The Interesting Test - Answer 2

A woman and her husband attended a party with four other couples. As is normal at parties, handshaking took place. Of course, no one shook their own hand or the hand of the person they came with. And not everyone shook everyone else's hand. But when the woman asked the other (9) people present how many different people's hands they had shaken they all gave a different answer.

Question *(this is NOT a trick!)*: How many different people's hands did the woman's husband shake?

The maximum number of hands that any person might have shaken is eight.
Therefore, the nine people asked by the woman must have given the answers
0, 1, 2, 3, 4, 5, 6, 7, 8.

Let's refer to the person who answered 1 as person 1. Person 8 must have shaken everybody's hand but their own and their spouse's. Thus, everyone except their spouse has shaken at least one hand. Therefore, 8 and 0 are married.

Similarly, 7 must have shaken everybody's hand except for 0 and 1 (who used up his/her shake with 8). So 1 must be 7's spouse (0 is spoken for). Continuing in this way we see that (6 and 2) and (5 and 3) are married to each other.

This leaves 4 as the only unmatched person. 4 must therefore be matched to the woman.

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