Logic Masters Deutschland e.V.

This is a puzzle I made for Andrewsarchus' birthday a few years ago as part of an organised puzzle exchange. He likes difficult puzzles with a certain mathematical focus, and a good deal of complexity, so it was made with that in mind. It won't be everyone's cup of tea, but if you like that kind of thing please give it a try.

The Rules:

• Normal Sudoku rules apply.
• The teal lines are Mean Mod lines.
• Squares: a digit, X, in a square is the average (mean) value of all of the digits on the same line as that square. For example - if there are 5 digits on a line (including all digits in circles and squares), and the line sums to 30, then X = 6, and the square must contain a 6.
• Circles: a digit, N, in a circle must divide exactly into the sum, S, of all the digits on its line, i.e. S mod N = 0. For example - if the total of the digits on a line is 12 (including all digits in circles and squares), then N could be 1, 2, 3, 4 or 6, because these all divide into 12 with no remainder. However, N could not be 5, 7, 8 and 9 because they do not divide exactly into 12.
• Repeats: Digits, including X and N, can repeat on lines if other rules allow. All circles must contain different digits, but different squares may contain the same digit. However, all possible squares are given, so there is a negative constraint on squares.
• The lines in box 5 all go straight across each other.
• A white dot separating two cells indicates the digits in those cells are consecutive. Not all white dots are necessarily given.
  Mean Mods

  by Chilly

  

  Link for solving on SudokuPad