MathDB

There are

2n

cards. On each card some real number

x

(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

s_1

and

s_2

so that

\frac{n}{n+1}\le\frac{s_1}{s_2}\le 1

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