Shaking Hands

At a recent joint session of Congress, each member shook hands with every other member exactly once.

How many handshakes occurred?

Answer

The first member of congress shares 534 hands (because there are 535 members of Congress)!
So all members shake 535 x 534 times.
The number must be adjusted by half to avoid double counting when B shakes with a and then A shakes with B.

The answer is 535 X 534 X 1/2 or 142,845 handshakes.

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