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Maximal Value of Product

Source: 2013 Baltic Way, Problem 1

December 30, 2013
algebra unsolvedalgebra

Problem Statement

Let nn be a positive integer. Assume that nn numbers are to be chosen from the table
\begin{array}{cccc}0 & 1 & \cdots & n-1\\ n & n+1 & \cdots & 2n-1\\ \vdots & \vdots & \ddots & \vdots\$n-1)n & (n-1)n+1 & \cdots & n^2-1\end{array} </br>withnotwoofthemfromthesameroworthesamecolumn.Findthemaximalvalueoftheproductofthese</br>with no two of them from the same row or the same column. Find the maximal value of the product of these n$ numbers.
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