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. Can this be done without carrying over? If not can it be done without carrying over into the hundreds column? thank you Victoria 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. Claude