Logic Masters Deutschland e.V.

Normal sudoku rules apply: Fill the grid with digits from 1 to 9, so that every row, column, and 3x3 box contains each of the 9 digits exactly once.

The blue line is an "average line": In every group of 3 successive digits along it, one digit is the average of the other two. For example, 4 successive cells might contain 2135; 2 is the average of 1 and 3 and 3 is the average of 1 and 5.

Digits joined by a black kropki dot are in a 1 to 2 ratio. Not all dots are given.

You can solve this in SudokuPad.

My previous puzzles with this rule, Average line sudoku #1 and Whispering averages in the fog, both had several short average lines. I've been wondering how long an average line could be; could it include every cell in the grid? I don't know the answer to that; the longest one I've found has 73 cells. Unfortunately such a long line doesn't make a very good puzzle: Although the breakin may be difficult, after that it gets too easy. So I experimented with shorter lines, and chose the 46-cell line above. I think this puzzle is easier than #1.

Finally, a note about pencil marks, which may help with this puzzle. I suppose this could be considered a hint, so if you don't want it, stop reading now. When I solve a sudoku on paper, I often underline or overline some of the candidate marks, to show how a choice in one cell would affect those in other cells. SudokuPad doesn't let you do that, so I sometimes use corner marks to show one possibility and center marks for another.