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another logic puzzle
This came up today. I'm not 100% sure the answer I have in mind is unique, but I think it is.
You and your spouse invite 4 other couples over for a dinner party. During the course of the party, many people shake hands with other people, except that no one shakes hands with their partner or themselves. At the end of the party, you realize that each of the other 9 people (that is, everyone but you) shook a different number of hands from each other. How many different hands did you shake?
Again, the answer doesn't involve tricks, like some people shaking with both their left and right hands or shaking the hand of someone not at the party.All comments screened for now, like before. Questions and bad guesses will be unscreened sooner; good guesses and right answers will be unscreened later. No googling allowed! Comments now contain spoilers.
You and your spouse invite 4 other couples over for a dinner party. During the course of the party, many people shake hands with other people, except that no one shakes hands with their partner or themselves. At the end of the party, you realize that each of the other 9 people (that is, everyone but you) shook a different number of hands from each other. How many different hands did you shake?
Again, the answer doesn't involve tricks, like some people shaking with both their left and right hands or shaking the hand of someone not at the party.
no subject
The long way to reach this is to assuming that everyone except for you will have a unique number of handshakes. This means that one person will have 0 handshakes, 1 person will 1 handshake, 1 person will have 2 handshakes, ...., 1 person will have 8 handshakes. Lets take the person who shook 8 hands first. The only person he did not shake hands with is his wife; because everyone must have a unique handshake number (i.e. there can be only one person with 0 handshakes), she must be the person with 0 handshakes. Now lets pick one of the people who shook hands with mr 8 hand shakes, and designate them as the person who shakes hands with 7 other people. There are only 2 people left who this person who has not shaked hands with, and one of them is ms 0 handshakes. So the remaining person is the wife. Now we take one of the people mr 7 handshakes shook with, and designate them as mr 6 handshakes.....we just keep repeating the process until we reach a point where two people have the same handshake count - this is your answer.
The short way : we can assume that the number of people at the party will always be even (since we are always dealing with couples). The number of handshakes you make will be half the number of you and your spouse's guests (i.e. if there are 10 people at the party, 2 people are you and your spouse, so you have 8 guests, and thus you make 4 handshakes). It should be trivial to prove this as a correct answer, although the proof that this is the only answer would be interesting.
no subject
Your other answer is right, of course.