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Why always be 9?

I can't to explain it why, but one thing is certain, if the reduction with the base number is summed. Then the result will be end with the number 9.

it's like a matter of psychotes, iQ intelligence game, I really like such questions, I used to test to work in a company, offered a lot of test like that, your question is very complicated, experts like you just ask us, let alone us ?? hahahahha
my ability is only limited to the example below, looking for matching final numbers ,, but can not be like your problem.
maybe one day I can get the answer @mes , thanks for sharing this simple but complicated science.success always

example,

60- (1 + 29) = 30

30- (1 + 14) = 15

I think it has something to do with the base you use. If you use base 9(from 0 to 8) you will always get 8. If you use base 8(from 0 to 7) you get 7 and so on.

So the thing is that just before you get to 1 digit(18 for example) you subtract 8(the second digit) and 1 so after subtracting the second digit you always get 10 or in other words the base you use. And then subtract 1 you get one less.

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