The Smiths, the Andrings and the Cliffords all hold a big party. Everyone shakes hands with every member of the other two families (no one shakes hands with members of their own family), 142 handshakes in all.

Assuming that there at least as many Andrings as Smiths, and at least as many Cliffords as Andrings, how many of each family are present?

(In reply to re(2): 1/2 Surface of a Rectangular Solid... by Erik O.)

Your right, Eric O.,  but I was talking about a 3-way handshake where 3 people simultaneously touch hands.  Like when The Three Stooges would put their hands in the middle and say "I'm in", "Me too", "Me three".  Which I think would be:  ABC  or volume
(clearly a departure from what this problem was about)

But I like your analysis which seems to indicate that the number of "normal" handshakes between N families is the same as:
2^(-(N-2)) * Surface Area of an N dimensional hyper rectangular parallelopiped  (if that's really a word)

I like it when totally different things in the real world have the same math.  But the concept of The N Stooges is a little scary.

Posted by Larry on 2004-06-15 00:21:09