You didn’t really think one puzzle was the end of it, did you?

Fred and Norma held a dinner party and invited 4 other couples. As people arrived, Fred noticed that people who knew each other hugged or kissed, but if they were strangers they just shook hands. After all the arrivals and all the introductions, Fred asked everyone including Norma how many hands they had shaken. To his surprise he got 9 different answers.

How many of the dinner guests were strangers to Norma?

Answer over the fold

Answer: 4


  1. The 9 different answers must be the numbers 0 to 8, since no-one shakes hands with themselves or their partner.
  2. Say A shook 8 hands. Those 8 people shook at least 1 hand (A’s). So A’s partner shook no hands.
  3. Then say B shook 7 hands. Those 7 people shook at least 2 hands (A’s and B’s). So B’s partner shook 1 hand.
  4. And so on through C (6) and partner (2), D (5) and partner (3).
  5. Finally E and partner each shook 4 hands. E must be Fred (who did not give an answer) and his partner, Norma, shook 4 hands.