Hard sudoku – today's 4 free puzzles

Hard sudoku is a training ground for technique

If scanning plus candidate notes carries you through medium, hard is the first level where you genuinely need techniques that eliminate candidates. The flip side is reassuring: master the three tools below — locked candidates, naked pairs and hidden pairs — and every puzzle at this level yields to pure logic. Trial and error is never required. Think of hard sudoku as both a test and the best possible practice range, because the candidate discipline you build here is exactly what you will lean on later when you go hunting for X-Wings.

The three techniques to learn first

Locked candidates

Inside one box, if the candidates for digit X survive in only a single row (or a single column), then X must land in that row within that box. Which means you can delete X from the rest of that row in the other boxes. Nothing gets confirmed and yet the board becomes simpler, that indirect squeeze is the doorway to intermediate play, and it is the highest-frequency technique in the set.

Naked pairs

If two cells in the same row, column or box carry exactly the candidates "3 and 7", then 3 and 7 are used up by those two cells, and you can erase them from every other cell of that unit. With candidates written out, you find these visually: the same two digits sitting side by side. The same reasoning extends to three cells and three digits (a naked triple), which occasionally decides the endgame of a hard grid. Learn to see pairs instantly first.

Hidden pairs

The mirror image of the naked pair. If, in one unit, the digits 4 and 9 can only go into two cells, then those two cells belong to 4 and 9, so every other candidate written in them can be erased. They are buried among other candidates and therefore harder to see, but they are precisely the move that unlocks a cluttered mid-game.

Note-keeping is what makes the techniques work

Most people who stall at this level are not missing the techniques; their notes have drifted and the patterns have become invisible. Three habits fix that. First, take the time at the start to write accurate candidates for every cell — inaccurate opening notes make everything after them castles in the air. Second, when you confirm a digit, erase in a fixed order: row, then column, then box. A fixed order all but eliminates missed erasures. Third, immediately after you eliminate candidates with a pair or a lock, re-examine that unit: one elimination very often cascades straight into the next placement.

Which technique should you look for first?

The usual question once all three are learned is what order to search in. Go cheapest first: locked candidates → naked pairs → hidden pairs. Locked candidates can be checked mechanically, box by box, and they occur most often. Naked pairs jump out of the notes visually. Hidden pairs require counting, for each digit, how many cells in a unit can host it: a heavier search. Fix that loop as your routine and the paralysing "what do I even do now?" moment disappears; the puzzle starts to have a rhythm. In time you'll develop a nose for it, sensing from the shape of the notes that a pair is probably lurking.

Target times and how to measure progress

On this site's hard puzzles, twenty to thirty minutes with notes is normal, and dipping under fifteen means intermediate graduation is in sight. Time matters less than one question, though: did you solve it without guessing? To improve, make the four hard puzzles in the daily 20 a habit, then binge a batch from the puzzle archive at the weekend. If you like thinking on paper, the printable sheets are there. Times bounce around from day to day, so watch your weekly average rather than any single run. Once the three techniques appear to you without effort and without guessing, the door to expert sudoku — where the X-Wing lives — is already open.