Logic Masters Deutschland e.V.

The following puzzle is the 3rd entry of my BYOK concept that I'd like to call Red and Blue Prototype. This one also has what's certainly considered as one of the most intricate openings that I've ever done so far, but there are also plenty of engaging moments as well. Prepare yourself to experience the incredible power of arithmetic in this puzzle!

For previous entries of the concept, check out:

Criminal Mind

Moral Dilemmas

Rules:

- Normal Sudoku rules apply: every row, column and 3x3 box contains digits from 1 to 9 each once.

- A given one-cell cage is used to construct a real killer cage that starts from that cell and goes straight horizontally or vertically in the direction of the given arrow in it, the length of each cage is to be deduced (the limit one can reach to is the 9x9 grid borders). Once a cage is finished, digits within that cage sum to the small number written in that cage.
- There are two types of color: red and blue.
+ If a red cage has the length of N cell[s] then that red cage must contain digit N (which can be anywhere within the cage).
+ If a blue cage has the length of N cell[s] then that blue cage must not contain digit N.

Note: there can be some occasions where a cage is one cell long, and some cages can overlap each other regardless of their colors.


Some of the examples in the following image:
(+) For red cage, the 20 red cage can be 3 cells long or 4 cells long with configurations like in the image.
(+) For blue cage, the blue 8 cage can be only 1 cell long (contains only digit 8, which is possible), can be 2 cells but mustn't contain digit 2 in it.
The blue 10 cage can't be 1 cell long because 10 is not a single digit, and can't be 4 cells long because the only way it works is with 1+2+3+4 cage, but it contains a 4 and is a blue cage so it's not valid.
The blue 12 cage can only be 2 cells long or 3 cells long because of how close it is to the border.

Puzzle:

F-puzzle link

Sudokulab (alt. link)

Penpa plus (alt. link)

CTC app (alt. link)

Good luck and have fun solving!