Question

Given `50` distinct natural numbers between `1` and `100`. It is known that no two of these numbers sum to `100`. Is it necessarily true that one of these numbers must be a perfect square?

Difficulty level (1 very easy - 10 very hard): 2

Number Theory -> Prime Numbers Arithmetic Combinatorics -> Pigeonhole Principle Combinatorics -> Matchings Logic -> Reasoning / Logic Proof and Example -> Constructing an Example / Counterexample Set Theory Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Proof and Example -> Proof by Contradiction

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