Question

the sum of all the digit of the result of subtraction
$10 {}^{99} - 99$
​

Answer 1

9 x 97 + 2

= 873 + 2

= 875

Answer 2

Here's a quick explanation of how to solve this*****

Realize that 10^99 is just 1 followed by 99 zeros.

When you subtract 99, from 100000....00, you must borrow from every column all the way to the left.

So now, every 0 changes into a 9, except the last zero, which is 10 after the borrow. That means you have 98 nines.  And the 1 in the front becomes a 0.

Perform the subtraction in the one's place: 10 - 9 = 1.

Perform the subtraction in the ten's place 9 - 9 = 0.

Perform the subtraction all the way across: 9 - 0 = 9 (same thing 97 times)

Sum up 1 + 0 + 97*9.  You get 874.