First of all, you clearly can't use numbers with three
digits or more, because even one such number is already too much. So every
number in the sum has to be either a one-digit number or a two-digit number
so,if you take a digit used on the tens place, and you move it to the tens
place of a different number, then that doesn't change anything.
For example,
12+3+4+57+6+8+9=99
2+13+4+57+6+8+9=99
2+13+4+7+6+58+9=99
52+3+4+17+6+8+9=99
etc.
....
The only question we have to answer is: Which
digits go in the tens place, and which digits go in the ones place?
