Logic Masters Deutschland e.V.

So phil_the asked for more puzzles using curve lines, in particular curves that hold information on their curviness. The curves in this puzzle hold information about the two directions along them, even on their intersections, where they meet smoothly, like train tracks do.

• Normal sudoku rules apply.
• The grid is toroidal:
  • Each edge of the grid is considered to be adjacent/orthogonal to its opposite edge. (For example, r3c1 is considered orthogonally adjacent to r3c9.)
  • Lines wrap around opposite sides of the grid.
• The graph is a train track:
  • A point where lines meet is a switch, and cells with switches are marked with red circles.
  • By removing all switches the graph is cut into non-branching segments.
  • Each segment has a value equal to the average of the digits in the cells it covers, not including its endpoints.
  • For each switch, the sum of the values of the branches on either side of the switch is the same. The sides of a switch are indicated by the openings of the red circles. (For example for the switch on r5c2 the sum of the values of the three branches on the left is equal to the value of the right branch.)
• Cells joined by an X contain digits that sum to 10, not all possible X are given.

Online in Sudokupad

Example: The segment [r3c3] has an average value of 3 and on either switch it is equal to the sum of the values for segment [r1c3 r4c2] (1+1)/2 = 1, and segment [r1c4 r2c14 r3c1] (2+1+3+2)/4 = 2.

You can find another mini version of this puzzle here.

See also: pseudo-Anosov