Question

Every person who ever lived on Earth performed a certain number of handshakes (including 0). Prove that the number of people who performed an odd number of handshakes is even.

Difficulty level (1 very easy - 10 very hard): 3

Topics:
Combinatorics -> Double Counting Combinatorics -> Graph Theory Number Theory -> Division -> Parity (Even/Odd) Proof and Example -> Proof by Contradiction
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