I want to know if it's possible to get any possible combination of a 4x4 integer array given three rules:

• you may shift any column up or down
• you may shift any row left or right
• you may shift the entire array left, right, up, or down

That is, you can transform:

[1]  [2]  [3]  [4]
[5]  [6]  [7]  [8]
[9]  [10] [11] [12]
[13] [14] [15] [16]

into any possible combination of a 4x4 array of the same 16 values, given those three rules.

Basically, I just want to know if there are impossible combinations.