Tightwad!

Multiplayer mode is here, Tightwad is glowing!
In this game, you and my algorithm will take elements one after the other from a NxN matrix with random numbers.
You are allowed to take only one element per column and per row, so is my algorithm. Once you have picked your elements, one at each row and each column, we compare the sum of your combination to my algorithm's. The smallest sum wins, so you must be a Tightwad!