We choose two numbers between $0$ and $9$, and the sum of the numbers should not be $9$. In addition, we cannot choose a number which we have already taken. How many digits does the sum have at most?
The sum of two one digit number is clearly less than $100$ and so cannot have $3$ digits. $6+5=11$ demonstrates that there can be $2$ digits, and so the answer is $2$.