Handshake Puzzle

April 10, 2025

Handshake Puzzle

Solve the Handshake Puzzle here on this page.
At a party, everyone shook hands with everybody else. There were 66 handshakes.

How many people were at the party?

handshake puzzle

Solution:

If there are n people,

  1. The first person will shake hands with an n-1 person,
  2. The second with n-2,
  3. The third with n-3, and
  4. The (n-1)th person with n-(n-1)=1 person means the last person.

Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1

Which can be equated using n(n-1)/2=66

Hence, n=12

handshake puzzle question

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