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2n cards

Source: Baltic Way 2001

November 17, 2010
algebra unsolvedalgebra

Problem Statement

There are 2n2n cards. On each card some real number xx, (1≤x≤2n)(1\le x\le 2n), is written (there can be different numbers on different cards). Prove that the cards can be divided into two heaps with sums s1s_1 and s2s_2 so that nn+1≤s1s2≤1\frac{n}{n+1}\le\frac{s_1}{s_2}\le 1.
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