A note on the examples
Cells are named the way the game’s hints name them: R3C8 is row 3, column 8, counting rows from the top and columns from the left. Boxes are numbered 1 to 9 from the top left, left to right, so box 5 is the centre box. A unit is any row, column or box, and each must end up holding 1 to 9 exactly once.
How our puzzles are graded
Every puzzle in our Sudoku has exactly one solution. The generator starts from a complete grid and removes clues, in 180° symmetric pairs where it can. After each removal it checks that the solution is still unique, then runs a second solver that uses only human techniques. If that solver can’t finish, or needs a technique above the chosen level, the clue goes back.
So a level is defined by the techniques it needs, not by how many cells are empty:
- Easy: naked and hidden singles only; the generator stops at about 40 clues. No notes needed.
- Normal: adds pointing pairs and claiming (box-line reduction); about 32 clues.
- Hard: adds naked and hidden pairs and triples and naked quads; about 27 clues. Notes become practically necessary.
- Expert: adds X-Wing, XY-Wing and Swordfish; about 21 clues.
Effort counts too
A second measure adds up effort. Each technique has a cost, so a puzzle that needs forty hidden singles scores higher than one that needs twenty, even though both use the same techniques. The difficulty shown in the header is the grade the puzzle actually received. When it differs from the level you picked — in a sample of 300 puzzles per level, about one Hard or Expert puzzle in six — the level you asked for is shown underneath in small type, and your record is still filed under the level you picked.
Scanning
Scanning, sometimes called cross-hatching, finds most of the early digits. Pick one digit and one box. Every row and column that already contains that digit rules out its cells inside the box. If only one cell is left, the digit goes there.
Worked example: you are placing 7 in box 1 (rows 1–3, columns 1–3). Row 1 has a 7 in box 3 and row 2 has a 7 in box 2, so rows 1 and 2 of box 1 are out. A 7 further down column 1, at R6C1, rules out R3C1. If R3C2 is a given, the only cell left is R3C3, and that is the 7.
Work digit by digit, starting with the digits already on the board most often, because they rule out the most cells. The game helps with this: selecting a filled cell highlights every cell holding the same digit, the selected cell’s row, column and box are shaded, and each number button shows how many of that digit are still to place, with a ✓ once all nine are down.
Naked singles and hidden singles
A naked single is a cell with only one possible digit. If the row, column and box of R5C5 between them already contain 1, 2, 3, 4, 6, 7, 8 and 9, then R5C5 is 5.
A hidden single is the same idea seen from the digit’s side. The cell may have several candidates, but within one unit a particular digit fits in only one cell. If 3 is blocked everywhere in row 4 except R4C7, then R4C7 is 3, even though 6 and 8 would also fit there on their own. Scanning finds hidden singles, and they are the step beginners miss most often, because the cell itself looks undecided.
When you select an empty cell, the line above the board lists the digits its row, column and box still allow, and the number buttons for the other digits are greyed out. If that line shows a single digit, you are looking at a naked single. Easy puzzles never need more than these two techniques.
Pencil marks
From Normal upward you will reach positions with no visible single, and you need to write candidates. Notes are the small digits inside a cell: switch Notes on (or press N), or hold Shift and press a digit to write a note directly.
Two chores are handled for you. When you place a correct digit, it is removed from the notes of every cell in the same row, column and box; a wrong digit clears nothing. And because the number buttons are disabled for digits already placed in the cell’s row, column or box, you can’t tap in a note the placed digits already exclude.
Once singles run dry, fill the notes for a whole unit at a time and keep them complete. Every technique below depends on knowing all the candidates in a unit; one missing note can make a triple look like a pair, or hide an X-Wing entirely.
Naked pairs and triples
Worked example: in row 6, R6C2 and R6C8 both have exactly the candidates 4 and 9. One of them is 4 and the other is 9, whichever way round, so no other cell in row 6 can be 4 or 9, and those notes can be erased. If the two cells also share a box, the same removal applies inside the box.
A naked triple is three cells in one unit whose candidates together contain only three digits. Each cell doesn’t need all three: {2,5}, {2,7} and {5,7} form a triple, and 2, 5 and 7 can be removed from the rest of the unit. Our grader also uses naked quads, four cells sharing four digits.
Hidden pairs and triples
Hidden subsets work from the digits. Suppose that in box 5 the digits 1 and 6 can only go in R4C4 and R5C6. Those two cells must hold 1 and 6 between them, so every other candidate in those two cells can be erased, even if each shows four or five notes. A hidden triple is three digits confined to the same three cells of a unit.
Pairs, triples and quads are the Hard toolkit. The grader ranks a hidden pair above a naked pair, because the digits that matter are buried among other candidates.
Pointing pairs and box-line reduction
These connect a box with a line. Pointing: if every candidate for 8 in box 1 lies in row 2, say at R2C1 and R2C3, then the 8 of box 1 is somewhere in row 2, so 8 can be removed from the rest of row 2, R2C4 to R2C9.
Box-line reduction, called Claiming in the game, is the mirror image. If every candidate for 4 in column 7 lies inside box 9, at R7C7 and R9C7, then column 7’s 4 is inside box 9, so 4 can be removed from the other cells of box 9.
Neither places a digit directly. They remove candidates, and the removal usually exposes a single. These are the hardest techniques a Normal puzzle can require.
X-Wing and beyond
Worked example: in row 2, the digit 6 can only go in columns 3 and 8, and in row 7 it can also only go in columns 3 and 8. Either R2C3 and R7C8 are 6, or R2C8 and R7C3 are. Both ways, columns 3 and 8 get their 6 from rows 2 and 7, so 6 can be removed from every other cell in those two columns. The same pattern works with two columns as the base and rows as the targets.
Swordfish stretches this to three lines sharing three positions. XY-Wing uses three cells with two candidates each: a pivot {X,Y} that sees one wing {X,Z} and another wing {Y,Z}. Whichever digit the pivot takes, one of the wings becomes Z, so any cell that sees both wings cannot be Z. Only an Expert puzzle may require these three, and they are practically impossible to spot without complete notes.
You never need to guess
Because every puzzle was built so the human-technique solver can finish it, a logical next step always exists somewhere in this list: naked single, hidden single, pointing, claiming, naked pair, hidden pair, naked triple, hidden triple, naked quad, X-Wing, XY-Wing, Swordfish. When you are stuck, go down the list in that order instead of trying a digit.
Guessing is also expensive here. A mistake is any digit that differs from the solution, not only one that clashes with a visible digit, so a wrong guess is flagged at once: the cell shakes, the digit turns red with a wavy underline, and the mistake counter goes up. Undo removes the digit but never the mistake. In solo play, mistakes are only counted. In a Duel, three mistakes lose on the spot, and if the 12-minute limit runs out, the player with more correctly filled cells wins, with fewer mistakes as the tiebreak.
Using the three hints
A solo puzzle allows three hints. A hint is counted when you open it, not when you apply it, because the panel already states the conclusion. The panel is titled with the technique’s name, gives the result first — such as 'R3C8 is 2' or '2 can be removed from 3 cells' — and then explains why, while the cells it relies on light up on the board. 'Place it' or 'Update notes' applies it.
The hint always returns the easiest technique that makes progress, in the order listed above. If it says Hidden Single, there was nothing harder to find, which tells you where to look next time. It works from the digits on the board, not from your notes, so it can point at a pair you haven’t noted yet. If a digit on the board is wrong, the hint asks you to remove it first, and that reminder doesn’t use up a hint.
A daily puzzle solved with hints is not ranked. When a puzzle ends, a 'Review techniques' button replays each technique you were hinted, using the exact position, the highlighted clue cells and three choices to pick from. Reviews you haven’t completed come back after later puzzles. Duels have no hint button.