Sudoku looks like a number puzzle, but there is no arithmetic in it. The digits could just as well be letters or colors. What it takes is logic: every puzzle has exactly one solution, and each digit can be placed by reasoning about where it can and cannot go. This guide walks through the techniques in the order you will need them.
The rules
A standard sudoku is a 9×9 grid divided into nine 3×3 boxes. Fill it so that every row, every column, and every box contains the digits 1 to 9 exactly once. Some digits, the clues, are given at the start.
Smaller grids follow the same rule with fewer digits: a 4×4 sudoku uses 1 to 4 in 2×2 boxes, and a 6×6 sudoku uses 1 to 6 in boxes two rows tall and three columns wide. They are the best place for children, and anyone new to the puzzle, to start.
The two basic moves
Easy and medium puzzles can be solved entirely with these two moves.
Hidden single: one place for a digit. Pick a digit, say 5. Look at a box that has no 5 yet, and rule out every cell whose row or column already holds a 5. If only one cell in the box is left, the 5 goes there. Work through each digit and each box in turn. This "cross-hatching" is the most productive move in sudoku, and it is where to look first.
Naked single: one digit for a place. Pick an empty cell and list which digits already appear in its row, column, and box. If eight of the nine are there, the missing one goes in the cell. This works best on cells in crowded rows and columns.
A good rhythm: scan for hidden singles digit by digit, then check crowded cells for naked singles, and repeat. Each digit you place opens up new moves.
Pencil marks
When scanning stops finding moves, start writing candidates: the small digits that could still go in each empty cell. Write them in the corners or along the top of the cell, and erase them as digits are placed nearby. Every technique below works on candidates.
Locked candidates
Sometimes a digit's possible cells in a box all lie in a single row (or column). The digit has to go somewhere in that row inside the box, so it cannot appear anywhere else in that row. Cross it off the candidates in the rest of the row.
It also works the other way round: if a digit's only cells in a row all fall inside one box, it cannot go anywhere else in that box.
Pairs and triples
Naked pair. Two cells in the same row, column, or box that can each hold only the same two digits, say 3 and 8. Those two digits must go in those two cells, in some order, so no other cell in that unit can have a 3 or an 8.
Hidden pair. Two digits that can only go in the same two cells of a unit. Those cells must hold those two digits, so any other candidates in them can be erased.
Naked triple. The same idea as a naked pair, with three cells sharing three digits between them. Not every cell needs all three digits.
The X-wing
Look for a digit that has exactly two possible places in each of two rows, and those places line up in the same two columns. They form the corners of a rectangle. The digit must sit on one diagonal of the rectangle or the other; either way, both columns get their copy of that digit from these two rows. So the digit can be crossed off everywhere else in those two columns. The same works with rows and columns swapped.
How the difficulty levels compare
On the printable sheets here, easy and medium puzzles need only the two basic moves; easy ones keep extra clues so the next move is never far away. Hard puzzles need at least one of the techniques beyond singles. If you get stuck on one, the sudoku solver can show the next move and explain the reasoning, without giving away the rest of the puzzle.