Suppose you are married and you and your partner attend a party with three other married couples. Several handshakes took place. No one shook hands with himself (or herself) or with their partner, and no one shook hands with the same person more than once. After all handshaking was completed, you asked each person, including your partner, how many hands they had shaken. Each person gave a different answer. How many hands did your spouse shake?
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Correct answer: C. 3
Explanation
8 people, each can shake at most 6 hands, so the 7 different answers are 0–6. The person with 6 is married to the one with 0, 5 to 1, 4 to 2. The remaining answer 3 belongs to your spouse (you also shook 3).More Discrete Structures and Optimization questions
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