Hi Victoria,
My answer of 164 + 538 = 702 has two problems: It uses the digits 0  8 rather than 19, and it carries over in the tens and in the hundreds. However, it shows an important property of any possible solution:
If I check my sum by casting out nines, I do on the left side
1 + 6 + 4 + 5 + 3 + 8 = 27, 2 + 7 = 9, I cast out the 9 I get 0,
and on the right side
7 + 0 + 2 = 9, I cast out the 9 I get 0.
On both sides I get the same value (since my sum is correct), and moreover this value is 0 because of the format of the question:
If you cast out nines in abc + def = ghi, then on the left side you are casting out nines in a + b + c + d + e + f and you should get the same answer as when you cast out the nines in g + h + i. On the other hand
a + b + c + d + e + f + g + h + i = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
which is a multiple of 9, so casting out nines in a + b + c + d + e + f should be (a multiple of 9)  (the result of casting out nines in g + h + i) . Thus,
(the result of casting out nines in g + h + i)
= (a multiple of 9)  (the result of casting out nines in g + h + i),
and the only possibility is that this result is 0.
Claude
