Question
The numbers from `1` to `2n` are written in a row in some order. Add to each number the index of the position it stands on. Prove that among the `2n` sums we obtained, there are two whose difference is divisible by `2n`.
Difficulty level (1 very easy - 10 very hard): 4
Topics:
Number Theory
->
Modular Arithmetic / Remainder Arithmetic
Combinatorics
->
Pigeonhole Principle
Proof and Example
->
Proof by Contradiction
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