Logic Masters Deutschland e.V.

This sudoku advent calendar contains 24 variants that were included in my Sudoku Variants Series (SVS) but turned out to be too hard to be solved by a wide range of puzzlers. I aim for difficulties of 1-2 stars and have written some general and/or specific hints as well. I hope some players will try the original SVS puzzle #245 after solving the advent version.

Counting Neighbours
Apply classic sudoku rules.
A digit in a cell with a circle indicates the number of distinct digits in all horizontal, vertical or diagonal neighbouring cells. A digit in a cell with a cross indicates the number of different digits in all diagonal neighbouring cells. When no cross or circle is placed, none of these constraints hold!

General hint for this type:

Corners and edges are the best place to start with this puzzle, since the digit in a cross is either 1 (in case the cross is in a corner) or 2 (elsewhere on the edge).
A circle is either 3 (in case it is in a corner) or 3, 4 or 5, depending on it’s position.
Also a cross or circle in the central cell of a 3x3 block can contain only one digit.