I have not yet solved that one, but I suspect my code for #67/#18 could solve it with a little bit of modification. Check out those first.
Indeed, they are similar. I used almost exactly the same code for all three of them.
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Just for verification:
#18 -> sum of solution digits = 12
#67 -> sum of solution digits = 19
#81 -> sum of solution digits = 26
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
I'm trying to figure out 82 and 83 now. They're harder than I thought at first... :/