Sudoku is a 9x9 grid puzzle with one rule applied three ways. This guide covers the grid, the rule, why every proper puzzle has exactly one solution, and what makes one puzzle harder than another.

A working order for solving a Sudoku: where to look first, how to cross-hatch a box, when to start writing pencil marks, and why you should never guess.

Pencil marks are the digits still possible in a cell. This guide covers how to work one out, why you mark a whole unit instead of a cell, how to keep marks true after every placement, and when writing them is a waste of an hour.

A naked single is a cell with one candidate left. A hidden single is a digit with one home left in a unit. This guide covers how to spot each, why cross-hatching finds the second without pencil marks, and which to hunt first.

Fog of war Sudoku is an ordinary Sudoku with most of the grid hidden, and every correct digit lifts the fog around it. This guide covers what you can see at the start, what one placement uncovers, why the puzzle is still solvable without guessing, and a board to try it on.

Fog can hide a constraint but never invent one, which makes naked singles safe and makes hidden singles unsafe outside a fully visible unit. This guide covers where the first move comes from, how to tell a proved move from a plausible one, and which of several proved moves to play first.

Three Sudoku variants add the same kind of rule: a set of cells, beyond the row, column and box, where a digit may not repeat. This guide covers what each one actually adds, a worked deduction for all three, and the one way they are not alike.

A Kropki dot sits between two neighbouring cells: white means the digits differ by one, black means one is double the other. This guide covers what each dot is worth, why a black dot is far more restrictive than a white one, and how to solve using the dots that are not drawn when the puzzle marks every dot it can.

A thermometer runs from a round bulb to a tip, and its digits must increase strictly along the way. This guide covers what a thermometer tells you from its length alone, how one known digit propagates in both directions, and why the two ends are where the information is.

Arrow Sudoku puts a circle at the head of a path. The digit in the circle equals the sum of the digits along the arrow. Learn the small sums that make an arrow useful before every cell is known.

A Renban line contains a run of consecutive digits in any order. Learn how the length of the line limits its possible digit sets, then let normal Sudoku place them.

Consecutive and XV Sudoku put arithmetic clues between neighbouring cells. A bar means a difference of one; X and V mean sums of ten and five. Whether a blank edge means anything depends on the puzzle.