Logic Masters Deutschland e.V.

---- RULES ----

Normal Sudoku rules apply: Fill the grid with digits 1 to 9 appearing once each in every row, column, and 3x3 box.

Galaxies: Divide the grid into regions of orthogonally connected cells. Each region contains exactly one red circle and is rotationally symmetric around the circle. Every cell must be part of exactly one such region.

Parity Loop: After determining the galaxies, draw a 1-cell-wide loop (orthogonally connected cells) into the grid which fulfills the following requirements:

• The loop must go through all cells containing red circles. If a red circle is on an edge or corner, the loop must only pass through at least one of the adjacent cells.
• The loop cannot enter any galaxy more than once.
• The loop cannot touch itself, not even diagonally.
• The loop encloses as few cells as possible (while still obeying the previous rules).

The found loop will act as a parity line. Adjacent digits along the loop have opposite parity.

Row Indexer: Green cells are row indexers. If a green cell (R,C) contains the digit X then cell (X,C) contains the digit R. Thus, here, the digit in a green cell indicates in which row the 4 can be found in the same column.

Column Indexer: Red cells are column indexers. If a red cell (R,C) contains the digit X then cell (R,X) contains the digit C. Thus, here, the digit in a red cell indicates in which column the 5 can be found in the same row.

Kropki dots: Cells connected by a white dot contain consecutive digits. Digits in cells connected by a black dot are in a 1:2 ratio.

---- LINKS ----

Solve this puzzle in the CtC app

Solve this puzzle on f-puzzles.com

---- EXAMPLE ----

Solve this example in the CtC app

Solve this example on f-puzzles.com

---

This is the third sudoku in my series of “Build-your-own-loop Sudokus". If you liked solving this puzzle or if you prefer other combinations of loop logic and constraints, feel free to give the other sudokus of the series a go too:

	Loop Logic	Loop Constraint	Further Constraints
Road Running Loop	Road Runner	Parity Line	Kropki Dots
Magically Modifying Loop	-	Incrementers, Decrementers, Nullifiers	Magic Squares, Killer cages, Kropki Dots
Skiing Loop	Gates	German Whispers	Kropki Dot, Between Lines
Behaving Loop	3x3 boxes	Polarity Line	Kropki Dots
Magical Loop	Guiding cells	Modular Line	Magic Squares
Foggy Loop	Guiding cells	Parity Line	Fog of War, Killer Cages
10-Suȵ Loop	Moon-or-Sun	10-Line	Killer Cages
Counting Loop	Galaxies	Counting Line	Killer Cages, Kropki Dots, Quadruple Clues
Shining Loop	Moon-or-Sun	Parity Line	Killer Cages
Interfering Loops	Slitherlink + Masyu	Entropic Line + Parity Line	Killer Cages
Slithering Loop	Slitherlink	Entropic Line	Killer Cages, Little Killer
BigBang Loop	Galaxies	Parity Line	Row/Column Indexer, Kropki Dots
Summing Loop	Star Battle	Region Sum Line	Killer Cages, Skyscraper, Kropki Dots
Whispering Loop	Star Battle	German Whispers	Sandwich Sum

---