Are you not overthinking this?
I would make cards with the numbers 0 to 20 on them, about 5 of each number. Shuffle and deal cards equally between players. each places card in turn, if it adds to the previous card to make 20 you cry SNAP and get the pile...
For example, the cards placed may go
1,5,4,6,14 SNAP. 4,8,11,2,15,5 SNAP
We often play with a regular deck of cards SNAP+1, SNAP+2 - so same numbers don't snap, only ones that are one different (or 2) from the one below.
Seeing as it's an addition, subtraction - maybe you need to go higher than 20 (?to 30), such that 10,30 can be SNAPPED, as 30-10=20. I wouldn't get hung up on the order that the subtraction needed to happen, so a 30 then a 10 would be snap, as would a 10 and then a 30.