This is only tangentially related, but until now I never really thought about how I sum single digit numbers, but it's not by having memorized all combinations. I'd say I have all combinations that sum to 10 or less memorized, which adds up to 25 unique combos (plus the rule that number + 0 = number).
If I can tell it sums to more than 10, I break it up mentally into [larger number] + [smaller number] = [larger number] + ([smaller number] - remainder) + remainder, where [larger number] + ([smaller number] - remainder) = 10
You could break it down further by just memorizing what each digit less than 10 is when you add 1. Then you can do addition like 5 + 4 = 1 + 1 + 1 + ... = 2 + 1 + ... = 8 + 1 = 9. Then you'd only have to memorize 9 things (10 if you include 0). I guess this assumes that you know the order numbers go in though, whereas memorizing all of the combinations doesn't require that.
If I can tell it sums to more than 10, I break it up mentally into [larger number] + [smaller number] = [larger number] + ([smaller number] - remainder) + remainder, where [larger number] + ([smaller number] - remainder) = 10
You could break it down further by just memorizing what each digit less than 10 is when you add 1. Then you can do addition like 5 + 4 = 1 + 1 + 1 + ... = 2 + 1 + ... = 8 + 1 = 9. Then you'd only have to memorize 9 things (10 if you include 0). I guess this assumes that you know the order numbers go in though, whereas memorizing all of the combinations doesn't require that.