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--- pow:problem6 [2020/04/28 03:25] – mazur
+++ pow:problem6 [2020/04/28 03:26] (current) – mazur
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+<box 80% round orange|Problem 6 (due Monday, April 27)>
+Let $M$ be an $m\times n$ matrix whose entries are positive real numbers. For each column of $M$
+compute the product of all the numbers in that column. Let $S(M)$ be the sum of all these products.
+Now let $N$ be the matrix obtained form $M$ by putting entries in each row in a non-decreasing order.
+Prove that $S(N)\geq S(M)$.
+</box>
+This problem was solved by only one participant: Yuqiao Huang. The submitted solution is
+correct and similar to our original solution, but a justification of a key claim is missing.
+Detailed solution is discussed in the following link {{:pow:2020sproblem6.pdf|Solution}}