Hey feferon11.

You have nine independent variables to start off with.

If c + f + i = *3 (* is a number from 0 to 2 since max is 9+9+9 = 27) then you have one constraint. Now tke the * and move it the 10's group. Let * = p.

(b + e + h + p) = *6. Where again * = (0,1,2 for the same reason as above). If * = q we have

(a + d + g + q) = 9

So in total we have the following constraints:

All numbers between 0 and 9 inclusive

a, d, g > 0

c + f + i = 10*p + 3 (p = 0,1,2)

b + e + h + p = 10*q + 6 (q = 0,1,2)

(a + d + g + q) = 9

These constraints though do not make it easy so I will suggest another way.

Consider the two variable case.

Let abc + def = 963. Since a, d != 0 we start abc = 100.

Now def = 963 - def. This means that you have 963 - 100 = 863 different combinations for both numbers.

In the three variable case you do the same thing but twice.

abc + def + ghi = 963. Fix abc = 100 which means (def + ghi) = 963 - 100 = 863. Now figure out how many possibilities for 863 (it will be 863 - 100 = 763). Then do it for abc = 101, 102, ...., 863.

You should find a pattern in this and I suggest you write it all out to see it for yourself. (Hint: Try and find the relationship given that abc = some number for how many combinations between def and ghi and add up all possibilities for each abc).