Handshake Riddle
Posted by Rob Herman at September 21st, 2006
This riddle was related to me by intrepid reader John Rhoadhouse. If nobody has posted the answer by the time the next article goes up, I will post the answer in a comment at that time.
John went to a party with his date, Marie. At the party were three other couples, for a total of 8 people. During the night a certain number of people shook hands with each other. Nobody shook hands with their own date, nor with themselves. Afterwards John asked each person how many hands he or she had shaken. Each person gave a different answer.
How many hands did Marie shake?
Clarifications: John doesn’t ask himself how many hands he has shaken, and he is allowed to duplicate one of the other guests; in fact, a little consideration reveals that his number of handshakes must duplicate one of the other guests’.
Hint 0: A solution exists. There is no need for guessing or trickery.
more clarification for people who like to find “loop holes”. Nobody shakes the same persons hand more than once. Nobody shakes hands with someone who is not one of the eight people (including myself) that I went to the party with.
Marie shook 3 hands. The person who shook 6 hands was with the person who shook 0, the person who shook 5 hands was with the person who shook one, the person who shook 4 hands was with the person who shook 2, leaving John to be with the person who shook three hands, Marie. John also shook three hands.
Yup.
I like this riddle because at first, it doesn’t seem like there is enough information to solve it. But if you think backwards starting from Hint 0, the solution presents itself nicely.