Logic Masters Deutschland e.V.

Hey everyone! Thank you for the feedback on my last published puzzle, it helps me learn a lot and hopefully set better puzzles. Here's my new puzzle, hope you enjoy it))

The puzzle

Normal sudoku rules apply.

Outside clues: Each number outside the grid is a clue for the column it sits above or below. It is read in three ways at once:
Sandwich: The sum of the digits between 1 and 9 are equal to the clue.
Numbered Rooms: If the digit in the cell nearest to the clue is X, then the clue's value is placed in the X-th cell of that column, counting from the clue's side.
Skyscrapers: Each digit is a skyscraper whose height equals its value. The clue is the number of the skyscrapers that are visible from the clue's side. The taller skyscraper blocks the view for shorter ones behind it.

Odd/even cells: A cell containing a gray circle is odd. A cell containing a gray square is even.

Distance rule: Two identical digits N may not be closer than √N to each other (distance < √N). Distance is measured between cell centers, with every cell being 1x1. (See the list at the end for the implications for each digit.)

Solve in SudokuPad

Distance rule implications:
1 – none
2 – orthogonally adjacent
3, 4, 5 – additionally diagonally adjacent (chess king's move)
6, 7, 8 – additionally chess knight's move
9 – additionally 2 cells diagonally
5 does not see a knight's move away because the distance is exactly √5, not less than.
8 does not see 2 cells diagonally away because the distance is exactly √8, not less than.