⚫ How to play Kropki Sudoku

By Miguel Arechaga

Kropki Sudoku is a variant of Polish origin (kropki means "dots" in Polish) that's become very popular in competitions and on channels like Cracking the Cryptic. White and black dots appear between cells, giving clues about the relationship between neighboring numbers. Here are the rules and a few tips.

What is Kropki Sudoku?

It's a standard 9x9 sudoku where, between some neighboring cells, a dot appears. A white dot means the two numbers are consecutive (they differ by 1). A black dot means one is double the other. In the full version, the absence of a dot also gives information: if two neighbors have no dot, they're neither consecutive nor double.

Rules and how to play step by step

1. The sudoku rules apply: 1 to 9 without repeats in each row, column and 3x3 box.
2. White dot: the two cells are consecutive (a difference of 1).
3. Black dot: one cell is double the other (1-2, 2-4, 3-6, 4-8).
4. No dot: neither of the two relationships applies. Every puzzle has a unique solution.

Tips to solve Kropki Sudoku

• The pair 1-2 carries a black dot: it's both consecutive and double; by convention it's marked black.
• Black dots are very restrictive: a 5, 7 or 9 has no possible double within 1-9, so those cells never touch a black dot.
• Chains of black dots: 1-2-4-8 forms a chain of doubles; spotting it solves several cells at once.
• Don't forget the absence of a dot: it tells you two neighbors are NOT consecutive or double, ruling out many options. Combine it with the classic techniques.

How it differs from regular sudoku

Compared to classic sudoku, Kropki adds arithmetic relationships (consecutive and double) between neighboring cells. It's a cousin of Consecutive Sudoku, but with the extra layer of doubles. If you enjoy variants with marks, you'll also enjoy Arrow Sudoku.