MathDB
Easy combinatorics

Source: Mexico Regional Contest 2012-Problem 1

September 13, 2015
combinatoricspigeonhole principle

Problem Statement

Consider the set: A={1,2,...,100}A = \{1, 2,..., 100\} Prove that if we take 1111 different elements from AA, there are x,yx, y such that x≠yx \neq y and 0<∣x−y∣<10 < |\sqrt{x} - \sqrt{y}| < 1
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