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?

Paul would answer 3 digits if he saw the number 256 or 625 on George's forehead. George knows that these are the only numbers which Paul would see and be able to tell exactly which 3 didgits are left in the bag. 0, 3, 9 are definately in the bag. George now sees either 784 or 841 on Paul's forehead, leaving either 7 or 1 to be the last digit left in the bag.

There George will answer 4, but this is only case if the numbers 049 and 081 are not counted as three digit squares.

Posted by Avinash Narain on 2005-08-08 10:13:49