Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.