Expert Sudoku

Sudoku is played on a grid of 9 rows and 9 columns, split into nine 3×3 boxes. Some cells start with a digit (the clues). You fill in the rest.

Expert puzzles start with as few clues as our generator could remove while keeping a single solution.

• Each row holds the digits 1 to 9, each exactly once.
• Each column holds the digits 1 to 9, each exactly once.
• Each 3×3 box holds the digits 1 to 9, each exactly once.
• The clues can't be changed. The puzzle is solved when every cell is filled and no digit repeats in a row, column or box.

Each expert puzzle here gets stuck after singles, pointing and pairs. It needs at least one of: a naked or hidden triple or quad, an X-Wing, a Swordfish, a Jellyfish, an XY-Wing or an XYZ-Wing.

We don't list puzzles that need trial and error or chains longer than these. Our own solver, using only these named techniques, finished every one, so a logical path always exists.

X-Wing: look at one digit. If on two rows it can only go in the same two columns, the four cells form a rectangle and the digit takes two opposite corners. Either way both columns are used up, so the digit can be removed from those columns everywhere else. Swordfish is the same idea with three rows and three columns, Jellyfish with four.

XY-Wing: find a cell with two candidates, X and Y (the pivot). It sees one cell with X and Z and another with Y and Z. If the pivot is X, the first cell is Z; if it is Y, the second cell is Z. So any cell that sees both of those cells can't be Z.

XYZ-Wing: the pivot has X, Y and Z, and sees cells with X and Z and with Y and Z. Z can be removed from any cell that sees all three.

Triples and quads: three cells of a unit that between them can only hold three digits (not every cell needs all three) lock those digits in, just like a pair.

Tap or click a cell, then a number below the grid. On a keyboard, the arrow keys move between cells, 1 to 9 fill a cell, and Backspace or Delete clears it.

Notes turns the number buttons into pencil marks: small digits that remind you what can still go in a cell. Press N to switch on a keyboard, or hold Shift while you type a digit. When you place a digit, it is taken out of the notes in its row, column and box.

Undo takes back as many steps as you like. Hint first points out any wrong digit, then shows the next step a person could find, with the technique and why it works; press Hint again to fill it in. "Show mistakes" marks a wrong digit in red as soon as you enter it; switch it off to check your own work. Your game is saved in this browser, so you can close the page and come back.

Fill in complete notes early. Then always try the easy steps first: after each elimination, look again for singles and pairs before you search for a wing.

Search for XY-Wings among cells with two candidates; they are the easiest pattern to spot on a crowded grid. For fish, pick the digit with the fewest notes left and look at where it can go on each row and column.

If you are stuck, Hint names the technique the next step needs and marks its cells, which is a good way to learn the patterns.