# Semi-Magic Squares

**Discrete Mathematics**Level 5

The squares of a \(3 \times 3\) grid are filled with non-negative integers such that the sum of each row and the sum of each column is \(7.\) How many different ways can the squares be filled?

**Details and assumptions**

The numbers in each grid square **does not** need to be distinct.

Rotations and reflections are distinct arrangements.