Clues outside the grid are A-Sums. The first digits in the clue's row or column must sum to the number in the clue (a bit like a straight Killer Cage). All A-Sums of the same color are followed by the same digit. Each color's A-Sum digit is different. (thanks to DiMono for this clear explanation)
For each color, we have a different number A. An A-Sum is the sum of all the numbers in the row/column from the start of the row/column which come before the number A in that row/column.
Eg. Suppose a blue A is 2 and a black A is 3. Then for the row with numbers 782564319, we have the following:
Blue A-sum = 7+8 = 15
Black A-sum = 7+8+2+5+6+4 = 32
(also thanks to SudokuExplorer)
The number outside the grid is a sandwich-sum between the edge of the grid and the corresponding A.
My explanation on the other two puzzles weren't that clear. So if you like this puzzle you can may solve the others now. (0004MW and 0004O9)
Solution code: Column 1 and 2 (18 digits)
on 30. January 2023, 22:32 by dennischen
Great puzzle, took me 25 minutes
on 12. January 2021, 19:37 by SudokuExplorer
It's a lovely puzzle!
----
Thanks
on 10. January 2021, 15:55 by panthchesh
Thanks for the puzzle! :) And thanks for the clarification. I didn't try the other puzzles because I was confused by the rules.
on 10. January 2021, 13:15 by SirWoezel
Right, that fixed it. I'll delete my earlier note as it includes most of the solution and I don't like that, even when it's hidden...