Stuck on a Sudoku? What to look for next

1. Sweep each digit for singles

   Take the digits 1 to 9 in turn and cross-hatch every box, row and column for a hidden single. Then look for cells with only one candidate left (naked singles). Most stalls end here, because one missed single is easy to overlook.

2. Fill in every pencil mark

   Past the singles, you need complete candidates. Write every possible digit in every empty cell, and clear marks as you place digits. Half the "stuck" moments come from an out-of-date mark.

3. Look for pairs

   Two cells in one unit with the same two candidates form a naked pair. A digit whose places in a box sit on one line is a pointing pair. Both clear candidates and usually open up a new single.

4. Check lines against boxes, and triples

   If a digit's places in a row all sit in one box, the box loses it elsewhere (box/line reduction). Three cells that share three candidates make a naked triple.

5. Try an X-Wing, one digit at a time

   For each digit, find rows where it has exactly two places. Two rows with those places in the same two columns make an X-Wing.

6. Then the Fiendish moves

   A Swordfish (an X-Wing on three lines), the XY-Wing and XYZ-Wing, simple colouring and the unique rectangle. You rarely need more than one of these in a puzzle.

Before you go further

• Check for a mistake. A cell with no candidates, or a digit with nowhere to go, means an earlier digit was wrong.
• Do not guess. A guess that works teaches nothing, and one that fails is hard to undo on paper.
• Take a break. Patterns you missed often jump out after five minutes away.