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?

I think George's no is 169 or 961. it is the only no, possible. 8 and 5 always goes with 1 and 6 in the list of 3 digit squares. so 8,5,and 0 are the ones left in the bag. That leaves out 2,3,4,7. George will follow this deduction and then can find his no to be 324, as the only square possible out of the 4 digits. 

Posted by riten on 2005-08-08 17:52:06