for how many integers from 1 through 99999 is the sum of the

for how many integers from 1 through 99999 is the sum of their digits equal to 10?

Solution

The correct answer is 996

1 digit number = 0 ( since the maximum sum obtained is 9)

2 digit number = 9 (numbers are 19,28,37,46,55,64,73,82,91)

3 digit numbers = 54(numbers are 109,118,127,136,...,901)

4 digit numbers = 219(numbers are 1009,1018,1027,...,9001)

5 digit numbers are 714

Hence the total numbers which satisfy this property are equal to sum of all the above counts

=> (0 + 9 + 54 + 219 + 714)

=> 996 numbers