SudokuBoku

Expert sudoku

At this level the answer stops being inside any one row, column or box. You start looking at the geometry of the whole grid.

Easy Medium Hard Expert Evil Extreme

00:00 Mistakes 0
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

What actually changes

Everything up to hard is local. A naked pair lives in one row. Locked candidates live in the overlap of a box and a line. You can find them by examining one unit at a time.

Expert patterns don't work like that. They're built from squares in different corners of the grid that have no unit in common at all, connected only by the logic of "if this one isn't the digit, that one must be". Learning them is less about memorising shapes and more about learning to see the grid as a network.

Every expert puzzle here is verified to need at least one of the patterns below — and verified to be solvable without going deeper than them.

X-wing

Find a digit that appears in exactly two squares of one row, and exactly two squares of another row, with all four sitting in the same two columns. Those four squares form a rectangle.

Whichever way it resolves, the digit ends up in one corner of the rectangle on each row, and therefore in both of those columns. So it can be deleted from those two columns everywhere else. Two rows of information, converted into two columns of eliminations.

Skyscraper

A near-relation with a friendlier shape. Take a digit with exactly two homes in each of two rows, where one pair of those homes shares a column — that shared column is the base.

The two remaining squares are the roof. One of them must hold the digit, so any square seeing both roof squares can lose it. It's easier to spot than an X-wing because you only need the base to line up, not all four corners.

Two columns with two homes each for a digit, the lower pair lined up as the base. One roof square must take it, and the two squares that see both roofs cannot.

The wings

These are built from squares holding exactly two candidates, and they're where the "if… then" reasoning becomes explicit.

An XY-wing uses a pivot holding X and Y, which sees one square holding X and Z, and another holding Y and Z. Whichever the pivot turns out to be, one of the other two is forced to Z — so anything seeing both of them cannot be Z.

An XYZ-wing is the same trick with the pivot holding all three digits. Because the pivot itself might be the Z, the eliminations are restricted to squares that see all three, which makes it rarer but no harder to understand.

A W-wing uses two squares holding the same pair, linked by a unit where one of the digits has exactly two homes — one seeing each square. That link forces the pair to split, and any square seeing both loses the other digit.

Simple colouring

Pick one digit and find the units where it has exactly two possible squares. Each of those is a strong link: one of the two is the digit. Chain them together and colour alternate ends, and you have a network of "if this is true, that is false".

Two payoffs. If two squares of the same colour ever share a unit, that colour is impossible and every square wearing it loses the digit. And any square outside the chain that sees both colours can lose it too, because one colour is always correct.

Unique rectangle

The odd one out, because it reasons about the puzzle rather than the digits. If four squares across two rows, two columns and two boxes all held the same two candidates, the grid would have two valid solutions — you could swap them. Our puzzles are verified to have exactly one, so that configuration cannot happen, and you can eliminate whatever would bring it about.

Some solvers consider this a cheat, since it uses a property of the puzzle rather than the numbers. It's sound here because uniqueness is guaranteed at generation, not assumed.

How to hunt rather than stare

These patterns don't reveal themselves to a general sweep. Go looking for one specific thing at a time: pick a digit, mark every square that can still hold it, and see whether the shape suggests a rectangle or a chain. Then the next digit. Grinding through nine digits deliberately is far faster than waiting for a pattern to catch your eye.

If you'd rather see one worked, ask for a hint — it names the pattern and highlights the squares involved, which is a much quicker way to learn what an X-wing looks like in the wild than reading another diagram.

Better still, practise them one at a time. The technique trainer drops you straight into a position where an X-wing is the only move left, pencil marks already written, so you skip the forty moves of scanning that normally stand between you and the interesting part. It does the same for the skyscraper, the XY-wing and colouring.

Beyond here

Evil keeps the same style of reasoning but pushes to swordfish and almost locked sets. Extreme abandons the ladder altogether.