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Number of Handshakes

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Number of Handshakes is a cooked quant interview question on puzzles.

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What this combinatorics puzzle tests

This is an easy puzzle that appears frequently in quant and finance interviews as a warm-up or filter question. It tests whether you can quickly translate a real-world scenario into a counting problem and apply basic combinatorial reasoning without over-complicating it.

The key skill is recognizing that you're counting pairs of distinct objects from a fixed set, and avoiding the common trap of double-counting. Interviewers value clean, confident reasoning here—a clear explanation of why your formula works matters more than speed.

  • Combinations and the binomial coefficient
  • Symmetry and avoiding double-counting
  • Translating word problems into mathematical notation