How Sudoku works
Hard puzzles start with 30 clues and will stall you early. Scanning gets you a handful of placements and then stops, and from that point the grid only opens up through candidate elimination. Full pencil notes are effectively mandatory: you cannot find a naked pair you have not written down.
The two techniques that matter most here are naked pairs and box-line reduction. A naked pair is two cells in the same unit holding exactly the same two candidates, which lets you strike those digits from every other cell in that unit. Box-line reduction is the mirror image: when a digit within a row is confined to one box, it can be eliminated from the rest of that box.
Budget 20 to 40 minutes and expect to pause. The characteristic experience of a hard grid is long stretches of no progress broken by one elimination that cascades into eight or ten placements. If you are stuck, re-scan for pairs before anything else.
Hard Sudoku at a glance
| Hard | |
|---|---|
| Starting clues | 30 |
| Typical solve time | 20 – 40 minutes |
| Techniques needed | Naked pairs, box-line reduction |
| Empty cells | 51 |
| Pencil notes | Required |
How to solve faster
- Fill in complete candidate notes before you start eliminating. Hard grids cannot be solved by scanning, and you cannot find a naked pair you have not written down. Budget the first few minutes for notation and treat it as part of the puzzle.
- Hunt naked pairs first when stuck. Two cells in one unit holding exactly the same two candidates lets you strike both digits from every other cell in that unit. This one technique unlocks the majority of hard puzzles.
- Apply box-line reduction in both directions. If a digit in a row is confined to one box, remove it from the rest of that box. The reverse also holds. Solvers routinely check one direction and forget the other.
Frequently asked questions
What techniques does hard Sudoku require?
Primarily naked pairs and box-line reduction. Basic scanning and hidden singles will get you a handful of placements and then stall, and the rest comes from candidate elimination.
Do I have to use pencil notes on hard puzzles?
Effectively yes. Every technique needed above hidden singles operates on written candidate lists, so trying to hold them mentally caps you well short of finishing.
Why do I stall so often on hard Sudoku?
Because that is the shape of the level. Hard grids characteristically give you long stretches of no progress broken by one elimination that cascades into eight or ten placements. Stalling is not a sign you are doing it wrong.
How long should a hard Sudoku take?
Twenty to forty minutes is typical. Experienced solvers using full notation manage ten to fifteen. Taking an hour on a hard grid is completely normal while the techniques are still new.