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's number must be 256 or 625, because the remaining perfect three-digit squares would be either 784 or 841. Thus Paul knows that 3 of the digits left in the bag are 3, 9, and 0.
If George sees 784 or 841, then he's lucky he was not asked first, otherwise he wouldn't know very much. Because he knows that Paul could identify 3, he knows that his number is 256 or 625, and he knows all 4 numbers left in the bag...3, 9, 0 and either 1 or 7 (whichever is not on Paul's forehead).
George's answer
