Expert Sudoku
Play it here or print a sheet. The hardest level published, and the last one still honestly solvable by reasoning — anything beyond it would need guessing.
Print a sheet of 6
Six stern puzzles and their answers, on separate sheets so a puzzle cannot be spoiled by the page it is on.
The puzzles
Puzzle 1 — Stern 6 9 8 1 7 1 9 8 3 7 6 3 1 7 5 9 8 4 7 7 9 2 8 1 3 8 5 6 Puzzle 2 — Stern 2 3 8 4 6 8 6 5 3 2 5 9 1 4 3 5 7 3 8 6 1 2 2 4 7 Puzzle 3 — Stern 9 6 9 4 5 1 7 6 5 2 9 2 9 5 6 4 4 9 6 6 2 7 4 5 1 3 8 6 1 2 Puzzle 4 — Stern 7 2 1 8 6 4 9 3 7 2 9 6 6 5 3 8 9 9 1 3 8 6 2 9 8 5 1 8 7 Puzzle 5 — Stern 8 2 1 3 4 7 5 9 3 7 8 8 4 7 4 9 3 3 6 2 8 5 4 7 1 4 6 2 Puzzle 6 — Stern 3 4 8 7 1 5 6 2 3 1 4 8 7 4 9 1 2 5 7 8 3 4 7 5 2 7
The answers
Puzzle 1 — Stern (answer) 6 9 5 8 4 1 3 7 2 2 7 1 5 9 3 6 4 8 4 8 3 2 6 7 9 1 5 7 4 2 9 1 6 5 8 3 1 3 6 7 8 5 4 2 9 8 5 9 4 3 2 1 6 7 3 2 8 6 5 4 7 9 1 5 6 7 1 2 9 8 3 4 9 1 4 3 7 8 2 5 6 Puzzle 2 — Stern (answer) 7 6 2 9 5 3 4 8 1 4 5 9 2 8 1 6 7 3 1 8 3 6 7 4 9 2 5 6 1 4 3 9 2 8 5 7 9 7 5 8 1 6 2 3 4 2 3 8 5 4 7 1 9 6 3 4 7 1 2 8 5 6 9 8 9 1 7 6 5 3 4 2 5 2 6 4 3 9 7 1 8 Puzzle 3 — Stern (answer) 8 2 5 7 1 9 3 6 4 3 6 9 4 8 2 5 1 7 1 7 4 6 5 3 2 8 9 2 9 1 8 4 6 7 3 5 7 5 6 9 3 1 4 2 8 4 3 8 5 2 7 1 9 6 6 8 2 3 7 4 9 5 1 5 4 3 1 9 8 6 7 2 9 1 7 2 6 5 8 4 3 Puzzle 4 — Stern (answer) 5 4 9 7 2 3 1 8 6 7 2 6 8 4 1 9 5 3 8 1 3 9 5 6 7 2 4 2 9 5 6 1 4 3 7 8 1 6 7 5 3 8 4 9 2 3 8 4 2 7 9 6 1 5 9 3 8 1 6 2 5 4 7 6 7 2 4 9 5 8 3 1 4 5 1 3 8 7 2 6 9 Puzzle 5 — Stern (answer) 7 8 2 4 6 5 9 1 3 4 1 3 8 7 9 5 6 2 6 5 9 1 3 2 4 7 8 5 7 6 9 1 3 2 8 4 8 2 1 7 5 4 3 9 6 9 3 4 2 8 6 7 5 1 3 6 7 5 2 1 8 4 9 2 9 5 6 4 8 1 3 7 1 4 8 3 9 7 6 2 5 Puzzle 6 — Stern (answer) 3 1 6 4 2 5 8 7 9 8 2 9 3 6 7 5 1 4 4 5 7 1 8 9 6 2 3 2 3 1 5 4 8 7 9 6 9 8 5 2 7 6 3 4 1 7 6 4 9 1 3 2 5 8 5 7 8 6 9 4 1 3 2 6 4 2 7 3 1 9 8 5 1 9 3 8 5 2 4 6 7
Box/line reduction, the converse argument
A pointing pair reasons from a box out to a line. Box/line reduction reasons the other way: if every square in a row that could hold a digit happens to sit inside one box, then that digit is in that row within that box — so it can be removed from the rest of the box.
The two are mirror images and they are easy to confuse, which is most of what makes this level hard. Keeping them straight is a matter of asking which unit you are certain about: with a pointing pair you are certain about the box; here you are certain about the line.
Together they cover the whole of what this site publishes. There are harder techniques — X-wings, swordfish, chains — and they are deliberately not here, for the reason in the next section.
Where this site stops, and why
The next tier of techniques is real and people do learn them, but a puzzle requiring them is a poor printed puzzle. They demand extensive candidate bookkeeping that is genuinely unpleasant in pen, and the failure mode is a wrong entry twenty moves earlier that cannot be found.
The more common failure is worse: a generator advertises "evil" or "diabolical" and ships a puzzle that simply cannot be solved by reasoning at all. The honest description of that puzzle is not that it is hard — it is that it is broken, and no amount of skill will finish it without a guess.
So the ceiling here is the hardest level that stays solvable by a technique somebody can learn from a paragraph. That is a smaller claim than most Sudoku sites make, and it is one that holds.
Finishing an expert grid
Expect long stretches with no placement at all. At this level most moves are eliminations, and it is normal to remove candidates for several minutes before a single digit goes in.
Work the techniques strictly in order every time you stall — singles, naked pairs, pointing pairs, box/line — and restart the sequence from the top after every change. The temptation to keep applying the technique that just worked is strong and it is usually wrong.
If you are truly stuck, the deduction available is one of four things, and one of them is there. That is a guarantee about the puzzle rather than encouragement: it was verified before printing.
Common questions
What is box/line reduction?
When every square in a row or column that could hold a digit sits inside one box, the digit must be in that line within that box — so it can be removed from the rest of the box. It is the converse of a pointing pair.
Are there harder Sudoku levels than expert?
Techniques harder than these exist, but a printed puzzle requiring them is unpleasant rather than interesting, and many puzzles advertised that way cannot be solved by logic at all. This site stops at the hardest level that is still genuinely solvable.
Is expert Sudoku ever unsolvable without guessing?
Not here. A puzzle that a human-technique solver could not finish was discarded during generation rather than relabelled as harder.