Handshakes at a dinner party
A host couple invites 4 other couples to dinner (10 people total). People shake hands but never with their own partner or themselves. Afterward the host asks the other 9 people how many hands each shook and receives 9 distinct answers. How many hands did the host's partner shake?
Show hints (2)+
- Nine distinct answers among 5 couples force the values 0 through 8.
- Pair the 8-shaker with the 0-shaker, the 7 with the 1, and work inward.
Answer
Reveal answer →Final answer
4
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