Suppose you are married and you and your partner attend a party with three…
2022
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 hand shaking was completed, suppose 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?
- A.
1
- B.
2
- C.
3
- D.
4
Attempted by 20 students.
Show answer & explanation
Correct answer: C
Answer: 3 — your spouse shook 3 hands.
Explanation:
There are 4 couples (you plus three other couples), so 8 people total. Each person could have shaken between 0 and 6 hands (they cannot shake their own hand or their partner's). You asked the other seven people and heard seven different answers, so those answers must be the numbers 0, 1, 2, 3, 4, 5, 6.
If someone shook 6 hands, they shook hands with every person except their partner. That partner therefore shook 0 hands.
More generally, if a person shook k hands, their partner must have shaken 6 − k hands. So answers pair up to sum to 6 (0 with 6, 1 with 5, 2 with 4).
Those three complementary pairs account for six of the seven people you asked. The only remaining answer among the seven is 3, so the person left (your spouse) must have shaken 3 hands.
Therefore your spouse shook 3 hands.
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