What is Kropki Sudoku?
Kropki sudoku (kropki is Polish for “dots”) is classic sudoku with small black and white dots on the edges between cells. The dots describe how neighbouring digits relate — and because every qualifying pair is marked, the places without a dot speak just as loudly.
The rules
The usual sudoku rules apply: every row, every column and every 3×3 box contains the digits 1 to 9 exactly once. On top of that: a black dot between two cells means one value is exactly double the other (3 and 6, 4 and 8); a white dot means the values are consecutive (3 and 4). A pair of 1 and 2 qualifies for both, so it may carry either colour. A kropki often starts with almost no digits at all — the dots carry the whole puzzle.
White = consecutive (3–4), black = double (4–8, 3–6, 4–8). The 2–1 pair fits both, so its dot could be either colour — and the edges without dots (like 8–6) are neither.
The power of no dot
The crucial rule is the one about absence: all dots are given. If there is no dot between two cells, their digits are neither consecutive nor double. That turns every empty edge into a clue — place a 4, and every dotless neighbour can no longer be 3, 5, 2 or 8. Beginners read only the dots; strong solvers read the silences.
How to get started
- A cell touching a black dot can never hold 9, 7 or 5 — those digits have no doubling partner in 1–9. Long black-dot chains are even tighter: three cells in a chain must be something like 1–2–4 or 2–4–8.
- A chain of white dots is a run of consecutive digits going up or down — pencil in both directions and let the row eliminate one.
- Use the negative constraint constantly: every digit you place prunes candidates in all dotless neighbours. This is where most of the solving power hides.
- Watch for the 1–2 pair: it is the only pair that can sit behind either colour, which sometimes matters at the end of a chain.