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Question in a high school math contest

Given 1,2,3,...2015,2016 ( the first 2016 natural numbers) divide into 3 assemblage A,B,C which no 2 particles are the same in two assemblage. Given the numbers of particles in A,B,C are equal ( each contain 672 particles. Prove that we can pick 3 numbers a,b,c each from 3 assemblage so that the largest number equal the sum of the other two.

Note by Quang Minh
3 months, 3 weeks ago

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