Handshake Problem Mr and Mrs Smith recently hosted a party a

Handshake Problem. Mr. and Mrs. Smith recently hosted a party at which three other couples attended. Various handshakes took place. No one shook hands with his/her own spouse, no one shook hands with the same person twice, and of course, no one shook his/her own hand.

After all handshakes were finished, Mr. Smith asked each person, including his wife, how many hands he or she had shaken. To his surprise, each person gave a different answer. How many hands did Mrs. Smith shake?

Please answer with a proof.

Solution

There are totally 4 couples i.e. 8 persons attending a party.

Consider Mrs. Smith. She will not shake hands with Mr. Smith.

She will shake with remaining 6 persons.

So 6 handshakes she will do.

Answer is 6.