How to Play Kropki Sudoku: White & Black Dot Rules

A white dot means the two digits are consecutive, one apart. A black dot means one digit is exactly twice the other. Everything else is ordinary Sudoku.

Kropki Sudoku rules in 30 seconds

1Every row, column and 3×3 box contains 1–9 exactly once.
2White dot: the two digits differ by exactly 1 (like 3 and 4).
3Black dot: one digit is exactly double the other (like 2 and 4).
4Either side of a dot can hold the larger digit.

See it on a board

White dots join digits one apart (3–4). Black dots join a digit and its double (2–4). Here every dot is shown; a 1–2 pair is drawn black, though it fits both.

Watch: how to play Kropki Sudoku

Still not sure? Some puzzles click faster when you see them solved. This 17-minute video from Steven Scott shows Kropki Sudoku in action.

“Kropki Sudoku - Rules & Strategies” by Steven ScottWatch on YouTube

The white dot

A white dot joins consecutive digits: 1–2, 2–3, 3–4, 4–5, 5–6, 6–7, 7–8 or 8–9, in either order. Beside a known 4, a white-dot neighbour can only be 3 or 5. Beside a 1, it can only be 2. Beside a 9, only 8.

The black dot

A black dot joins a digit and its double. With 1 to 9 there are only four such pairs: 1–2, 2–4, 3–6 and 4–8. Memorise them and black dots become easy.

That also means 5, 7 and 9 can never sit on a black dot, because neither double nor half of them is a digit from 1 to 9.

The special 1 and 2

1 and 2 are consecutive and 2 is double 1, so a 1–2 pair satisfies both kinds of dot. Keep that in mind: a white dot doesn't rule out 1–2, and neither does a black one.

What does no dot mean?

It depends on the puzzle. Some Kropki puzzles show every possible dot, so a missing dot means "neither relationship". Others only show some. Unless the puzzle says every dot is shown, don't treat a missing dot as a clue.

Worked example

1A black dot sits between two cells, and one of them is already a 3.
2The only black-dot partner for 3 is 6 (half of 3 isn't a whole number).
3So the neighbour is 6, and every other 6 in that row, column and box is ruled out.

Kropki Sudoku tips and strategies

Learn the four black pairs

1–2, 2–4, 3–6, 4–8. Every black dot is one of these.

Remove 5, 7 and 9 from black dots

Any cell touching a black dot can't be 5, 7 or 9.

Chase chains of dots

A cell with dots on two or three sides has very few digits that satisfy all of them at once.

Use the edges of the range

1 on a white dot must pair with 2; 9 on a white dot must pair with 8.

Common mistakes to avoid

Thinking a white dot means "the next digit up" only. It works in either direction.
Forgetting that 1–2 fits both a white and a black dot.
Treating a missing dot as a clue when the puzzle doesn't show every dot.

Play Kropki Sudoku in 10+ Number Puzzles

Dots stay visible between cells while the selected cell's row, column and box are highlighted.
Auto Notes fills candidates that satisfy both the Sudoku rules and every dot around a cell.
You have 3 lives. A wrong digit costs one.
Five difficulty levels, each a ladder of stages from Easy to Genius.
Go online for free: ranked 1v1 duels, rooms where you race, co-op or play in teams, and tournaments.
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