SUDOKU

Hard Sudoku: how to solve it

Hard puzzles stop giving way to singles alone. After the opening moves the grid locks, and progress comes from writing every candidate and removing the ones that patterns rule out.

What changes at the hard level

In easy and medium puzzles you can usually find the next digit by scanning. In a hard puzzle there are long stretches where no cell has a single option. That is the signal to switch from looking for placements to looking for eliminations: every candidate you remove brings a cell closer to one remaining digit.

A routine that works

1. Place every hidden and naked single you can find.
2. Write the full list of candidates in every empty cell. Partial notes hide the patterns you need.
3. Go box by box and look for locked candidates: a digit whose candidates in a box sit in one row or column (pointing), or a row or column whose candidates sit in one box (claiming).
4. Scan each row, column and box for naked and hidden pairs and triples.
5. For each digit, look for two rows where it has exactly two possible cells in the same two columns. That is an X-Wing.
6. Every time you place a digit, update the notes in its row, column and box, then return to step 1.

Techniques you will need

The numbers are each technique's Sudoku Explainer (SE) rating: the higher the number, the harder the step.

• Pointing and claiming (2.6–2.8): remove a digit from a row, column or box because it must sit in the overlap.
• Naked and hidden pairs (3.0 and 3.4): two cells that must hold two digits clear those digits, or other candidates, from the unit.
• X-Wing (3.2) and Swordfish (3.8): a digit confined to the same columns in two or three rows is removed from the rest of those columns.
• Naked and hidden triples (3.6 and 4.0): the same idea as pairs, with three cells.
• XY-Wing (4.2): three two-candidate cells that together remove a digit from any cell seeing both ends.

Common traps

• Hunting for an X-Wing before checking for simple pairs. Try the easier patterns first; they appear far more often.
• Forgetting to update notes after a placement. One stale candidate can hide a single for a long time.
• Guessing. A fair hard puzzle can always be solved by logic; if you are stuck, there is a pattern you have not checked yet.