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?
Can this be solved without doing any math?
The fact that Paul answers "three" means that he's figured out 8 of the 10 digits...3 on George, 3 in the bag and 2 on his forehead. Does this then imply that George will always be able to figure out them all because he can see which of the remaining 2 digits is on Paul's forehead?
Just logic
