Play 6×6 Sudoku Online

What is 6×6 Sudoku?

6×6 Sudoku is Sudoku on a grid of 36 cells: six rows, six columns and six boxes, each box two rows tall and three columns wide. You fill it with the digits 1 to 6 so that:

• each row holds 1 to 6 exactly once;
• each column holds 1 to 6 exactly once;
• each 2×3 box holds 1 to 6 exactly once.

It is often sold as mini Sudoku, and apart from the size its rules are those of classic 9×9 Sudoku. The one real change is the box. Six cells cannot make a square, so the boxes are oblongs, and some publishers turn them the other way, three rows tall and two wide. A puzzle written for one shape cannot simply be read in the other: our 6×6 Sudoku solver page shows one that has no answer at all once its boxes are turned.

There is exactly one answer to every puzzle the game above deals. Its generator fills a grid, takes clues away in random order, and puts a clue straight back if removing it would let a second answer in. We re-checked 40,000 of its puzzles, 10,000 per level, with a separate solver, and every one had a single answer. That is what lets the game mark a wrong digit red the moment you enter it.

How does the 2×3 box change the way you solve?

Cut the grid into horizontal bands — rows 1–2, 3–4 and 5–6 — and each band holds just two boxes, side by side. Cut it into vertical stacks — columns 1–3 and 4–6 — and each stack holds three boxes, one above another. The two directions behave differently, and that difference is most of what there is to learn about 6×6 scanning.

Across a band, a digit in one box tells you which row its copy must take in the other box: the other row, since the digit can appear in each row only once. One clue rules out half a box. Down a stack it works as it does across a 9×9 band: once a digit sits in two of the three boxes, its copy in the third is confined to the one column left, which here means two cells.

That find is a hidden single. The cell itself could still take four digits, so looking at the cell gets you nowhere; the 5 is what has run out of room. The habit that pays on a 6×6 is to scan digit by digit and band by band: for each box that lacks a digit, see whether the box beside it already holds that digit — if it does, half the box is gone — then check which of the cells left already see the digit down their columns.

What does it take to solve a 6×6 Sudoku?

Less than you might expect. We took 10,000 puzzles at each level from this page’s own generator and solved every one with a ladder of techniques, always using the simplest step available, to find the hardest step each puzzle really needs:

Measured on 10,000 seeded puzzles per level from the generator above, each solved using the simplest step available at every point. “Needs a hidden single” means naked singles alone stall but naked and hidden singles together finish the board.

Two techniques carry nearly the whole game. A naked single, a cell whose row, column and box already show five different digits, finishes every Easy board but one in 10,000 and all but 55 Medium boards. The hidden single is what Hard and Expert add. Look only at cells, and more than one Expert board in three will stall; look at digits as well, and 95% of Expert boards come out with nothing else.

The last 5% of Expert boards need more. Of the 499 in our 10,000, 54 fell to locked candidates and five to pairs or triples. The other 440 needed patterns that follow one digit across the grid or link cells with two candidates each: 377 fell to an X-Wing, a one-digit chain such as the skyscraper, or an XY-Wing, and 63 needed something longer than our solver tries. Expect one of these on about one Expert board in twenty.

How do the Easy, Medium, Hard and Expert levels differ?

The four levels differ only in how many clues the generator aims to leave: 20 on Easy, 16 on Medium, 12 on Hard and 9 on Expert. Easy and Medium always hit theirs, Hard does on 99.8% of boards and otherwise settles for 13, and Expert usually cannot — the next section explains why. Here is what a player meets at each level:

Same 10,000 puzzles per level. A cell is “in view” if a naked or hidden single fills it before you have written anything. A round fills every such cell at once and then looks again; rounds are counted on the boards singles can finish.

Between the first three levels, the difference is how much of the board is open at once. A fresh Easy board usually has 14 of its 16 empty cells ready to fill; a Hard board, 8 of 24. Naked singles dry up fastest. A typical Easy board shows 8 cells that can already see five different digits, a Hard board 2 and an Expert board 1, and 14% of Expert boards show none at all, so the first move there has to be a hidden single.

Why doesn’t an Expert 6×6 always have 9 clues?

Because the generator will not buy a lower clue count with a second answer. When it has tried every clue and none can go without letting another solution in, it stops, whatever the target says. On Expert that is the usual ending: of 10,000 boards, 19.3% reached 9 clues, 53.6% stopped at 10, 24.3% at 11, 2.7% at 12 and 0.1% at 13.

A puzzle in which every clue is needed like that is called minimal, and minimality, not the count, is what sets Expert apart. 99.5% of Expert boards are minimal, against 3% of Hard boards and none at all on Easy or Medium, which stop at their targets with clues to spare. So the occasional 12-clue Expert board is not a Hard board in disguise: 5.3% of them needed more than singles, against 1.9% of Hard’s 12-clue boards. Fewer clues do make Expert slower going — 47% of 9-clue Expert boards fall to naked singles alone, against 82% of 12-clue ones — but the share that needs more than singles stays close to 5% all the way from 9 clues to 12.

That rectangle is why a clue like the 6 at R4C2 cannot go. Four cells, two digits, two boxes, and nothing in the rows, columns or boxes to tell the two orders apart. Experienced solvers turn the same shape into a technique, the unique rectangle: because the puzzle has one answer, no move can be right if it would leave such a rectangle free to swap.

What is the fewest clues a 6×6 Sudoku can have?

Eight. We searched rather than sampled. Every completed 6×6 grid belongs to one of 49 families (see the next section), and for one grid from each family we found every set of eight or fewer clues that leaves exactly one answer. None has seven or fewer. Eight-clue puzzles exist in 29 of the 49 families, which between them cover 75.4% of all grids, and there are 1,310,100,480 of them in all. The remaining quarter of grids cannot be pinned down with fewer than nine clues.

The search works backwards from the answer. A clue set has one solution only if it touches every group of cells that could be rearranged into a different valid grid — like the rectangle above — so we listed those groups, looked for clue sets that touch all of them, and solved each candidate outright. A second, deliberately plain program then tried all 30,260,340 eight-clue sets on three of the grids by brute force and arrived at exactly the same counts: 7, none and 12.

For comparison, a 4×4 Sudoku needs at least four clues, and classic 9×9 needs 17, which took until 2012 to prove; our 17-clue Sudoku page explains how.

How many 6×6 Sudoku grids are there?

28,200,960. We counted them by filling in every grid there is, which takes a computer about ten seconds. Most are the same grid in disguise: relabel the digits, swap two bands, swap the rows inside a band, swap the two stacks or the columns inside a stack, and you get another valid grid. Allow those moves and 49 genuinely different grids are left. One move that works on 9×9 is missing here: you cannot turn a 6×6 grid on its side, because that turns its 2×3 boxes into 3×2 ones.

For scale, a 4×4 has 288 grids and two genuinely different ones, and a 9×9 has 6,670,903,752,021,072,936,960.

What do the buttons do?

Pick a cell and press a digit from 1 to 6. The buttons under the grid:

• Notes toggles pencil mode. Placing a right answer wipes that digit from the notes in its row, column and box; placing a wrong one wipes nothing.
• Erase empties the selected cell, as does pressing the digit already in it. The clues are locked.
• Undo reverses your last change, one cell at a time, but leaves two things as they are: notes that a placement wiped from other cells, and the Mistakes count.
• Hint puts the answer into one cell that is empty or wrongly filled.
• Solve shows the full solution once you confirm, and stops the clock.
• New Game starts another puzzle at the level you are on; the Easy, Medium, Hard and Expert buttons start one at theirs.

Mistakes are counted the moment they happen. A digit that is not the answer turns red and the counter goes up, even when nothing on the board yet contradicts it — the game compares every entry with the puzzle’s one solution. The keys 1–6, the arrows, Backspace or Delete and Ctrl+Z all work from a keyboard. Progress is saved in your browser with every move, so a closed tab reopens on the same puzzle with the clock where it stood at your last move, though Undo starts from scratch.

4×4, 6×6 or 9×9: which should you play?

The three sizes make a ladder:

The levels listed are the buttons on each size’s game page. The 4×4 and 6×6 floors come from our own exhaustive searches; the 9×9 floor is the 2012 result of McGuire, Tugemann and Civario.

If 4×4 feels automatic — and it should, since every 4×4 puzzle falls to naked singles — 6×6 is the next step: a cell now has to see five different digits instead of three, and Hard and Expert start asking for hidden singles. When Expert 6×6 boards stop needing a second look, move on to classic Sudoku at Easy.

Teaching children? Our Sudoku for Kids page is about introducing the game at home or in class. For a worksheet, the Sudoku generator builds 6×6 PDFs with your choice of difficulty, layout, paper size and answer key.

Printable 6×6 Sudoku

Prefer a pencil? Each level also comes as a ready-made PDF of 100 puzzles, answers at the back, free to download: Easy, Medium, Hard and Expert. They are gathered on the printable 6×6 Sudoku page, and other sizes are in the printable Sudoku collection.