What do you get if you add up all of the output values?
Stick with our 2-elem tuples, but make the inside bits charlists. This makes
it easy to "subtract" other charlists via -- without ordering, etc.
We start with our known numbers: 1, 4, 7, 8. We can grok these out of the segment list just like before. Then we can apply logic rules to find the other numbers. 2, 3, & 5 are all 5 segments; 0, 6 & 9 are all 6.
Since 9 is inclusive of 4 segment-wise, but 0 & 6 are not, we can "subtract" 0, 6, & 9 from 4, and determine 9 be seeing which operation leaves no segments. Once we have 9, we can just look at 0 & 6. Since 0 is inclusive of 7 segment-wise, but 6 is not, we do the same thing and determine 0. The leftover is 6.
Slightly different, 5 is inclusive of 6 save 1 segment, whereas 2 & 3 are inclusive save 2 segments. We can filter the same way, just looking for one segment left instead of none.
Then we sort the segment ids, so we can match the jumbled output et voila.
mix run
mix test