I have a bag containing the digits 0 through 9, and used six of them to stick two different three-digit perfect squares on the foreheads of Paul and George. Both Paul and George know this fact, but each one can see only the other's number.

I ask Paul, "How many of the digits remaining in my bag can you exactly tell me?"

Paul replies, "Three."

If I now ask the same question to George, what should he reply?

(In reply to solution? by Lia)

Lia.....George knows that if Paul is able to state that he knows exactly 3 numbers in the bag then he (George) has the numbers 2, 5 and 6 on his head.  George also knows the three numbers on Paul's head so therefore he would know the other four numbers in the bag.

See Bob's or Charley's explanation below.

 

Posted by Nosher on 2005-08-05 04:26:47