Answer
There are 2 solutions for the 2X2 grid.
There are 6 solutions for the 3X3 grid.
There are 24 solutions for the 4X4 grid.
2 = 2 x 1 = 2! (called 2 factorial)
6 = 3 x 2 x 1 = 3!
24 = 4 x 3 x 2 x 1 = 4!
There would be 3628800 (10!) solutions for a 10X10 grid.
Most calculators have a factorial (!) button.