We have $n$ integers $a_1, a_2,. . . , a_n$, not necessarily distinct, with sum $2S.$ An integer $k$ is called separator if $k$ of the numbers can be chosen with sum equal to $S.$ What is the maximum possible number of separators?
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Tags: combinatorics
We have $n$ integers $a_1, a_2,. . . , a_n$, not necessarily distinct, with sum $2S.$ An integer $k$ is called separator if $k$ of the numbers can be chosen with sum equal to $S.$ What is the maximum possible number of separators?