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: almost a proof by Charlie)

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

first turn: Arthur(4) thinks:"Bertīs number is 9 or 12". So, his answer is "NO". Bert(9) thinks: "Arthurīs number is 4 or 7". So his answer is also "NO".

second turn: Arthur(4) thinks:"Bert knows that I have a 4 or a 7, and I know that his number is 9 or 12. If he had a 9, he would reason that my number could be 4 or 7, and if he had a 12, he would reason that my number would be 1 or 4. So, in both cases, he would be still in doubt (4 or 7) and then answered NO. Since I have a 4, I donīt know yet his number (9 or 12)". So, Arthurīs answer is "NO".

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.

What am I missing?

Edited on October 30, 2005, 3:34 pm

Edited on October 30, 2005, 3:42 pm

Edited on October 30, 2005, 4:02 pm

Edited on October 30, 2005, 4:06 pm

Posted by pcbouhid on 2005-10-30 15:22:31