SudokuBoku

X sudoku Diagonal 9×9

Classic rules, plus two lines drawn corner to corner — and a solve that punishes anyone who stops seeing them.

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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

X puzzles for the printer

Diagonal grids as a PDF, generated on your own machine with the crossing lines inked lightly beneath the digits. On paper the diagonals are even easier to lose track of than on screen, which is exactly what makes a printed batch such good training.

Difficulty

Two lines you keep forgetting

An X grid — diagonal sudoku, to give it its plainer name — changes nothing you can see in the empty cells. Rows still want 1 to 9, columns still want 1 to 9, and the nine boxes sit exactly where classic left them. The whole variant lives in two additional houses: the falling diagonal from R1C1 down to R9C9, and the rising diagonal from R9C1 up to R1C9. Each of those lines must carry all nine digits, once each, like any row would.

Seventeen squares answer to the new masters — the two lines overlap on the centre square — and that is the entire rulebook. Which is precisely the trap. There is nothing to learn here, only something to remember: years of classic solving have trained your eye to sweep along rows and columns and around boxes, and never once corner to corner. The most common X mistake is not a faulty deduction. It is a flawless classic deduction made two squares off a diagonal that slipped out of your attention a quarter of an hour ago.

The seventeen shaded squares belong to the two diagonal houses as well as their rows, columns and boxes. The centre square sits on both lines at once, and wears the deeper wash for it.

What a diagonal does to seeing

Sudoku is a game about which squares constrain which. In classic, the answer is uniform: every square belongs to three houses and directly restricts twenty others. Here the symmetry breaks. A square on one diagonal belongs to four houses and restricts twenty-six; the centre square belongs to five — row, column, box and both lines — and restricts thirty-two of the eighty squares around it. No cell on any board this site serves is watched from more directions.

R1C1 and R9C9 sit a whole grid apart, yet on this board they can never share a digit.

That long-distance sight is what makes the variant feel eerie in the best way. Opposite corners police each other. A digit dropped casually into R3C3 quietly forbids the same digit at R8C8, five rows and five columns away, through territory that classic instinct insists is unrelated. Experienced X solvers exploit the asymmetry deliberately: the diagonal squares — above all the centre — are where a placement buys the most, so that is where they aim their effort first.

The moves the diagonals bring

A scan that runs corner to corner

The first new habit is the cheapest: treat each line as a house you sweep, the way you already sweep a row. Ask where 5 can still fall on the falling diagonal. Because those nine squares thread through five different boxes and cross the busiest part of the grid, their candidates thin out fast, and a digit with a single home on a diagonal turns up more often than you would guess. The hint button here phrases such finds as diagonal scans, so the button teaches the habit even while it helps.

The crossover

The signature move is the variant's own version of locked candidates. A box and a diagonal can share up to three squares, and whenever every remaining spot for a digit inside the box lands on those shared squares, the diagonal's copy of that digit is trapped there — so the digit vanishes from the rest of the line, sometimes clear across the grid. Run the same logic the other way and a digit whose diagonal homes all sit in one box wipes itself from that box's other squares.

Corner a digit onto the diagonal inside one box, and the whole line is settled by it.

If the top-right box's last places for a digit are the three tinted squares, the rising diagonal must take that digit from one of them — and the amber squares along the rest of the line all lose it.

Our grader treats the crossover as its own rung on the technique ladder, and the hint panel names it — Diagonal Interaction — whenever it is the gentlest move on the board.

The deduction we switched off

One classic technique had to be handled with care. The unique-rectangle family reasons from the puzzle's promised single solution: four squares in a rectangle can't be left holding the same two candidates, the argument goes, because swapping the pair would give a second solution. On this board that argument has a hole. If a corner of the rectangle lies on a diagonal, the swap could break the diagonal's own 1-to-9 rule — meaning the "impossible" pattern may be entirely legal, and the elimination built on it unsound. So the engine behind our hints checks every rectangle it finds and simply declines the move when any corner touches either line, while still using it freely elsewhere. If you like uniqueness arguments in your own solving, carry the same caution onto X grids.

Fewer clues, the same ruler

Every puzzle on this page is built in your browser while you wait: a full grid is generated under the diagonal rules, clues are removed one by one with a proof after each removal that exactly one solution survives, and the result is graded by replaying it with the same ladder of human techniques that grades every board on this site. The labels mean here what they mean everywhere else — Easy never needs more than naked singles, Medium brings the hidden single, Hard demands subsets, locked candidates and the crossover, and Expert calls for wings, fish and colouring.

You will notice the grids start slightly emptier than their classic cousins. Twenty-nine houses constrain a grid harder than twenty-seven, so a dig reaches the same technique with fewer givens — our generator hits a Medium X grid around four clues leaner than a Medium classic. You'll also notice the ladder stops at Expert: the Evil and Extreme labels on the classic board are backed by large hand-verified puzzle banks, none of which exist for diagonal grids, and we won't stretch a label past what we can prove. The deep end still lives on the evil and extreme pages.

Reading the shading

On screen the seventeen diagonal squares wear a quiet sand wash, and the centre square — claimed by both lines — wears it a shade deeper. The wash is structure, not a highlight: it borrows the tone of the board's rules rather than any of the colours that carry meaning here, and when you select a square the highlight tints layer over it instead of replacing it, so the X never blinks out of view mid-thought. Losing sight of the diagonals is this variant's whole failure mode, and the board is built to make that hard. Tap any washed square and its entire line lights up alongside its row, column and box — the quickest way to grow the corner-to-corner reflex.

Links and paper

The share button copies a link that carries the givens and the variant name and nothing more — the diagonals never move, so no layout needs to travel with them, and X links stay short. A link opened on someone else's machine is checked under the diagonal rules before it is trusted, and their progress is stored apart from any game already running on this page. The pack builder above does the print translation: light corner-to-corner rules under crisp vector digits, with the same lines repeated on the answer key so a checked solution can be checked against all twenty-nine houses.