asd+fgh=jkl
Believe me - there are numerous solutions of the above alphametic.
I. What is the minimal possible sum of participating digits?
ii. Same question for as+df=gh
(In reply to
Both at once? by Brian Smith)
I found 10 solutions for solving both alphametics simultaneously (x is the unused digit):
asdfghjklx
1627439052
1926458370
2415397806
3145768902
3942816750
4152937086
4613598207
5142938076
5413679082
5712698403
To minimize the sum of the used digits, the unused digit must be as large as possible. This leaves the 7th solution as the solution with the smallest sum of digits used. 461+359=820 46+13=59