Kropki Sudoku keeps every Classic rule: each row, column and 3×3 box holds 1 to 9 once. On top of that, small dots sit on the lines between side-by-side cells. A white dot means the two digits are one apart, like 4 and 5. A black dot means one is double the other, like 3 and 6. Every dot is shown, so two cells with no dot between them are neither. The dots say so much that 211 of the Hard puzzles on this site start with no clues at all.
The rules
Fill the 9×9 grid so that every row, every column and every 3×3 box holds the digits 1 to 9 exactly once, as in Classic Sudoku.
A white dot between two cells: their digits are one apart (3 and 4, 8 and 7). A black dot: one digit is double the other (1 and 2, 2 and 4, 3 and 6, 4 and 8).
Every dot is shown. Two side-by-side cells with no dot are neither one apart nor one double the other. A 1 and a 2 are both, so either colour can join them.
What the dots change
A black dot is strong on its own. Only 1, 2, 3, 4, 6 and 8 have a double or a half from 1 to 9, so 5, 7 and 9 can never sit on a black dot.
A white dot ties a cell to its neighbour: a cell beside a 5 across a white dot is 4 or 6, nothing else.
The missing dots count as much as the dots. Beside a 4 with no dot, a cell cannot be 3, 5, 2 or 8. On this site every puzzle has 25 to 61 dots, about two in three of them white.
How to solve it
Start where the dots chain. Three cells in a row or column joined by two black dots can only hold 1, 2, 4 and 8, with 2 or 4 in the middle. The candidates the board shows already follow every placed digit and its dots.
Then check each dot against what its neighbour can still hold. A digit stays only if the cell next to it has a partner for it. Next Step calls this a White Dot or Black Dot step and lights the dot it means.
Use the empty edges too: the No Dot step eliminates a digit when everything left next to it is one apart, double or half. After that, solve as in Classic: singles, locked candidates, pairs.
Worked examples
Three positions from real puzzles on this site, walked through by the same Next Step teacher you get in a game. Step through each one.
A white dot
Look at R4C1 and R4C2, side by side. A white dot: the two digits are one apart.
A black dot
Look at R3C2 and R3C3, side by side. A black dot: one digit is double the other (1 and 2, 2 and 4, 3 and 6, 4 and 8).
No dot between them
Look at R1C3 and R1C4, side by side. No dot: the two digits are neither one apart nor one double the other.
The three levels
Kropki levels use the same technique scale as Classic, with the dot steps counted as Easy and the no-dot step as Medium. With every dot shown, a puzzle almost never needs an Extreme technique, so Hard is the top level. Every puzzle is solvable by logic alone.
Classic techniques, unchanged
The houses are the Classic rows, columns and boxes, so every Classic technique works as it is. These lessons teach them:
Frequently Asked Questions
Is Kropki Sudoku harder than Classic?
Not by its levels: they use the same technique scale as Classic. The dots give a lot of information, so the puzzles start with very few clues, and many Hard ones with none.
What does no dot mean?
On this site every dot is shown, so two side-by-side cells with no dot between them are neither one apart nor one double the other.
Which dot goes between a 1 and a 2?
Either. A 1 and a 2 are one apart and one is double the other, so a white or a black dot can join them.
Do dots join cells corner to corner?
No. A dot sits on the line between two cells that share a side, across a row or down a column.
How can a puzzle have no clues?
The dots and the missing dots together leave only one way to fill the grid. 211 of the 1,000 Hard puzzles here start empty, and every one has a single solution you can reach by logic.
Are the clues symmetric?
Yes. Turn the grid half a turn and the clues land on clues. The dots follow from each puzzle’s solution.
Why are there only three levels?
With every dot shown, a Kropki puzzle almost never needs an X-Wing or a Swordfish, so Hard is the top level. Every puzzle can be solved by logic, with no trial and error.
Which tools can I use?
All of them: pencil marks in corner or centre notation, candidates, Auto Check, Check Cell and Check Puzzle, and Next Step, which lights the dot whenever it is the reason for a move.
Try one now. Easy is a good place to start.