SudokuBoku

6×6 sudoku Mini · 36 squares

Six digits, six boxes, and a grid you can hold in your head all at once. Shrinking the board does more to the logic than you would expect.

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Puzzle
Rules
  • Fill every row, every column and every 3×3 box with the digits 1 to 9.
  • A digit can appear once in each of those — never twice.
  • There is exactly one solution, and logic alone will reach it.
  • Rows and columns each take the digits 1 to 9, once apiece.
  • The boxes are irregular shapes, drawn with the heavy outlines.
  • However a region bends, no digit repeats inside it.
  • The colour patches are cages; the small number is what a cage's digits add up to.
  • No digit repeats within a cage — nor in any row, column or 3×3 box.
  • There are no given digits: the sums alone pin down the whole grid.
  • Everything from classic applies: rows, columns and 3×3 boxes take 1 to 9.
  • The two tinted diagonals must each hold 1 to 9 exactly once as well.
  • All the classic constraints hold — rows, columns and 3×3 boxes take 1 to 9.
  • Each of the four shaded windows must also contain 1 to 9 exactly once.
  • The windows sit a step in from the corners, overlapping four boxes apiece.
  • Rows, columns and 3×3 boxes work exactly as they always have.
  • On top of that, two squares a chess knight's move apart may not hold the same digit.
  • Select a square and its knight partners are ringed with a dashed outline.
  • Every row, column and 3×3 box holds 1 to 9, exactly as in classic.
  • Along each grey path, digits strictly climb from the round bulb to the far end.
  • They don't have to be consecutive — each square just beats the one before it.
  • Rows, columns and 3×3 boxes take 1 to 9, exactly as in classic.
  • The digits along each arrow add up to the digit in the circle it comes from.
  • Digits may repeat along an arrow — as long as no row, column or box objects.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • Between squares in the same box you'll find a sign; its point aims at the smaller digit.
  • Every comparison inside every box is shown — a hundred and eight of them.
  • The higher levels hand you fewer digits, not fewer signs. Expert gives you four.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • A white dot between two squares means their digits differ by one.
  • A black dot means one digit is exactly double the other. 1 and 2 are both, and always show black.
  • A boundary with no dot is a clue too — those two digits are neither one apart nor double and half. Every boundary is marked or deliberately bare.
  • Expert hands you no digits at all. The dots and the gaps are the whole puzzle.
  • Fill every row, column and 3×3 box with the digits 1 to 9, as usual.
  • A square with a ring behind it holds an odd digit — 1, 3, 5, 7 or 9.
  • A square with a frame behind it holds an even one — 2, 4, 6 or 8.
  • Most squares are marked with neither, and those are genuinely unrestricted.
  • Every square switches to the fully marked board — one level, gentler than it looks, and two puzzles sharing a grid rather than one.
  • Every row, column and box holds five odd digits and four even ones — so once five squares of a house are known odd, the rest of it is even, marked or not.
  • Solve the 9×9 sudoku as usual — every row, column and box takes 1 to 9.
  • Ten ships are hidden on the same squares: one of four, two of three, three of two and four single squares.
  • Ships are straight, and no two of them touch — not even at a corner.
  • The numbers beside and below say how many ship squares each row and column holds.
  • A ship listed with digits sits on exactly those digits, in order — so the grid is your map.
  • Five 9×9 grids interlock: four corners and a centre, each corner sharing one 3×3 box with it.
  • Every grid obeys ordinary sudoku on its own — rows, columns and boxes each take 1 to 9 once.
  • A tinted box belongs to two grids at once, and only together do the five have one solution.
  • Fill every row, every column and every box with the digits 1 to 6.
  • The boxes are three squares wide and two tall.
  • Nothing repeats in any row, column or box.
  • Put 1, 2, 3 and 4 into each row, each column and each 2×2 box.
  • No digit may appear twice in any of them.
  • Every square can be worked out — no guessing needed.
Keyboard shortcuts
1–9
Place a digit, or toggle a pencil mark
Arrows
Move around the grid
N
Notes mode on or off
Backspace
Clear the square
Ctrl + Z
Undo · Ctrl + Y redo

Small grids, printed six to a page

Mini grids compress beautifully onto paper — six to a sheet still leaves squares big enough for an adult pen and a child's handwriting. Everything is built here on your machine, and every grid is proved to have one answer before it reaches the page.

Difficulty

Thirty-six squares, and a box that isn't square

The rules survive the shrink intact. Every row holds 1 to 6, every column holds 1 to 6, every box holds 1 to 6, and nothing repeats. What cannot survive is the shape of the box. Nine splits neatly into three threes, so a standard grid tiles with squares; six does not split into equal squares at all, so a mini grid is carved into six blocks three squares wide and two tall. That asymmetry is the first thing to notice and the easiest to forget: two boxes sit side by side across the width, three sit stacked down the height, and a horizontal sweep therefore crosses a box boundary in a different rhythm from a vertical one.

The indigo square in the corner cannot repeat any digit sitting in the twelve amber ones — five along its row, five down its column, and two more caught inside its wide, short box.

Count what that leaves. A square here is watched by twelve of the thirty-five others, better than a third of everything on the board. On a standard grid a square is watched by twenty of eighty, a flat quarter. Proportionally, every placement you make on a mini grid reaches further than the same placement would on a big one, and the effect compounds: fill one square and you have meaningfully narrowed a third of the puzzle. This is the real reason mini grids feel fast. It is not that there are fewer squares to fill. It is that each square you do fill does more work.

The same density shows up in the count of grids. We put our own solver to work enumerating every legal completed 6×6 arrangement and it found 28,200,960 of them — a number you could store in a spreadsheet column if you were determined. The equivalent count for a 9×9 grid, worked out by Bertram Felgenhauer and Frazer Jarvis in 2005, runs to twenty-two digits. Mini sudoku is not a smaller version of the same space. It is a different order of thing.

The techniques a small grid never gets round to

Here is where a mini grid stops being merely quicker and starts being genuinely different. Anyone taught sudoku in the usual order learns singles first, then naked and hidden pairs, then locked candidates, and only afterwards the patterns that stretch across the whole board. On six by six, that middle rung barely exists. We dug four thousand grids at nine clues apiece and graded every one by replaying it with the same ladder of human techniques that grades every board on this site. Only 215 of the four thousand needed anything beyond a single. Of those 215, just twelve topped out at locked candidates and precisely two at a subset.

Why the pairs and triples don't get their turn

A naked pair is two squares in one house that between them admit only two digits, which lets you strike both digits from everything else in that house. Notice what the technique needs to be worth anything: a house with several squares still open, at least two of them narrowed to the same two candidates, and other open squares left over to eliminate from. A house here has six squares. By the time two of them are down to two candidates each, the house is usually so short of options that some square in it is already a single — and our grader, which always takes the gentlest move available, records the single instead. Subsets are not absent from these boards; press the Hint button often enough and one will be offered to you. What almost never happens is a puzzle whose hardest required step is a subset, and that is the thing a level is measured by.

What turns up instead

The puzzles that do resist singles mostly step straight over the middle of the ladder and land on patterns spanning the grid. Three quarters of our 215 were a skyscraper or an XY-wing — deductions that follow one digit across two lines and pinch off a square neither line touches directly. Those thrive on exactly what makes subsets fail. A short line makes it far more likely that a digit has only two homes left in it, and two homes in each of two lines is the entire raw material of a skyscraper.

Rows 1 and 3 each have exactly two places left for a 6, tinted here, and both rows use column 1 as one of them. Whichever way that column falls, a 6 lands on R1C5 or on R3C4 — and the amber square sees both, so it can never be the 6.

Fewer squares in a house means fewer places for a digit, and a digit with two places left is where the interesting patterns start.

None of this is a special mini technique that we invented for the page. It is the same skyscraper you would meet on an expert 9×9 board, found by the same code, described in the same words by the same Hint button. What has changed is how often the position hands it to you. If you have been meaning to learn the single-digit patterns and have found them elusive on a full grid, a run of hard mini puzzles is the most concentrated practice we can offer: the pattern is short enough to see whole, and it turns up in almost every puzzle that isn't pure singles.

Three levels, and an honest reason there is no fourth

The selector above offers Easy, Medium and Hard. It stops there, and it stops there on purpose. Easy grids start with sixteen clues and never ask for more than a naked single; Medium grids start with ten and always need at least one hidden single; Hard grids start with nine and always need something above both. Because the top band lands on a different pattern from one puzzle to the next, it does not repeat a fixed promise — the line above the board names whatever technique that particular grid genuinely requires, whether that turns out to be a skyscraper, a wing, or something rarer.

A fourth level would need somewhere further to go, and there is nowhere. Two ceilings close in at once. The first is arithmetic: strip clues from a 6×6 grid as aggressively as the digger can and it settles around ten, reaches nine often, and touched eight ten times in three thousand attempts. Past that point a removal nearly always admits a second answer, and a puzzle with two answers is not a hard puzzle, it is a broken one. The second ceiling is the ladder itself, for all the reasons above. We could print a fourth chip on the selector easily enough. We could not make it mean anything, so it isn't there.

What we get in exchange is speed. A whole search for a Hard mini grid — up to seventy candidate puzzles, each one dug clue by clue with a fresh proof of uniqueness after every removal, then replayed technique by technique — finishes in about twenty milliseconds on an ordinary laptop. Pressing New puzzle here is instant in a way it never quite is on the diagonal or jigsaw boards, where a single grid can take the best part of a second to justify.

What a small board is actually good for

Two audiences, and they want opposite things from it. Someone learning gets a grid where the whole logical situation is visible at once: no need to write candidates in twenty squares to see a pattern in three, and a mistake shows up within a move or two instead of twenty minutes later. Someone experienced gets a puzzle that fits in the gap between two other things — a queue, a kettle, a train pulling in — and, on the Hard setting, concentrated exposure to the one family of techniques that a full grid rations out.

Everything the standard board does, this one does at six. Pencil marks arrange themselves two rows of three inside each square instead of three by three. The number pad runs 1 to 6 and keeps its count of how many of each digit are still to place. The Hint button names the deduction rather than handing over a digit, the share link carries the grid itself so it works with no account and never expires, and your game is stored under its own key, so a puzzle you start here survives a trip to the full-size board and back. The pack builder above prints the same grids as vector artwork, boxes three wide and two tall in heavier rule than the rest, with answers at the back.