Kropki Sudoku for Kids

Kropki Sudoku is normal sudoku with little dots printed on the lines between the squares. The board is the same 9×9 you already know, with the same nine 3×3 boxes, the same rows and the same columns. The new twist is the dots — and there are only three things to learn.

A white dot means the two squares it touches hold next-door numbers: numbers that are exactly one apart, like 4 and 5 or 8 and 9. A black dot means one of the two numbers is exactly double the other, like 3 and 6 or 4 and 8. And a line with no dot on it means neither: the two numbers are not one apart and not double. That last one is the secret of the whole game.

You can play Kropki Sudoku as soon as you are comfortable with our classic 9×9 sudoku. The number rules are exactly the same: each row, each column and each 3×3 box still has to contain the digits 1–9 with no repeats. The dots just add one more rule on top of the puzzle you already know — and because every dot that belongs on the board is always drawn, the empty lines are promises too.

Puzzle books sometimes call this game "dot sudoku" or "consecutive sudoku". The name Kropki is the Polish word for "dots" — the puzzle first became popular in Poland before spreading to puzzle championships around the world.

A white dot is a promise: the two numbers it touches are one apart. So as soon as you know one of them, the other has just two choices. Here is how that plays out on a real board.

That is the pattern you will use over and over: read the dot to shrink a square down to two choices, then let the row, the column or the box knock one of them out. Squares with a white dot next to a filled square are the fastest squares on the board to solve.

Black dots are even stronger than white ones. "One is double the other" sounds like a maths lesson, but there are only four pairs in the whole game that fit: 1 and 2, 2 and 4, 3 and 6, and 4 and 8. That is the full list.

Because the list is so short, some digits can never sit next to a black dot at all. Double 5 is 10, double 7 is 14 and double 9 is 18 — far too big for a sudoku — and half of 5, 7 or 9 is not a whole number. So the moment you see a black dot, you can cross 5, 7 and 9 out of both squares it touches, before you know anything else about them.

And if one side of a black dot is already filled in, the other side has at most two choices. Next to a 2 it can only be 1 or 4. Next to a 4 it can only be 2 or 8. Next to a 1, a 3, a 6 or an 8 it has exactly one choice.

Here is the idea that makes Kropki a real puzzle rather than a decorated sudoku. Because every dot that belongs on the board is always drawn, a line with nothing on it is also telling you something: the two numbers on either side are not one apart, and neither is double the other. Look what that does next to a single filled square.

One empty line, next to one number, and four candidates are gone. Next to a 2, an empty line rules out 1, 3 and 4. Next to a 6, it rules out 3, 5 and 7. Next to an 8, it rules out 4, 7 and 9. Most of the lines on the board are empty, so this is the move you will make most often — and it is the one new players forget, because there is nothing there to catch your eye.

This is also why the Expert level can hand you a board with no numbers on it at all. Forty-odd dots plus a hundred empty lines say so much about the grid that, almost always, only one filling fits.

The strongest clues come from chains: two or more dots in a line. Three squares in a row joined by white dots are the classic example.

The same idea works for any run of dots. Every dot in a chain narrows its neighbour, and the narrowing passes along the line like a whisper. Our Auto Notes button gives you a head start: it fills in pencil marks using the row, the column, the 3×3 box, the dot shapes (no 5, 7 or 9 beside a black dot, no 1 beside a white one) and every line — dot or empty — next to a square you have already filled. Walking the chains is left to you, because that is the fun part.

Most kids pick up Kropki Sudoku in about five puzzles. If you have never played sudoku of any kind, a couple of rounds at Easy 9×9 sudoku first will get the basic pattern into your head. Once rows, columns and boxes feel automatic, the dots are a fun new layer on top. If pencil marks are new to you, our guide to how pencil marks work is a good five-minute read.

Kropki Sudoku is an unusually good fit for the classroom because it rehearses three specific number skills — one more and one less, doubling, and halving — hundreds of times inside a puzzle a child actually wants to finish. The black dots quietly drill the 2-times table; the white dots drill counting on and counting back; and the empty lines teach something subtler still, that the absence of a mark can be evidence.

Every puzzle on this page is generated with exactly one solution and is proved by computer before it reaches the screen, so a child can never get stuck through no fault of their own. There is no timer pressure, no fail state and no advertising in the middle of the board. Mistakes are counted quietly and never punished.

Easy gives 36 starting numbers and suits roughly ages 8–9; Medium gives 26 and suits ages 9–10; Hard gives just 8 and suits ages 10–11; Expert gives none at all and is a real challenge for confident solvers of any age. A good classroom pattern is one Easy puzzle as a warm-up, then a shared Medium puzzle on the whiteboard with children explaining which line they read and why.

Once Easy Kropki Sudoku feels comfortable, try Medium Kropki Sudoku. From there you can graduate to Hard Kropki Sudoku, where only eight numbers are given, and finally take on Expert Kropki Sudoku — a board with no numbers on it at all.

Want a similar brain workout? Our Greater Than Sudoku is the closest cousin — instead of dots it prints > and < signs between the squares. Our Thermo Sudoku draws whole thermometers that numbers must climb, and Killer Sudoku asks you to add up little cages. Or try Hyper Sudoku, X-Sudoku and Jigsaw Sudoku for three completely different twists. Younger players can start with our 4×4 sudoku and 6×6 sudoku starter grids.