Four techniques that solve 95% of hard sudoku puzzles

Hard sudoku does not require secret knowledge. It requires four techniques and the discipline to apply them in order — the rest is pattern recognition, and that arrives on its own after a few dozen boards.

1. Naked single

The simplest rule: if only one digit fits a cell, place it. It sounds trivial and it is — the catch is that a hard board has none of these at the start. They appear only after the other three techniques have done their work, and then they cascade.

Practical consequence: don't hunt for naked singles first. Hunt for them after every successful placement, because one digit can unlock five more.

2. Hidden single

The mirror image, and the technique that does most of the work on hard boards. Instead of asking "what can go in this cell", you ask "where in this box can the seven go".

Sudoku grid with one 3×3 box highlighted; sevens in two rows and two columns rule out every cell of that box except one — Four sevens outside the box leave exactly one place for a seven inside it — that is a hidden single

If the answer is "only here", you place it — even if three other digits would also fit that cell. This is where most players lose time: a cell with four candidates is not undecided if one of those candidates fits nowhere else in the box.

3. Naked pair

Two cells in the same row, column or box holding exactly the same two candidates — say only 3 and 8. You don't know which is which, but you know both digits live in those two cells. Therefore neither 3 nor 8 appears anywhere else in that unit.

A 3×3 sudoku box with pencil marks; two cells hold only the candidates 3 and 8, while threes and eights are crossed out in the remaining cells — Naked pair: since 3 and 8 occupy those two cells, they appear nowhere else in the box

A naked pair rarely places a digit directly. It removes candidates — and that removal creates a single somewhere else. If you play with pencil marks, this is the moment they pay for themselves.

4. Locked candidates

The technique that separates a medium board from a hard one. If every possible position for the digit 5 inside a box lies in a single row, then that box's five will end up in that row — so the rest of that row, outside the box, cannot contain a five.

A band of three sudoku boxes; both possible positions for a five in the first box sit in the same row, so fives are crossed out further along that row — Locked candidates: the box's five must land in the highlighted row, so it disappears from that row outside the box

It works in reverse too: if every position for a five in a row lies inside one box, the rest of that box is free of fives.

This is the only one of the four that requires deliberate searching. The other three eventually become automatic.

What you do NOT need

X-Wing, swordfish, XY-wing and the rest of the zoo have their fans, but our hard boards never require them. The generator rejects any puzzle that cannot be solved with the set above — so if you are stuck, it is not because you are missing an advanced technique. Usually you are missing one systematic pass over the boxes asking "where can this digit go".

How to get faster

Order matters. The fastest players work like this:

sweep digits 1 through 9, looking for hidden singles in boxes,
place naked singles wherever they appeared,
only when that dries up — pencil marks, naked pairs and locked candidates,
back to step 1, because every removed candidate changes the board.

The biggest time saving is not in the techniques themselves. It is in not jumping around the grid at random. A full pass over nine digits takes fifteen seconds and almost always beats a minute of staring at one box.

Try it on today's puzzle

The daily puzzle is the same board for everyone in the world and your time goes on a shared leaderboard — so you can see immediately what these four techniques are worth in practice. The techniques are also covered with worked examples in the sudoku strategy guide.