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Erdős problem 1026

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For a sequence of nn distinct reals, determine the largest constant cc such that some monotonic subsequence always has sum exceeding (c−o(1))⋅(1/n)(c-o(1))\cdot(1/\sqrt{n}) times the total sum. Resolved as c=1c = 1.

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For a sequence of $n$ distinct reals, determine the largest constant $c$ such that some monotonic subsequence always has sum exceeding $(c-o(1))\cdot(1/\sqrt{n})$ times the total sum. Resolved as $c = 1$.

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