Sudoku Techniques

The order is the technique

Solvers stall far more often from searching for the wrong thing than from not knowing enough. Hunting for a triple while a cell with one candidate sits unnoticed two boxes away is the commonest way to spend ten minutes on a grid that had five minutes in it. The discipline is to run the list from the top after every single placement, because placing a digit changes the candidates of twenty other cells and can easily hand you three cheap moves in a row.

The six deductions the boards here use

Name	What you look at	What it does
Naked single	One cell	Places a digit: only one candidate is left in it
Hidden single	One unit, one digit	Places a digit: the unit has only one cell left that can take it
Naked pair	Two cells in a unit	Removes two digits from every other cell in that unit
Pointing pair	A box, one digit	The digit is confined to one row of the box, so it leaves the rest of that row
Box line	A box, one digit	The same argument down a column instead of across a row
Naked triple	Three cells in a unit	Removes three digits from every other cell in that unit

Only the first two put a number in a square. The other four remove possibilities, and the placement arrives afterwards when some cell has been narrowed to one. That distinction is worth internalising: past the gentle grades, most of the moves you make will leave the board looking exactly as it did before.

When to stop scanning and start pencilling

Scanning – picking a digit and finding where it must go – needs nothing written down and finds the first two techniques. Pencil marks are what the last four are made of, because a pair, a triple or a confined digit cannot be seen unless the candidates are visible. The switch is worth making late and then making completely: half-marked grids are where errors breed, since a cell whose marks are out of date will happily support a deduction that is false. If you mark, mark every empty cell, and correct the marks of all twenty peers every time you place a digit.

The X-wing, and why no board here needs one

It is the famous next rung, and it is simpler than its reputation. Take one digit, say 5, and two rows in which the 5 can only go in two places each. If those two places sit in the same pair of columns in both rows, then the two 5s of those rows will occupy that two-by-two arrangement between them, one per column – so the 5 can be struck from every other cell of both columns. No puzzle on this site requires it, and that is a structural fact rather than a boast: the generator refuses to hand out a board its own solver cannot finish, and its solver stops at the naked triple. You will meet X-wings in printed collections and in the harder end of other people’s software.

The technique that is not a technique

Trying a candidate to see whether it leads to a contradiction is what a computer does, and it will always work, and it is the reason people abandon grids in disgust. The objection is not that it is cheating; it is that it converts a puzzle into bookkeeping, and a mistake made eight moves into a speculative line is nearly impossible to unpick with a pencil. If a properly graded puzzle appears to need it, one of your earlier eliminations was wrong.

A sudoku strategy that costs nothing

Write the candidates in a fixed position within each cell – 1 always top left, 9 always bottom right – rather than in the order you thought of them. Reading a grid then becomes a matter of shape rather than of reading text, pairs and triples stand out at a glance, and a missing mark is visible as a gap. It is the single change that most reliably speeds people up, and it applies equally on paper and on a board that keeps its own notes.