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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.

robjohn
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haytham abutair
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  • You might look at this question which is for a different number of people. – Ross Millikan Nov 20 '12 at 05:04
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    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 06 '13 at 04:36
  • This question had been given in the book, Art and craft of problem solving by Paul Zeitz. – Hemant Agarwal Jul 11 '23 at 21:53

1 Answers1

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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.

Deven Ware
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