** 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**

17 is the minimal possible sum.

For instance, 13 + 27 = 40

This is clearly better than using 1-6 (sums to 21), so we need a solution with a 0.

0 - 5 does not work because we need two digits that sum to 10.

0 1 2 3 4 6 Does not work. Since we need a carry, the sum of the digits must be odd.

And any other solution sums to more than 17.