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I am searching for a smart way of calculating all numbers in a special matrix kind of game.

The game board consist of numbers between 1 and 9 in a 4x4 matrix.

Swiping over numbers will either add up (swiping left or right), subtract (swiping up or down) or do nothing (diagonal swiping).

I wonder how many combinations there are and if there is a simple way of getting all the results. There is a free iOS app that resembles of this game idea:

http://itunes.apple.com/us/app/addictive/id543137735?l=sv&ls=1&mt=8

I would be glad for any answers, there seems to be a lot of different combinations.