So the 2nd column that has the $9$ has to equal to $39$, since there is a 3 being carried. I guess for the 3rd column there is no digits being carried, so the sum has to be less than 10. So i was thinking $0,1,2$ which is $6$ but is there a possibility there could be more than one answer?
Any ideas?

Hint: Note that $$ 39\#=*3\;+\;**\;+\;**\;+\;**\;\leq93+99+99+99=390\leq 39\#. $$