Hi,
Can you answer this problem, does an answer exist?

• Get a set of numbers 1-9 !
• Using the whole set of nine number tiles (digits 1-9), try to arrange them to make three 3-digit numbers so that the sum of the first two is the third.

Hi Victoria,

My answer of 164 + 538 = 702 has two problems: It uses the digits 0 -- 8 rather than 1--9, 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.