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Happy Handshaking

Jack and his wife went to a party where four other married couples were present. Every person shook hands with everyone he or she was not acquainted with. When the handshaking was over, Jack asked everyone, including his own wife, how many hands they shook. To his surprise, Jack got nine different answers.

How many hands did Jack’s wife shake?

Because, obviously, no person shook hands with himself or herself, or with his or her partner, nobody shook hands with more than eight other people. And since nine people shook hands with different numbers of people, these numbers must be 0, 1, 2, 3, 4, 5, 6, 7, and 8. The person who shook 8 hands, shook hands with all other persons (who therefore shook each at least 1 hand), except with his or her partner. Therefore, the partner of the person who shook 8 hands, must be the person who shook 0 hands.

The person who shook 7 hands, shook hands with all other persons (who therefore shook each at least 2 hands), except with his or her partner and the person who shook 0 hands. Therefore, the partner of the person who shook 7 hands, must be the person who shook 1 hand.

The person who shook 6 hands, shook hands with all other persons (who therefore shook each at least 3 hands), except with his or her partner and the persons who shook 1 and 0 hands. Therefore, the partner of the person who shook 6 hands, must be the person who shook 2 hands.

The person who shook 5 hands, shook hands with all other persons (who therefore shook each at least 4 hands), except with his or her partner and the persons who shook 2, 1, and 0 hands. Therefore, the partner of the person who shook 5 hands, must be the person who shook 3 hands.

The only person left, is the one who shook 4 hands, and which must be Jack’s wife. The answer is: Jack’s wife shook 4 hands.

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brainfry

Why can't Jack or her wife be any of the other persons who shook varying numbers of hands? Where in the question was that dictated?

  

Puzzlezuzu

Of the 9 non-Jack people who answered Jack, we have reasoned that the ones who shook 8, 7, 6, and 5 hands are married to the ones who shook 0, 1, 2, and 3 hands, and are therefore not married to Jack. The only one not married to one of the other 9 non-Jack people is the one who shook 4 hands, who must therefore be Jack's wife.


Wiktor Piotr

Jack and his wife needed to both shake the same number of hands in order for Jack to receive 9 different answers. For example, if Jack were to be the person who shook 5 hands, his wife would be the one who shook 3. Then, Jack would receive only 8 unique answers from the people he asked: 0,1,2,4,4,5,6,7,8


Wiktor Piotr

Jack and his wife needed to both shake the same number of hands in order for Jack to receive 9 different answers. For example, if Jack were to be the person who shook 5 hands, his wife would be the one who shook 3. Then, Jack would receive only 8 unique answers from the people he asked: 0,1,2,4,4,5,6,7,8


Wiktor Piotr

Jack and his wife needed to both shake the same number of hands in order for Jack to receive 9 different answers. For example, if Jack were to be the person who shook 5 hands, his wife would be the one who shook 3. Then, Jack would receive only 8 unique answers from the people he asked: 0,1,2,4,4,5,6,7,8


Wiktor Piotr

Jack and his wife needed to both shake the same number of hands in order for Jack to receive 9 different answers. For example, if Jack were to be the person who shook 5 hands, his wife would be the one who shook 3. Then, Jack would receive only 8 unique answers from the people he asked: 0,1,2,4,4,5,6,7,8


Wiktor Piotr

Jack and his wife needed to both shake the same number of hands in order for Jack to receive 9 different answers. For example, if Jack were to be the person who shook 5 hands, his wife would be the one who shook 3. Then, Jack would receive only 8 unique answers from the people he asked: 0,1,2,4,4,5,6,7,8


Satya Singamsetti

Good question. The question should have mentioned that Jack shook hands with 4 people.. How many hands did Jack's wife shook hands with?

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Submitted by
Valentin
over 5 years ago
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Difficulty 8.0 ?

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