How many three digit whole numbers have digits that sum to 25?

Answer 1

The first digit must be 7 or greater, because the digits of 699 only sum to 24.

Of the numbers beginning with 7, only 799 sums to 25, because if either of the other two digits are less than 9, the sum will be less than 25.

That's one so far.

For number beginning with 8, the other two digits must sum to 17. That means they must be 9 and 8. So there are two suitable numbers beginning with 8, namely 889 and 898.

That's a total of three so far.

Finally, we have numbers beginning with 9. The other two digits must sum to 16, so the candidates are: 9 and 7, or 8 and 8. That gives us three numbers that fit the bill: 997, 979 and 988.

That's six altogether.

So the answer is six.