RAY: As you might expect, the number 53 had nothing to do with anything. It could have been 15 people or seven people or any other number.

Each person could have shaken the hands of any number of people from zero to 52. There were 53 people present and no one of course shakes hands with himself, right?

TOM: Right!

RAY: So, let's imagine all the people lined up with a number on their chest equal to the number of people that they had shaken hands with. Here's the crux of the puzzle. If anyone had the number zero, meaning he shook, he or she shook no hands, then no one could have the number 52. Because in order for that to happen, that person would have had to shake hands with himself.

So, zero to 51 hang on the chests of 53 people. So when you get to the end, you get to the 53rd person, you say how many hands did you shake? He's got no choice but to repeat a number that's already been used.

The crux of the puzzler is knowing that if the number zero is used, if there is anyone there who shook no hands, then there's no one who could have shaken 52 hands.

TOM: Exactly. And this did not confuse Dominic Guerra from Wallkill, New York, because he got it right. And for getting it right Dominic is going to get a $26 gift certificate to the Shameless Commerce Division of Cartalk.Com

[ Car Talk Puzzler ]