Every Sudoku solving technique, in the order you should learn them

There are 37 solving techniques on this list, ordered from the one you use on your first puzzle to the one that only turns up in an Extreme grid. Each has its own page with the rule, the reason it works, and a worked example board you can step through.

The order is not editorial. It is the exact ladder the app's hint engine walks: it always offers you the easiest technique that applies to the position in front of you, so the list below doubles as a curriculum.

Easy

The moves you make before you write a single note. Everything here comes from counting what is already on the board.

Last Remaining CellOne empty cell left in a unit, and the missing number goes there.Nearly CompleteTwo cells left, and one of the two missing numbers is blocked.Naked SingleA cell with one candidate left has to hold it.

Medium

One technique, and it is the one that carries most of the puzzles people actually play.

Hidden SingleA number that fits in only one cell of a unit, even if that cell has other candidates.

Hard

The first techniques that clear candidates instead of placing numbers. From here on, notes are not optional.

Pointing PairA number stuck on one line inside a box clears that line outside the box.Pointing TripleThe three-cell version of a Pointing Pair.Box/Line ReductionA number stuck inside one box along a line clears the rest of that box.Naked PairTwo cells sharing the same two candidates reserve both numbers.Hidden PairTwo numbers that fit in only two cells claim those cells.Naked TripleThree cells using only three numbers between them.Hidden TripleThree numbers confined to three cells, buried under other candidates.

Expert

Patterns that reach across the board: fish, wings and the first chains.

X-WingA number locked to the same two columns in two rows.Naked QuadFour cells using only four numbers between them.Hidden QuadFour numbers confined to four cells.SwordfishAn X-Wing with three rows and three columns.Y-WingA pivot cell and two wings force a shared number.SkyscraperTwo strong links on one number whose bases share a line.Simple ColoringPaint a chain of strong links two colours; one colour is true.Empty RectangleA box whose spots for a number form a row-plus-column hinge.

Master

Chains: longer arguments, built from links rather than shapes.

XYZ-WingA Y-Wing whose pivot carries all three candidates.Two-String KiteA row link and a column link meeting in a shared box.Grouped Two-String KiteA Two-String Kite whose strings enter the box as groups of cells.W-WingTwo matching bivalue cells bridged by a strong link.X-ChainAn alternating chain on one number, strong at both ends.XY-ChainA chain of bivalue cells passing one candidate along.WXYZ-WingA pivot and three wings covering four candidates.Remote PairsA chain of identical bivalue cells whose ends are opposites.

Extreme

The deep end: uniqueness arguments, finned fish, almost locked sets and multi-digit colouring.

BUG+1One cell with three candidates where every other has two.Unique RectangleAvoid the four-corner pattern that would allow two solutions.Finned X-WingAn X-Wing spoiled by one extra cell, which still eliminates.JellyfishA fish across four rows and four columns.Finned SwordfishA Swordfish with one extra cell on a base line.ALS-XZTwo Almost Locked Sets sharing a restricted candidate.ALS-XY-WingTwo ALS wings joined through a hinge ALS.Sue de CoqA box-line crossing plus two helpers that place a whole candidate pool.3D MedusaA two-colour chain spanning several numbers at once.Forcing ChainTest one of two possibilities and follow it to a contradiction.