Agree, analytics can get it done. Here is another way:

After my first post, I kept going.

Starting with

(the number of 3 digit numbers with sod between 1 and 5) +

2*(the number of 3 digit numbers with sod between 6 and 10) +

(the number of 3 digit numbers with sod between 11 and 15)

I determined that this was the same as

15*the number of 2 digit numbers with sod of 1 +

15*the number of 2 digit numbers with sod of 2 +

15*the number of 2 digit numbers with sod of 3 +

15*the number of 2 digit numbers with sod of 4 +

15*the number of 2 digit numbers with sod of 5 +

15*the number of 2 digit numbers with sod of 6 +

13*the number of 2 digit numbers with sod of 7 +

11*the number of 2 digit numbers with sod of 8 +

9*the number of 2 digit numbers with sod of 9 +

7*the number of 2 digit numbers with sod of 10 +

5*the number of 2 digit numbers with sod of 11 +

4*the number of 2 digit numbers with sod of 12 +

3*the number of 2 digit numbers with sod of 13 +

2*the number of 2 digit numbers with sod of 14 +

1*the number of 2 digit numbers with sod of 15

These I could work out in my head.

It counts to 15*(1+2+3+4+5+6) + 13*7 + 11*8 + 9*9 + 7*9 + 5*8 + 4*7 + 3*6 + 2*5 + 1*4

= 738