# Alphametic from programming class

The below question is from one of my assignments for Login Programming for Artificial Intelligence.

ABCDE
CFGH
--——-
DEHIJ


Each letter A,..., J represents a different digit 0,...,9 and A>0, C>0, D>0, and A<6. How can this kind of puzzle be solved?

• I have no idea how to do it, so posted it over here Sep 4, 2019 at 17:48
• @RuchirNaphade , Where did you encounter the question, if you provide the source, I can add it in the question and your question will be unholded. Sep 4, 2019 at 18:26
• Hi, and welcome to PSE! Unfortunately, this is not how this site works; you cannot just take someone else's puzzle, and post it here. Most of the questions here are the poster's own puzzles, but you can also post someone else's puzzle IF (and only if, for copyright reasons) you have permission to do so, OR if you clearly state the original author, which is enough as long as the puzzle is "kind of not really a literary work in itself". (As is the case here.) Happy puzzling!
– Bass
Sep 4, 2019 at 18:28
• More than 1 solution for sure.
– DrD
Sep 4, 2019 at 20:47
• @Oray..Thanks for the link but I am not looking for answer only. I want to know how to solve this as this will be helpful for me to solve problems like this in future.. Sep 9, 2019 at 11:10

Given all the conditions, there is just one solution

$$(A,B,C,D,E,F,G,H,I,J) = (2,8,7,3,5,1,6,9,0,4)$$
that is
$$28735+7169 = 35904$$

Reasoning

If we add a $$4$$-digit number to a $$5$$-digit number, the starting digit of the result must be the same as or one more than the starting digit of the $$5$$-digit number. This means that $$D$$ is one more than $$A$$.
Since we have $$0, this means the possibilities for $$(A,D)$$ are $$(1,2), (2,3), (3,4), (4,5)$$ or $$(5,6)$$.

We also require that the last digit of $$E+H$$ be $$J$$. This leads us to the following ($$158$$) possibilities for $$(A,D,E,H,J)$$:
$$(1, 2, 3, 4, 7), (1, 2, 3, 5, 8), (1, 2, 3, 6, 9), (1, 2, 3, 7, 0), (1, 2, 4, 3, 7), (1, 2, 4, 5, 9), (1, 2, 4, 6, 0), (1, 2, 4, 9, 3), (1, 2, 5, 3, 8), (1, 2, 5, 4, 9), (1, 2, 5, 8, 3), (1, 2, 5, 9, 4), (1, 2, 6, 3, 9), (1, 2, 6, 4, 0), (1, 2, 6, 7, 3), (1, 2, 6, 8, 4), (1, 2, 6, 9, 5), (1, 2, 7, 3, 0), (1, 2, 7, 6, 3), (1, 2, 7, 8, 5), (1, 2, 7, 9, 6), (1, 2, 8, 5, 3), (1, 2, 8, 6, 4), (1, 2, 8, 7, 5), (1, 2, 8, 9, 7), (1, 2, 9, 4, 3), (1, 2, 9, 5, 4), (1, 2, 9, 6, 5), (1, 2, 9, 7, 6), (1, 2, 9, 8, 7), (2, 3, 1, 4, 5), (2, 3, 1, 5, 6), (2, 3, 1, 6, 7), (2, 3, 1, 7, 8), (2, 3, 1, 8, 9), (2, 3, 1, 9, 0), (2, 3, 4, 1, 5), (2, 3, 4, 5, 9), (2, 3, 4, 6, 0), (2, 3, 4, 7, 1), (2, 3, 5, 1, 6), (2, 3, 5, 4, 9), (2, 3, 5, 6, 1), (2, 3, 5, 9, 4), (2, 3, 6, 1, 7), (2, 3, 6, 4, 0), (2, 3, 6, 5, 1), (2, 3, 6, 8, 4), (2, 3, 6, 9, 5), (2, 3, 7, 1, 8), (2, 3, 7, 4, 1), (2, 3, 7, 8, 5), (2, 3, 7, 9, 6), (2, 3, 8, 1, 9), (2, 3, 8, 6, 4), (2, 3, 8, 7, 5), (2, 3, 8, 9, 7), (2, 3, 9, 1, 0), (2, 3, 9, 5, 4), (2, 3, 9, 6, 5), (2, 3, 9, 7, 6), (2, 3, 9, 8, 7), (3, 4, 1, 5, 6), (3, 4, 1, 6, 7), (3, 4, 1, 7, 8), (3, 4, 1, 8, 9), (3, 4, 1, 9, 0), (3, 4, 2, 5, 7), (3, 4, 2, 6, 8), (3, 4, 2, 7, 9), (3, 4, 2, 8, 0), (3, 4, 2, 9, 1), (3, 4, 5, 1, 6), (3, 4, 5, 2, 7), (3, 4, 5, 6, 1), (3, 4, 5, 7, 2), (3, 4, 6, 1, 7), (3, 4, 6, 2, 8), (3, 4, 6, 5, 1), (3, 4, 6, 9, 5), (3, 4, 7, 1, 8), (3, 4, 7, 2, 9), (3, 4, 7, 5, 2), (3, 4, 7, 8, 5), (3, 4, 7, 9, 6), (3, 4, 8, 1, 9), (3, 4, 8, 2, 0), (3, 4, 8, 7, 5), (3, 4, 8, 9, 7), (3, 4, 9, 1, 0), (3, 4, 9, 2, 1), (3, 4, 9, 6, 5), (3, 4, 9, 7, 6), (3, 4, 9, 8, 7), (4, 5, 1, 2, 3), (4, 5, 1, 6, 7), (4, 5, 1, 7, 8), (4, 5, 1, 8, 9), (4, 5, 1, 9, 0), (4, 5, 2, 1, 3), (4, 5, 2, 6, 8), (4, 5, 2, 7, 9), (4, 5, 2, 8, 0), (4, 5, 2, 9, 1), (4, 5, 3, 6, 9), (4, 5, 3, 7, 0), (4, 5, 3, 8, 1), (4, 5, 3, 9, 2), (4, 5, 6, 1, 7), (4, 5, 6, 2, 8), (4, 5, 6, 3, 9), (4, 5, 6, 7, 3), (4, 5, 7, 1, 8), (4, 5, 7, 2, 9), (4, 5, 7, 3, 0), (4, 5, 7, 6, 3), (4, 5, 7, 9, 6), (4, 5, 8, 1, 9), (4, 5, 8, 2, 0), (4, 5, 8, 3, 1), (4, 5, 8, 9, 7), (4, 5, 9, 1, 0), (4, 5, 9, 2, 1), (4, 5, 9, 3, 2), (4, 5, 9, 7, 6), (4, 5, 9, 8, 7), (5, 6, 1, 6, 7), (5, 6, 1, 7, 8), (5, 6, 1, 8, 9), (5, 6, 1, 9, 0), (5, 6, 2, 4, 6), (5, 6, 2, 6, 8), (5, 6, 2, 7, 9), (5, 6, 2, 8, 0), (5, 6, 2, 9, 1), (5, 6, 3, 1, 4), (5, 6, 3, 4, 7), (5, 6, 3, 6, 9), (5, 6, 3, 7, 0), (5, 6, 3, 8, 1), (5, 6, 3, 9, 2), (5, 6, 4, 2, 6), (5, 6, 4, 6, 0), (5, 6, 4, 7, 1), (5, 6, 4, 8, 2), (5, 6, 7, 1, 8), (5, 6, 7, 2, 9), (5, 6, 7, 4, 1), (5, 6, 7, 9, 6), (5, 6, 8, 1, 9), (5, 6, 8, 2, 0), (5, 6, 8, 4, 2), (5, 6, 8, 6, 4), (5, 6, 8, 9, 7), (5, 6, 9, 1, 0), (5, 6, 9, 2, 1), (5, 6, 9, 7, 6), (5, 6, 9, 8, 7)$$

Then, it must be the case that $$D+G$$ plus the carry-over term from $$E+H$$ must end in $$I$$. This leaves the number of possibilities for $$(A,D,E,H,J,G,I)$$ at $$324$$:
$$(1, 2, 3, 4, 7, 6, 8), (1, 2, 3, 4, 7, 8, 0), (1, 2, 3, 5, 8, 4, 6), (1, 2, 3, 5, 8, 7, 9), (1, 2, 3, 6, 9, 5, 7), (1, 2, 3, 6, 9, 8, 0), (1, 2, 3, 7, 0, 5, 8), (1, 2, 3, 7, 0, 6, 9), (1, 2, 4, 3, 7, 6, 8), (1, 2, 4, 3, 7, 8, 0), (1, 2, 4, 5, 9, 6, 8), (1, 2, 4, 5, 9, 8, 0), (1, 2, 4, 6, 0, 5, 8), (1, 2, 4, 9, 3, 5, 8), (1, 2, 4, 9, 3, 7, 0), (1, 2, 5, 3, 8, 4, 6), (1, 2, 5, 3, 8, 7, 9), (1, 2, 5, 4, 9, 6, 8), (1, 2, 5, 4, 9, 8, 0), (1, 2, 5, 8, 3, 4, 7), (1, 2, 5, 8, 3, 6, 9), (1, 2, 5, 8, 3, 7, 0), (1, 2, 5, 9, 4, 0, 3), (1, 2, 5, 9, 4, 3, 6), (1, 2, 5, 9, 4, 7, 0), (1, 2, 6, 3, 9, 5, 7), (1, 2, 6, 3, 9, 8, 0), (1, 2, 6, 4, 0, 5, 8), (1, 2, 6, 7, 3, 5, 8), (1, 2, 6, 8, 4, 0, 3), (1, 2, 6, 8, 4, 7, 0), (1, 2, 6, 9, 5, 0, 3), (1, 2, 6, 9, 5, 4, 7), (1, 2, 6, 9, 5, 7, 0), (1, 2, 7, 3, 0, 5, 8), (1, 2, 7, 3, 0, 6, 9), (1, 2, 7, 6, 3, 5, 8), (1, 2, 7, 8, 5, 0, 3), (1, 2, 7, 8, 5, 3, 6), (1, 2, 7, 8, 5, 6, 9), (1, 2, 7, 9, 6, 0, 3), (1, 2, 7, 9, 6, 5, 8), (1, 2, 8, 5, 3, 4, 7), (1, 2, 8, 5, 3, 6, 9), (1, 2, 8, 5, 3, 7, 0), (1, 2, 8, 6, 4, 0, 3), (1, 2, 8, 6, 4, 7, 0), (1, 2, 8, 7, 5, 0, 3), (1, 2, 8, 7, 5, 3, 6), (1, 2, 8, 7, 5, 6, 9), (1, 2, 8, 9, 7, 0, 3), (1, 2, 8, 9, 7, 3, 6), (1, 2, 9, 4, 3, 5, 8), (1, 2, 9, 4, 3, 7, 0), (1, 2, 9, 5, 4, 0, 3), (1, 2, 9, 5, 4, 3, 6), (1, 2, 9, 5, 4, 7, 0), (1, 2, 9, 6, 5, 0, 3), (1, 2, 9, 6, 5, 4, 7), (1, 2, 9, 6, 5, 7, 0), (1, 2, 9, 7, 6, 0, 3), (1, 2, 9, 7, 6, 5, 8), (1, 2, 9, 8, 7, 0, 3), (1, 2, 9, 8, 7, 3, 6), (2, 3, 1, 4, 5, 6, 9), (2, 3, 1, 4, 5, 7, 0), (2, 3, 1, 5, 6, 4, 7), (2, 3, 1, 5, 6, 7, 0), (2, 3, 1, 6, 7, 5, 8), (2, 3, 1, 7, 8, 6, 9), (2, 3, 1, 8, 9, 4, 7), (2, 3, 1, 8, 9, 7, 0), (2, 3, 1, 9, 0, 4, 8), (2, 3, 4, 1, 5, 6, 9), (2, 3, 4, 1, 5, 7, 0), (2, 3, 4, 5, 9, 7, 0), (2, 3, 4, 5, 9, 8, 1), (2, 3, 4, 6, 0, 1, 5), (2, 3, 4, 6, 0, 5, 9), (2, 3, 4, 6, 0, 7, 1), (2, 3, 4, 7, 1, 5, 9), (2, 3, 4, 7, 1, 6, 0), (2, 3, 5, 1, 6, 4, 7), (2, 3, 5, 1, 6, 7, 0), (2, 3, 5, 4, 9, 7, 0), (2, 3, 5, 4, 9, 8, 1), (2, 3, 5, 6, 1, 0, 4), (2, 3, 5, 6, 1, 4, 8), (2, 3, 5, 9, 4, 6, 0), (2, 3, 5, 9, 4, 7, 1), (2, 3, 6, 1, 7, 5, 8), (2, 3, 6, 4, 0, 1, 5), (2, 3, 6, 4, 0, 5, 9), (2, 3, 6, 4, 0, 7, 1), (2, 3, 6, 5, 1, 0, 4), (2, 3, 6, 5, 1, 4, 8), (2, 3, 6, 8, 4, 1, 5), (2, 3, 6, 8, 4, 5, 9), (2, 3, 6, 8, 4, 7, 1), (2, 3, 6, 9, 5, 0, 4), (2, 3, 6, 9, 5, 4, 8), (2, 3, 6, 9, 5, 7, 1), (2, 3, 7, 1, 8, 6, 9), (2, 3, 7, 4, 1, 5, 9), (2, 3, 7, 4, 1, 6, 0), (2, 3, 7, 8, 5, 0, 4), (2, 3, 7, 8, 5, 6, 0), (2, 3, 7, 9, 6, 0, 4), (2, 3, 7, 9, 6, 1, 5), (2, 3, 7, 9, 6, 4, 8), (2, 3, 8, 1, 9, 4, 7), (2, 3, 8, 1, 9, 7, 0), (2, 3, 8, 6, 4, 1, 5), (2, 3, 8, 6, 4, 5, 9), (2, 3, 8, 6, 4, 7, 1), (2, 3, 8, 7, 5, 0, 4), (2, 3, 8, 7, 5, 6, 0), (2, 3, 8, 9, 7, 0, 4), (2, 3, 8, 9, 7, 1, 5), (2, 3, 8, 9, 7, 6, 0), (2, 3, 9, 1, 0, 4, 8), (2, 3, 9, 5, 4, 6, 0), (2, 3, 9, 5, 4, 7, 1), (2, 3, 9, 6, 5, 0, 4), (2, 3, 9, 6, 5, 4, 8), (2, 3, 9, 6, 5, 7, 1), (2, 3, 9, 7, 6, 0, 4), (2, 3, 9, 7, 6, 1, 5), (2, 3, 9, 7, 6, 4, 8), (2, 3, 9, 8, 7, 0, 4), (2, 3, 9, 8, 7, 1, 5), (2, 3, 9, 8, 7, 6, 0), (3, 4, 1, 5, 6, 8, 2), (3, 4, 1, 6, 7, 5, 9), (3, 4, 1, 6, 7, 8, 2), (3, 4, 1, 7, 8, 2, 6), (3, 4, 1, 7, 8, 5, 9), (3, 4, 1, 7, 8, 6, 0), (3, 4, 1, 8, 9, 2, 6), (3, 4, 1, 8, 9, 6, 0), (3, 4, 1, 9, 0, 2, 7), (3, 4, 1, 9, 0, 7, 2), (3, 4, 2, 5, 7, 6, 0), (3, 4, 2, 6, 8, 1, 5), (3, 4, 2, 6, 8, 5, 9), (3, 4, 2, 6, 8, 7, 1), (3, 4, 2, 7, 9, 1, 5), (3, 4, 2, 7, 9, 6, 0), (3, 4, 2, 8, 0, 1, 6), (3, 4, 2, 8, 0, 6, 1), (3, 4, 2, 9, 1, 0, 5), (3, 4, 2, 9, 1, 5, 0), (3, 4, 5, 1, 6, 8, 2), (3, 4, 5, 2, 7, 6, 0), (3, 4, 5, 6, 1, 2, 7), (3, 4, 5, 6, 1, 7, 2), (3, 4, 5, 7, 2, 1, 6), (3, 4, 5, 7, 2, 6, 1), (3, 4, 6, 1, 7, 5, 9), (3, 4, 6, 1, 7, 8, 2), (3, 4, 6, 2, 8, 1, 5), (3, 4, 6, 2, 8, 5, 9), (3, 4, 6, 2, 8, 7, 1), (3, 4, 6, 5, 1, 2, 7), (3, 4, 6, 5, 1, 7, 2), (3, 4, 6, 9, 5, 2, 7), (3, 4, 6, 9, 5, 7, 2), (3, 4, 7, 1, 8, 2, 6), (3, 4, 7, 1, 8, 5, 9), (3, 4, 7, 1, 8, 6, 0), (3, 4, 7, 2, 9, 1, 5), (3, 4, 7, 2, 9, 6, 0), (3, 4, 7, 5, 2, 1, 6), (3, 4, 7, 5, 2, 6, 1), (3, 4, 7, 8, 5, 1, 6), (3, 4, 7, 8, 5, 6, 1), (3, 4, 7, 9, 6, 0, 5), (3, 4, 7, 9, 6, 5, 0), (3, 4, 8, 1, 9, 2, 6), (3, 4, 8, 1, 9, 6, 0), (3, 4, 8, 2, 0, 1, 6), (3, 4, 8, 2, 0, 6, 1), (3, 4, 8, 7, 5, 1, 6), (3, 4, 8, 7, 5, 6, 1), (3, 4, 8, 9, 7, 0, 5), (3, 4, 8, 9, 7, 1, 6), (3, 4, 8, 9, 7, 5, 0), (3, 4, 8, 9, 7, 6, 1), (3, 4, 9, 1, 0, 2, 7), (3, 4, 9, 1, 0, 7, 2), (3, 4, 9, 2, 1, 0, 5), (3, 4, 9, 2, 1, 5, 0), (3, 4, 9, 6, 5, 2, 7), (3, 4, 9, 6, 5, 7, 2), (3, 4, 9, 7, 6, 0, 5), (3, 4, 9, 7, 6, 5, 0), (3, 4, 9, 8, 7, 0, 5), (3, 4, 9, 8, 7, 1, 6), (3, 4, 9, 8, 7, 5, 0), (3, 4, 9, 8, 7, 6, 1), (4, 5, 1, 6, 7, 3, 8), (4, 5, 1, 6, 7, 8, 3), (4, 5, 1, 8, 9, 2, 7), (4, 5, 1, 8, 9, 7, 2), (4, 5, 1, 9, 0, 2, 8), (4, 5, 1, 9, 0, 6, 2), (4, 5, 1, 9, 0, 7, 3), (4, 5, 2, 7, 9, 1, 6), (4, 5, 2, 7, 9, 3, 8), (4, 5, 2, 7, 9, 6, 1), (4, 5, 2, 7, 9, 8, 3), (4, 5, 2, 8, 0, 1, 7), (4, 5, 2, 8, 0, 3, 9), (4, 5, 2, 8, 0, 7, 3), (4, 5, 2, 9, 1, 0, 6), (4, 5, 2, 9, 1, 7, 3), (4, 5, 3, 6, 9, 2, 7), (4, 5, 3, 6, 9, 7, 2), (4, 5, 3, 7, 0, 2, 8), (4, 5, 3, 7, 0, 6, 2), (4, 5, 3, 8, 1, 0, 6), (4, 5, 3, 8, 1, 6, 2), (4, 5, 3, 9, 2, 0, 6), (4, 5, 3, 9, 2, 1, 7), (4, 5, 6, 1, 7, 3, 8), (4, 5, 6, 1, 7, 8, 3), (4, 5, 6, 3, 9, 2, 7), (4, 5, 6, 3, 9, 7, 2), (4, 5, 6, 7, 3, 2, 8), (4, 5, 7, 2, 9, 1, 6), (4, 5, 7, 2, 9, 3, 8), (4, 5, 7, 2, 9, 6, 1), (4, 5, 7, 2, 9, 8, 3), (4, 5, 7, 3, 0, 2, 8), (4, 5, 7, 3, 0, 6, 2), (4, 5, 7, 6, 3, 2, 8), (4, 5, 7, 9, 6, 2, 8), (4, 5, 8, 1, 9, 2, 7), (4, 5, 8, 1, 9, 7, 2), (4, 5, 8, 2, 0, 1, 7), (4, 5, 8, 2, 0, 3, 9), (4, 5, 8, 2, 0, 7, 3), (4, 5, 8, 3, 1, 0, 6), (4, 5, 8, 3, 1, 6, 2), (4, 5, 8, 9, 7, 0, 6), (4, 5, 8, 9, 7, 6, 2), (4, 5, 9, 1, 0, 2, 8), (4, 5, 9, 1, 0, 6, 2), (4, 5, 9, 1, 0, 7, 3), (4, 5, 9, 2, 1, 0, 6), (4, 5, 9, 2, 1, 7, 3), (4, 5, 9, 3, 2, 0, 6), (4, 5, 9, 3, 2, 1, 7), (4, 5, 9, 7, 6, 2, 8), (4, 5, 9, 8, 7, 0, 6), (4, 5, 9, 8, 7, 6, 2), (5, 6, 1, 2, 3, 4, 0), (5, 6, 1, 2, 3, 8, 4), (5, 6, 1, 3, 4, 2, 8), (5, 6, 1, 7, 8, 3, 9), (5, 6, 1, 7, 8, 4, 0), (5, 6, 1, 8, 9, 4, 0), (5, 6, 1, 8, 9, 7, 3), (5, 6, 1, 9, 0, 7, 4), (5, 6, 2, 1, 3, 4, 0), (5, 6, 2, 1, 3, 8, 4), (5, 6, 2, 7, 9, 4, 0), (5, 6, 2, 7, 9, 8, 4), (5, 6, 2, 8, 0, 4, 1), (5, 6, 2, 8, 0, 7, 4), (5, 6, 2, 9, 1, 0, 7), (5, 6, 2, 9, 1, 3, 0), (5, 6, 2, 9, 1, 7, 4), (5, 6, 3, 1, 4, 2, 8), (5, 6, 3, 4, 7, 2, 8), (5, 6, 3, 7, 0, 1, 8), (5, 6, 3, 7, 0, 2, 9), (5, 6, 3, 7, 0, 4, 1), (5, 6, 3, 8, 1, 0, 7), (5, 6, 3, 8, 1, 2, 9), (5, 6, 3, 8, 1, 7, 4), (5, 6, 3, 9, 2, 0, 7), (5, 6, 3, 9, 2, 1, 8), (5, 6, 3, 9, 2, 4, 1), (5, 6, 3, 9, 2, 7, 4), (5, 6, 4, 3, 7, 2, 8), (5, 6, 4, 7, 1, 2, 9), (5, 6, 4, 7, 1, 3, 0), (5, 6, 4, 8, 2, 0, 7), (5, 6, 4, 8, 2, 3, 0), (5, 6, 4, 9, 3, 0, 7), (5, 6, 4, 9, 3, 1, 8), (5, 6, 7, 1, 8, 3, 9), (5, 6, 7, 1, 8, 4, 0), (5, 6, 7, 2, 9, 4, 0), (5, 6, 7, 2, 9, 8, 4), (5, 6, 7, 3, 0, 1, 8), (5, 6, 7, 3, 0, 2, 9), (5, 6, 7, 3, 0, 4, 1), (5, 6, 7, 4, 1, 2, 9), (5, 6, 7, 4, 1, 3, 0), (5, 6, 8, 1, 9, 4, 0), (5, 6, 8, 1, 9, 7, 3), (5, 6, 8, 2, 0, 4, 1), (5, 6, 8, 2, 0, 7, 4), (5, 6, 8, 3, 1, 0, 7), (5, 6, 8, 3, 1, 2, 9), (5, 6, 8, 3, 1, 7, 4), (5, 6, 8, 4, 2, 0, 7), (5, 6, 8, 4, 2, 3, 0), (5, 6, 8, 9, 7, 3, 0), (5, 6, 8, 9, 7, 4, 1), (5, 6, 9, 1, 0, 7, 4), (5, 6, 9, 2, 1, 0, 7), (5, 6, 9, 2, 1, 3, 0), (5, 6, 9, 2, 1, 7, 4), (5, 6, 9, 3, 2, 0, 7), (5, 6, 9, 3, 2, 1, 8), (5, 6, 9, 3, 2, 4, 1), (5, 6, 9, 3, 2, 7, 4), (5, 6, 9, 4, 3, 0, 7), (5, 6, 9, 4, 3, 1, 8), (5, 6, 9, 8, 7, 3, 0), (5, 6, 9, 8, 7, 4, 1)$$

Now, if we impose the condition that $$C+F$$ plus the carry over term from the tens ends in $$H$$, only some of these cases can be made to work and the number of possibilities for $$(A,D,E,H,J,G,I,C,F)$$ reduces to $$159$$:
$$(1, 2, 3, 4, 7, 6, 8, 5, 9), (1, 2, 3, 4, 7, 6, 8, 9, 5), (1, 2, 4, 6, 0, 5, 8, 7, 9), (1, 2, 4, 6, 0, 5, 8, 9, 7), (1, 2, 5, 4, 9, 8, 0, 6, 7), (1, 2, 5, 4, 9, 8, 0, 7, 6), (1, 2, 6, 3, 9, 8, 0, 5, 7), (1, 2, 6, 3, 9, 8, 0, 7, 5), (1, 2, 7, 3, 0, 5, 8, 4, 9), (1, 2, 7, 3, 0, 5, 8, 9, 4), (1, 2, 7, 3, 0, 6, 9, 5, 8), (1, 2, 7, 3, 0, 6, 9, 8, 5), (1, 2, 7, 9, 6, 0, 3, 4, 5), (1, 2, 7, 9, 6, 0, 3, 5, 4), (1, 2, 8, 5, 3, 4, 7, 6, 9), (1, 2, 8, 5, 3, 4, 7, 9, 6), (1, 2, 8, 6, 4, 0, 3, 7, 9), (1, 2, 8, 6, 4, 0, 3, 9, 7), (1, 2, 8, 7, 5, 6, 9, 3, 4), (1, 2, 8, 7, 5, 6, 9, 4, 3), (1, 2, 8, 9, 7, 0, 3, 4, 5), (1, 2, 8, 9, 7, 0, 3, 5, 4), (1, 2, 8, 9, 7, 3, 6, 4, 5), (1, 2, 8, 9, 7, 3, 6, 5, 4), (1, 2, 9, 4, 3, 7, 0, 5, 8), (1, 2, 9, 4, 3, 7, 0, 8, 5), (1, 2, 9, 5, 4, 0, 3, 7, 8), (1, 2, 9, 5, 4, 0, 3, 8, 7), (1, 2, 9, 5, 4, 3, 6, 7, 8), (1, 2, 9, 5, 4, 3, 6, 8, 7), (1, 2, 9, 5, 4, 7, 0, 6, 8), (1, 2, 9, 5, 4, 7, 0, 8, 6), (1, 2, 9, 7, 6, 5, 8, 3, 4), (1, 2, 9, 7, 6, 5, 8, 4, 3), (2, 3, 4, 5, 9, 7, 0, 6, 8), (2, 3, 4, 5, 9, 7, 0, 8, 6), (2, 3, 4, 6, 0, 1, 5, 7, 9), (2, 3, 4, 6, 0, 1, 5, 9, 7), (2, 3, 5, 4, 9, 8, 1, 6, 7), (2, 3, 5, 4, 9, 8, 1, 7, 6), (2, 3, 5, 6, 1, 0, 4, 7, 9), (2, 3, 5, 6, 1, 0, 4, 9, 7), (2, 3, 5, 6, 1, 4, 8, 7, 9), (2, 3, 5, 6, 1, 4, 8, 9, 7), (2, 3, 5, 9, 4, 6, 0, 1, 7), (2, 3, 5, 9, 4, 6, 0, 7, 1), (2, 3, 5, 9, 4, 7, 1, 8, 0), (2, 3, 6, 4, 0, 7, 1, 5, 8), (2, 3, 6, 4, 0, 7, 1, 8, 5), (2, 3, 6, 5, 1, 0, 4, 7, 8), (2, 3, 6, 5, 1, 0, 4, 8, 7), (2, 3, 6, 8, 4, 5, 9, 1, 7), (2, 3, 6, 8, 4, 5, 9, 7, 1), (2, 3, 6, 9, 5, 0, 4, 1, 8), (2, 3, 6, 9, 5, 0, 4, 8, 1), (2, 3, 6, 9, 5, 7, 1, 8, 0), (2, 3, 7, 4, 1, 5, 9, 6, 8), (2, 3, 7, 4, 1, 5, 9, 8, 6), (2, 3, 7, 4, 1, 6, 0, 5, 8), (2, 3, 7, 4, 1, 6, 0, 8, 5), (2, 3, 7, 9, 6, 0, 4, 1, 8), (2, 3, 7, 9, 6, 0, 4, 8, 1), (2, 3, 8, 1, 9, 4, 7, 5, 6), (2, 3, 8, 1, 9, 4, 7, 6, 5), (2, 3, 8, 1, 9, 7, 0, 4, 6), (2, 3, 8, 1, 9, 7, 0, 6, 4), (2, 3, 8, 6, 4, 1, 5, 7, 9), (2, 3, 8, 6, 4, 1, 5, 9, 7), (2, 3, 8, 6, 4, 7, 1, 5, 0), (2, 3, 8, 7, 5, 0, 4, 1, 6), (2, 3, 8, 7, 5, 0, 4, 6, 1), (2, 3, 9, 1, 0, 4, 8, 5, 6), (2, 3, 9, 1, 0, 4, 8, 6, 5), (2, 3, 9, 5, 4, 7, 1, 6, 8), (2, 3, 9, 5, 4, 7, 1, 8, 6), (3, 4, 1, 6, 7, 8, 2, 5, 0), (3, 4, 1, 8, 9, 6, 0, 2, 5), (3, 4, 1, 8, 9, 6, 0, 5, 2), (3, 4, 2, 6, 8, 1, 5, 7, 9), (3, 4, 2, 6, 8, 1, 5, 9, 7), (3, 4, 2, 6, 8, 7, 1, 5, 0), (3, 4, 2, 7, 9, 6, 0, 1, 5), (3, 4, 2, 7, 9, 6, 0, 5, 1), (3, 4, 5, 7, 2, 1, 6, 8, 9), (3, 4, 5, 7, 2, 1, 6, 9, 8), (3, 4, 6, 9, 5, 2, 7, 1, 8), (3, 4, 6, 9, 5, 2, 7, 8, 1), (3, 4, 6, 9, 5, 7, 2, 8, 0), (3, 4, 7, 9, 6, 0, 5, 1, 8), (3, 4, 7, 9, 6, 0, 5, 8, 1), (3, 4, 8, 2, 0, 1, 6, 5, 7), (3, 4, 8, 2, 0, 1, 6, 7, 5), (3, 4, 8, 9, 7, 5, 0, 2, 6), (3, 4, 8, 9, 7, 5, 0, 6, 2), (3, 4, 9, 1, 0, 2, 7, 5, 6), (3, 4, 9, 1, 0, 2, 7, 6, 5), (3, 4, 9, 8, 7, 0, 5, 2, 6), (3, 4, 9, 8, 7, 0, 5, 6, 2), (3, 4, 9, 8, 7, 5, 0, 1, 6), (3, 4, 9, 8, 7, 5, 0, 6, 1), (3, 4, 9, 8, 7, 6, 1, 2, 5), (3, 4, 9, 8, 7, 6, 1, 5, 2), (4, 5, 1, 9, 0, 2, 8, 3, 6), (4, 5, 1, 9, 0, 2, 8, 6, 3), (4, 5, 1, 9, 0, 7, 3, 2, 6), (4, 5, 1, 9, 0, 7, 3, 6, 2), (4, 5, 2, 7, 9, 3, 8, 1, 6), (4, 5, 2, 7, 9, 3, 8, 6, 1), (4, 5, 2, 7, 9, 8, 3, 6, 0), (4, 5, 2, 8, 0, 3, 9, 1, 7), (4, 5, 2, 8, 0, 3, 9, 7, 1), (4, 5, 2, 8, 0, 7, 3, 1, 6), (4, 5, 2, 8, 0, 7, 3, 6, 1), (4, 5, 2, 9, 1, 7, 3, 8, 0), (4, 5, 3, 7, 0, 2, 8, 1, 6), (4, 5, 3, 7, 0, 2, 8, 6, 1), (4, 5, 3, 8, 1, 6, 2, 7, 0), (4, 5, 3, 9, 2, 0, 6, 1, 8), (4, 5, 3, 9, 2, 0, 6, 8, 1), (4, 5, 6, 1, 7, 3, 8, 2, 9), (4, 5, 6, 1, 7, 3, 8, 9, 2), (4, 5, 7, 2, 9, 6, 1, 3, 8), (4, 5, 7, 2, 9, 6, 1, 8, 3), (4, 5, 7, 2, 9, 8, 3, 1, 0), (4, 5, 8, 2, 0, 1, 7, 3, 9), (4, 5, 8, 2, 0, 1, 7, 9, 3), (4, 5, 9, 1, 0, 6, 2, 3, 7), (4, 5, 9, 1, 0, 6, 2, 7, 3), (4, 5, 9, 1, 0, 7, 3, 2, 8), (4, 5, 9, 1, 0, 7, 3, 8, 2), (5, 6, 2, 9, 1, 7, 4, 8, 0), (5, 6, 3, 9, 2, 0, 7, 1, 8), (5, 6, 3, 9, 2, 0, 7, 8, 1), (5, 6, 3, 9, 2, 4, 1, 8, 0), (5, 6, 3, 9, 2, 7, 4, 8, 0), (5, 6, 4, 9, 3, 0, 7, 1, 8), (5, 6, 4, 9, 3, 0, 7, 8, 1), (5, 6, 4, 9, 3, 1, 8, 2, 7), (5, 6, 4, 9, 3, 1, 8, 7, 2), (5, 6, 7, 2, 9, 4, 0, 3, 8), (5, 6, 7, 2, 9, 4, 0, 8, 3), (5, 6, 7, 2, 9, 8, 4, 1, 0), (5, 6, 7, 3, 0, 1, 8, 4, 9), (5, 6, 7, 3, 0, 1, 8, 9, 4), (5, 6, 8, 1, 9, 4, 0, 3, 7), (5, 6, 8, 1, 9, 4, 0, 7, 3), (5, 6, 8, 3, 1, 0, 7, 4, 9), (5, 6, 8, 3, 1, 0, 7, 9, 4), (5, 6, 8, 3, 1, 7, 4, 2, 0), (5, 6, 8, 4, 2, 0, 7, 1, 3), (5, 6, 8, 4, 2, 0, 7, 3, 1), (5, 6, 9, 1, 0, 7, 4, 2, 8), (5, 6, 9, 1, 0, 7, 4, 8, 2), (5, 6, 9, 2, 1, 0, 7, 4, 8), (5, 6, 9, 2, 1, 0, 7, 8, 4), (5, 6, 9, 2, 1, 3, 0, 4, 7), (5, 6, 9, 2, 1, 3, 0, 7, 4), (5, 6, 9, 2, 1, 7, 4, 3, 8), (5, 6, 9, 2, 1, 7, 4, 8, 3)$$

Notice here that the remaining unused digit will be assigned to $$B$$ so we can try out the sum in each of these $$159$$ cases to see if it will work.
Only one of these (46th in the list) actually produces a valid solution.

• That seems awfully brute-forcey ... Sep 12, 2019 at 15:50
• @Randal'Thor Yep, I tried a couple of different approaches but they seemed to all reduce to more than 100 cases to check. For example, it's very easy to deduce that either F,G,I or J must be zero but even ruling out the case J=0 is a pain. Sep 12, 2019 at 16:01
• I guess the OP did say it's for a programming challenge, not a maths one. Sep 12, 2019 at 16:14
• Seems like a pretty anti-climactic question/answer for PSE then. Sep 12, 2019 at 16:20
• Note that this was posed as a Logic Programming exercise: You can easily formulate the conditions given in this answer as clauses in your logic programming language of choice, and then let it deal with all the brute forcing required. Nov 24, 2019 at 17:00