Hard sudoku
Puzzles that need triples, X-Wings or XY-Wings. Pencil marks recommended.
Puzzle
| 5 | 7 | |||||||
| 4 | 3 | 2 | 5 | |||||
| 8 | 2 | 1 | ||||||
| 7 | 1 | 4 | 3 | |||||
| 5 | 4 | |||||||
| 3 | 5 | 7 | ||||||
| 1 | 6 | 7 | ||||||
| 9 | 7 | 8 | 2 | |||||
| 6 |
Paused
Solved!
Keyboard shortcuts
- Arrow keys move between cells; Home and End jump to the start or end of the row.
- 1–9 enters a number (pressing the same number again clears it); Backspace, Delete or 0 clears the cell.
- N switches notes mode on or off; Shift + a number adds or removes a note.
- Ctrl + Z (Cmd + Z on a Mac) undoes; Ctrl + Y or Ctrl + Shift + Z redoes.
What “hard” means here
Hard puzzles need at least one technique beyond pairs and pointing: a naked or hidden triple, an X-Wing, or an XY-Wing. They usually start with fewer givens, around 25 on average and sometimes as few as 21, so the opening is slower too. In our hard bank, 90% of puzzles use an XY-Wing, 21% an X-Wing, 12% a naked triple and 4% a hidden triple. They lean heavily on the medium techniques as well: 78% use a pointing pair and 42% a naked pair.
The hard techniques
- Naked and hidden triples: the same idea as pairs, with three cells and three digits. The three cells do not all need all three candidates; together they must contain exactly three digits.
- X-Wing: a digit that can go in only two cells in each of two rows, and those cells line up in the same two columns. The digit must occupy two opposite corners of that rectangle, so it can be removed from the rest of both columns (or rows, the other way round).
- XY-Wing: a cell with two candidates (the pivot) that sees two other two-candidate cells (the pincers) sharing one digit, z. Whichever value the pivot takes, one pincer must be z, so any cell that sees both pincers cannot be z.
How to approach a hard sudoku
Full pencil marks are the key. Take every single first, then fill in candidates for every empty cell and keep them up to date (“Auto-remove notes” does this for you). Then work through the techniques from simple to advanced: pointing pairs and box/line reduction, naked and hidden pairs, triples, and only then the X-Wing and XY-Wing. Advanced patterns are much easier to spot once the simpler eliminations have thinned out the notes.
When you are looking for an XY-Wing, start from cells that have exactly two candidates. When you are looking for an X-Wing, pick one digit and check rows where it appears only twice. The hint button names the technique and unit first, so you can find the pattern yourself before asking for more.
Hard is still fair
None of these puzzles needs guessing or chains: if you get stuck, there is always a logical step from the list above. If you want the full reasoning for a puzzle, paste it into the solver, which explains every step. Ready for more? Expert sudoku adds the Swordfish, Jellyfish, XYZ-Wing and coloring.
Frequently asked questions
How many givens does a hard puzzle have?
21 to 36 in our hard bank, 25.1 on average. The level depends on the techniques needed, not on the number of givens.
Do hard puzzles ever need guessing?
No. Every puzzle has exactly one solution and can be solved by logic using the techniques listed for its level.
How do I get a new puzzle?
Press New puzzle under the grid. Your unfinished puzzle is saved and you can come back to it.
Can I print these puzzles?
Yes. Press Print under the grid for the current puzzle, or use the printable page for sheets of 1, 4 or 6 with an answer key.
What does the hint button do?
The first press names a technique and where to look, the second highlights the cells involved, and the third makes the move and explains it. If one of your numbers is wrong, the hint tells you that first.
Can I turn off mistake highlighting?
Yes. Highlighting of numbers that do not match the solution is off by default; switch it on under Options. Two equal digits in the same row, column or box are always marked.
Updated · Written by the NineByNine team