What makes a puzzle hard here
A hard puzzle on this page needs at least one of the advanced techniques below, and can be finished using only those techniques plus the basics. Our solver proves that before publication by solving each puzzle itself and recording what it used. Puzzles that would need forcing chains, uniqueness tricks or trial and error are discarded rather than labelled hard. So hard has a ceiling: it is demanding, but a clean logical path always exists.
Each puzzle is also checked by a second, independent solver to confirm it has exactly one solution.
The techniques you will meet
- Naked triple. Three squares in a unit whose candidates, combined, are only three digits. Those digits can be removed from the rest of the unit.
- Hidden triple. Three digits that only appear in three squares of a unit, so those squares cannot hold anything else.
- X-Wing. A digit that, in two rows, is confined to the same two columns. It can be removed from those columns everywhere else. The same works with rows and columns swapped.
- Swordfish. The three-row, three-column version of an X-Wing.
- XY-Wing. A pivot square with two candidates, XY, and two pincer squares XZ and YZ that each see the pivot. Any square that sees both pincers cannot hold Z.
Not every puzzle uses all of them. Many hard puzzles turn on a single X-Wing or one well-placed triple, with the rest of the grid falling to singles and pairs afterwards.
How to approach a hard puzzle
Fill in every naked and hidden single first, then write full candidate lists for the remaining squares. Hunt for pairs and triples to prune those lists. When progress stops, look for a digit with exactly two candidates in two different rows: that is where X-Wings hide. If you have cleared singles, pairs, triples and fish and are still stuck, look for an XY-Wing. It is almost always the key that is left.
Printing tips
Candidate lists need room. Choose one puzzle per page for large print, or two per page if you want a pair of puzzles on one sheet. Four per page is tight for hard puzzles unless your handwriting is small. Keep the answer key for checking a finished grid rather than for hints. An answer page next to a hard puzzle is a temptation.
Other levels
Need a warm-up? Medium sudoku uses the same basics without the advanced patterns. Want this every weekend? The daily sudoku is hard on Saturday and Sunday.