**Problem of the Week**

**Math Club**

**BUGCAT 2019**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

pow:problem6

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 $S(N)\geq S(M)$.

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 Solution

pow/problem6.txt · Last modified: 2020/04/27 23:26 by mazur

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 3.0 Unported