Party of five couples
- �I heard you are a genius. Then the following problem won�t be a problem …�
Mr. Smith and his wife throw a party and invite four married couples.
There are some of them who know each other, and some who don’t. Those who do not know each other, shake hands.
Mr. Smiths asks all the participants of the party, how many times did they shake hands. He remarked, that no two persons answered the same number.
Question: what number did Mrs. Smith say?
Hints:
- Everybody knows himself and his wife or her husband.
- If A shook hands with B, then this means that B shook hands with A as well.
- Mr. Smith didn’t ask himself about the number of handshakings.
- The number of persons in the problem is ten, five husbands and five wives.
(This one IS difficult)