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I invite 10 couples to a party to my house. I ask everyone present, including my wife, how many people they shook hands with. It turns out that everyone questioned - I didn't question myself of course - shook hands with a different number of people. If we assume that no one shook hands with his or her partner, how many people did my wife shake hands with?

I was thinking around 4.

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You might look at this question which is for a different number of people. –  Ross Millikan Nov 20 '12 at 5:04
    
I dislike questions like this. Instead of asking the question directly, it is rephrased into a contrived and ambiguously worded question, and we're left to decipher the author's intended meaning. (a) Contrived: Didn't you just ask your wife how many people she just shook hands with? (b) Ambiguous: Did all 10 couples attend the party? –  Douglas S. Stones Jan 6 '13 at 4:36

1 Answer 1

HINT: Interpret this situation as a graph.

Have a vertex for each person, and each edge is a handshake.

Consider the degree of each vertex. In particular the relation between the degree of someone and the degree of their partner.

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