Another puzzle combination (feat. Kakuro)

Question

Today, I am going to give you another puzzle combination. This time, it features a Kakuro! However, there are some things to note:

1. There are only two puzzles that I have combined, although you have to figure out which other puzzle I combined with it.
2. Unlike what the rules of Kakuro state, there are numbers larger than 9, however no smaller than 1.

Rules of Kakuro:

1. Place numbers in the white squares of the grid.
2. (except for this puzzle, where you are allowed to place larger numbers) You must place the numbers 1-9 only.
3. Numbers cannot repeat. (especially with this puzzle - each number that you use can only be used once)
4. The numbers in each run of squares must sum to the number given at the start of that run.

The puzzle:

To get the $\color{green}���$:

1. Solve the Kakuro
2. Figure out what the other puzzle is

_{Edit: Had to fix accidental incorrect sum, 21 is now 22}

Answer 1

Well, that's an unusually neat Kakuro solution:

Presumably the other puzzle is something that involves

creating a sort of "snake" of numbers in boxes going all over the board, forming a loop that starts from 1 and goes up to 26.

Yep, apparently it's called

Hidato (and I've actually solved both the puzzles in my intuitive understanding of what must be going on with the sequence of numbers here).