You have to have 3 sets of 3 digits each. The first set totals 10 (for the ones place). The second and third sets total 9 (for the tens and hundreds place). The 1 carries over from the total of 10 in the ones place, moving the 9 up to 10 in the tens place and the 9 up to 10 in the hundreds place.
Ways to make 10: 019, 028, 037, 046, 127, 136, 145, 235
Ways to make 9: 018, 027, 036, 045, 126, 135, 234
If 10 is 019, 9 leaves 234, not enough ways
If 10 is 028, 9 leaves 135, not enough ways
If 10 is 037, 9 leaves 126, not enough ways
If 10 is 046, 9 leaves 135, not enough ways
If 10 is 127, 9 leaves 036, 045, enough ways but 036 and 045 share 0
If 10 is 136, 9 leaves 027, 045, enough ways but 027 and 045 share 0
If 10 is 145, 9 leaves 027, 036, enough ways but 027 and 036 share 0
If 10 is 235, 9 leaves 018, not enough ways.
We checked all of the possible combinations of 3 digits totaling 10 and it looks like none of them leave any combinations to make two sets of 3 digits totaling 9 each.
Answer: No solution.
