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?

For Paul to know at least 3 numbers in the bag, the square on George's head must be either 256 or 625. This would mean that the square on Paul's head is either 784 or 841, thus meaning that Paul would know that at least 0, 3 and 9 remain in the bag. George would then only know one digit for certain in the bag, namely 0.

Posted by Lia on 2005-08-05 02:16:58