[d2v]

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.

[philwelch]

Honestly I feel like I do the same thing when I think about it, but it’s so well cached that whenever my brain sees 5+7 or 7+5, I simultaneously think “12”, forget the specific order, and imagine 5+5=10 with 2 overflow all at once and I can’t honestly tell you which concept arrives first.

And yeah, you can get by with less memorization and more counting, but eh...either you’re taught not to do that or you do enough arithmetic that your brain just caches the whole table eventually anyway.