I REALLY NEED HELP WITH THIS MATH PROBLEM!!?

Question

you pick a four digit number add them all together subtratct the number that you got from you four digit number you take one number away and you are able to figure out witch one you took away how?

Answer 1

the reason is that when you subtarct the sum of digits from the given 4 digit number the remaining number shall be divisible by 9

for the proof the number = 1000 a + 100 b + 10 c + d

sum of digits = a+ b+ c + d

remaining number = 999 a + 99 b + 99 c= 9(111 a + 11 b+ c)

it is divsible by 9

hence sum of digits is divisble by 9.

so when you take away a digit then we take the sum and subtract from  next multiple of 9 and get the result.

this shall not work if we take away 0 or 9.

as an example

number = 1729

sum of digits = 1+7 + 2 + 9 = 19

subtract to get 1710

if you take 7 i am left with 1 1 0 sum = 2 next multiple of 9= 9 so digit taken = 7

but if you took 0 I would not know if it was 0 or 9

I hope I clarified.