Hard Sudoku
How hard puzzles are defined
A hard Sudoku here has 26 to 31 givens and needs at least one technique from the third tier: a naked triple, a hidden triple or an X-Wing. Everything from the easy and medium levels is still in play, but at some point the grid stops yielding to pairs and pointing, and only one of these wider patterns lets you continue.
| Hard level | Value |
|---|---|
| Techniques needed | Medium techniques + naked/hidden triple, X-Wing |
| Givens | 26–31 |
| Solutions | Exactly one |
| Notes needed | Yes, usually for the whole middle game |
Strategies for hard puzzles
1. Take full notes early
On a hard grid it pays to have every candidate written down once the singles dry up. Use the fill-in-all-candidates button if you like, then keep the notes clean as you go. The triple and X-Wing patterns are almost impossible to see without them.
2. Look for triples in units with few empty cells
Three cells of a row that together allow only 2, 6 and 8 must contain exactly those three digits, even if no single cell shows all three. Remove 2, 6 and 8 from the rest of the row. Units with four to six empty cells are where triples hide most often.
3. Scan one digit for an X-Wing
Choose a digit and find two rows where it has exactly two possible cells, and those cells line up in the same two columns. The digit must occupy one diagonal of that rectangle, so it can be removed from the rest of both columns. The same works with columns and rows swapped.
4. Revisit pairs after every elimination
A triple or X-Wing rarely places a digit directly. Its job is to remove a handful of candidates, after which a pair, a pointing pattern or a plain single usually appears. After each advanced step, run through the simple checks again before looking for the next big pattern.
How many pencil marks does one hard grid need?
One hard grid from the collection is solved in 58 steps: 54 of them place a digit and 4 only erase candidates. It has 27 givens, so 54 empty cells, and writing every candidate into every one of them gives 191 marks, about 3.5 per cell. The logic engine placed six singles and then got stuck, with 48 empty cells and 156 marks left on the board.
The next four steps are the erasing ones. Pointing removed 1 candidate, claiming removed 3 and then 3 more, and finally a naked triple removed 7. The triple sits in column 7: the cells in rows 2, 5 and 7 have candidates only among 1, 7 and 9, so those three digits belong to them and vanish from the other cells of the column. With the board down to 142 marks, row 4, column 7 (r4c7) was left with only a 4, digits started flowing again, and the last 48 steps were all singles.
Why some hard puzzles feel harder than others
The level tells you the hardest technique needed, not how often you need it. One hard grid may need a single X-Wing near the end; another may need triples three times. Your solving time will vary, and that is part of the fun. If you want a steady challenge every day, the Daily Sudoku is hard on Fridays and Saturdays.
Hard Sudoku questions
- Do hard puzzles ever require guessing?
- No. Every hard puzzle is solved by our logic engine using only the techniques listed on this page. If a grid needed trial and error, it would be rejected.
- What is an X-Wing in Sudoku?
- It is a rectangle formed by one digit: in two rows the digit can only go in the same two columns. Because the digit must use opposite corners, it can be removed from those columns everywhere else.
- How long does a hard Sudoku take?
- Usually between 15 and 40 minutes, depending on how quickly you spot the key pattern. Writing full notes early tends to save time overall.
- What comes after hard?
- Expert puzzles, which add the XY-Wing, Swordfish and simple coloring. The techniques guide explains each one with a diagram taken from a real puzzle.