Question

at one of george washington's parties, each man shook hands with everyone except his spouse, and no handshakes took place between women. if 1313 married couples attended, how many handshakes were there among these 2626 people?

Answer 1

The total number of handshakes was 234.

• The first man shook hands with 12 other men.
• The second man shakes hands with 11 other men, as he had already shaken hands with the first man.
• Like-wise, the last man does not need to shake hands again as every man has already shaken hands with him in their respective turns.
• The number of handshakes among men is 0 + 1 + 2 + … + 12.
• The sum of "n" natural numbers = (n)(n+1)/2
• The number of handshakes among men is 12(13)/2.
• The number of handshakes among men is 78.
• Each man shakes hands with every woman except his spouse.
• Each man shakes hands with 12 other women.
• The number of handshakes between men and women is 13*12.
• The number of handshakes between men and women is 156.
• The total number of handshakes is 78 + 156.
• The total number of handshakes is 234.

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