For how many integers from 1 through 99,999 is the sum of their digits equal to 10?
To Find :
The number of integers from through which the sum of their
digits equal to .
The integers from up to and consider their digits that sum up to .
The number of non-negative solutions of the equation is equal to
First consider two-digit numbers among the given set of integers that sum up to
There are 11 solutions.
But from solutions we must subtract and
Then so we have solutions such as
We need to consider the given full integer set from through .
So, as we first determined the two digits that sum up to and found the solutions.
Next we must determine three digits that sum up to and so on.
Therefore three digits that sum up to
The solutions are;
solutions to be considered since we have to discard the solutions
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