6, so I must have a 9. Since he answered "NO", his number could only be 4.

The statement "Arthur, that have a 4 or a 7, knows that I have a 9 or a 12, " is wrong. Bert can only say If Arther has a 4 he knows that I have a 9 or a 12. If Arthur had a 7 there's no way he'd know Bert couldn't have a 6. How would he know that?

Posted by Charlie on 2005-10-30 19:51:55