How to solve Sudoku

Seeing it. Look for a row, column or box with eight digits filled in and one gap. In the diagram, row 1 reads 1 to 8 from left to right and only the cell in column 9 is empty.

Using it. Write in the missing digit. Row 1 has everything except 9, so the green cell is 9. These are the quickest wins in any puzzle, so check for them before you start pencil-marking. They turn up again near the end of a solve, when one placement completes a line and sets off a run of others.

Seeing it. Pick an empty cell and list every digit already in its row, column and box. If eight of the nine are taken, the one left over is the answer. In the diagram the green cell is row 5, column 5. Row 5 already has 1, 5 and 7, column 5 has 2, 4 and 6, and the centre box has 8 and 9.

Using it. Place the digit. The cell can only be 3, so it is 3, whether or not 3 could still fit somewhere else in the row. You'll also see this called a sole candidate.

Seeing it. This time start with a digit, not a cell. Pick a unit and ask where that digit can go. In the diagram, the dots in the centre box mark cells that can't take 8. Only the green cell, row 5, column 5, is left.

Using it. Write 8 there, even if that cell still has other pencil marks. The box needs an 8 and there's nowhere else for it to go. The quickest way to find hidden singles is to take one digit at a time and sweep it across the whole grid, box by box. You'll also see this called a unique candidate.

Seeing it. Look inside one box at one digit. If every candidate for that digit sits in a single row or a single column, you have a pointing pair (or a pointing triple, with three). In the diagram, the top-left box can only take 6 in row 2, at columns 1 and 3.

Using it. Wherever the box puts its 6, it lands in row 2. So no other cell in row 2 can be 6. Cross out the 6s in row 2 outside the box: here, the ones in columns 5 and 8. The box "points" along the line its digit is stuck on.

Seeing it. This is pointing turned round. Look along a row or column at one digit. If every candidate for it falls inside a single box, the line claims that box. In the diagram, row 5 can only take 7 in columns 4 and 6, and both cells are in the centre box.

Using it. Row 5's 7 has to be in the centre box, and a box holds only one 7. So the box's cells outside row 5 can't be 7. Remove the crossed 7s at row 4, column 5 and row 6, columns 4 and 6.

Seeing it. Look across three boxes side by side at one digit. If two of those boxes keep the digit in the same two rows, you have this pattern. In the diagram, the first box has 6 only in rows 1 and 3, and so does the second box. The same idea works down three stacked boxes, using columns instead of rows.

Using it. Each row needs exactly one 6. The first two boxes use up rows 1 and 3 between them, so the third box has to put its 6 in row 2. Remove 6 from the third box's other rows: the crossed 6s at row 1, column 7 and row 3, column 9.

Seeing it. Find two cells in the same unit that have the same two candidates and nothing else. In the diagram, column 5 has two cells, at rows 3 and 4, that can each only be 4 or 7.

Using it. One of them is 4 and the other is 7. You don't know which yet, and you don't need to: no other cell in column 5 can be 4 or 7. Cross out the 4 at row 1 and the 7 at row 7. If the pair also shares a box, clear those two digits from the box as well.

Seeing it. Look for three cells in a unit whose candidates, put together, come to just three digits. Each cell doesn't need all three. In row 5 of the diagram, column 2 has 1/2, column 4 has 1/3 and column 6 has 2/3. That's only 1, 2 and 3.

Using it. Three cells and three digits means those cells will use up 1, 2 and 3 for the row. Remove all three digits from every other cell in row 5, which takes the 1 out of column 9. Players miss triples because they look for three cells that all show the same three digits. Most real triples look like this one, with each cell showing only two.

Seeing it. The same idea with four cells and four digits. In row 2 of the diagram, the green cells hold 1/3, 3/6, 1/9 and 6/9. Only 1, 3, 6 and 9 appear.

Using it. Those four cells take 1, 3, 6 and 9 between them, so clear those digits from the rest of the row. The 9 in column 9 goes. Quads are rare and easy to overlook. Learn pairs and triples first and come back to these.

Seeing it. A hidden pair is a naked pair in disguise. Two digits can only go in the same two cells of a unit, but those cells carry other candidates too, which hides the pattern. In row 6 of the diagram, 6 and 7 appear only in column 2 (6/7 plus a 2) and column 8 (6/7 plus a 5).

Using it. Row 6 needs a 6 and a 7, and only these two cells can provide them. So the cells must be 6 and 7, and anything else in them goes. Erase the 2 from column 2 and the 5 from column 8. As with hidden singles, you find these by checking one digit at a time, not one cell at a time.

Seeing it. Three digits that only appear in the same three cells of a unit. In row 4 of the diagram, 1, 3 and 7 show up only in columns 2, 4 and 7. Each of those cells carries one extra candidate as well: 8, 2 and 9.

Using it. The three cells have to supply 1, 3 and 7 to the row, which leaves no room for anything else in them. Remove the 8 from column 2, the 2 from column 4 and the 9 from column 7. Like a naked triple, each cell can show just two of the three digits: here 1/3, 1/7 and 3/7.

Seeing it. Four digits that only appear in the same four cells. In row 8 of the diagram, 1, 4, 6 and 9 appear only in columns 1, 3, 5 and 7.

Using it. Clear every other candidate from those four cells: the 8 from column 1, the 2 from column 3, the 3 from column 5 and the 7 from column 7. Hidden quads are the hardest pattern on this page to see directly. Here's a shortcut. If a unit has, say, seven empty cells and three of them form a naked triple, the other four cells always form a hidden quad. Spotting the small naked set is usually easier than spotting the large hidden one.