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?

George answers four i.e. he knows all of the remaining numbers.

For Paul to say three he had to have seen 256 or 625 which eliminate all 3 digit squares except 784 or 841, so he must have one of these numbers. Either way the remaining numbers would include 0 3 and 9.

George infers all thisa instatnly because he spends all his time on perplexus and when he looks at Paul's number, the question of whether it is a 1 or a 7 remaining in the bag is answered.

Posted by scott on 2005-08-05 13:48:25