Sudoku Solving Techniques

Every sudoku worth playing can be solved without guessing. What separates an Easy puzzle from a Grandmaster one is not luck — it is which techniques the puzzle demands. A technique is a repeatable pattern of reasoning: you learn to recognize a configuration on the board, and the configuration tells you something certain — either a digit that must be placed, or candidates that can be safely removed.

This guide covers the techniques our in-app Technique Trainer teaches, in roughly the order players need them. The first two place digits directly; everything after that works by elimination — shrinking the candidate lists in your notes until placements fall out on their own. If you don't use notes yet, start: almost nothing past the Singles is findable without them.

Naked Single — the foundation

A cell has a Naked Single when only one candidate remains in it: the other eight digits all already appear somewhere in its row, column, or box. There is nothing to deduce beyond noticing it — the cell is "naked" because its single possibility is sitting in plain view of anyone keeping notes.

How to find them: when you place a digit, immediately strike that digit from the notes of every cell sharing its row, column, and box. Any cell that drops to one candidate is your next move. Easy puzzles can be solved with Naked Singles almost exclusively, which is why they make the best warm-up.

Hidden Single — same idea, opposite view

A Hidden Single is a digit that can go in only one cell of a unit — a row, column, or box — even though that cell still has other candidates. The single is "hidden" behind those other candidates: looking at the cell tells you nothing, but looking at the digit across the whole unit tells you everything.

How to find them: pick a digit and a box, and ask "where in this box can this digit still legally go?" If every cell but one is blocked by that digit elsewhere in its row or column, you have found a placement. Scanning digit by digit like this is the bread-and-butter rhythm of Medium-level solving.

Naked Pair — your first elimination

Find two cells in the same unit that hold exactly the same two candidates — say [2, 7] and [2, 7]. Those two digits must occupy those two cells, in one order or the other. You don't yet know which cell gets the 2 and which gets the 7, and you don't need to: either way, no other cell in that unit can hold a 2 or a 7. Strike both digits from every other cell in the unit.

The Naked Pair is the gateway technique. It is the first move that places nothing immediately — its entire value is in the notes it cleans up, which then expose new Singles. Once this click happens, the harder techniques are all variations on the same theme.

Hidden Pair — the pair behind the noise

Two digits that can each go in only the same two cells of a unit form a Hidden Pair — even if those two cells are cluttered with other candidates. Since the two digits must claim those two cells between them, every other candidate in those cells is impossible. Clear them out, and the hidden pair becomes a naked one.

Hidden Pairs are harder to spot than Naked Pairs because the pattern lives in the digit positions, not in the cell contents. Scan one digit at a time, note the cells where it fits in a unit, and watch for two digits whose lists match.

Pointing Pair — when a box talks to a row

Sometimes a digit's only possible cells within a box all fall on the same row (or the same column). Wherever that digit ends up inside the box, it occupies that line — so it cannot appear anywhere else on that row or column outside the box. The pair "points" along the line, and you erase the digit's candidates from the rest of it.

This is the first technique where two different unit types — a box and a line — exchange information, and it is the workhorse of Hard puzzles. Whenever you finish placing a digit's notes in a box, glance at whether they line up. If they do, follow the line.

X-Wing — elimination across the whole board

Take one digit. Suppose in two different rows it has exactly two possible cells each — and those cells sit in the same two columns, forming the corners of a rectangle. The digit must occupy two opposite corners of that rectangle: one per row, one per column. However it resolves, both columns receive the digit inside the rectangle — so you can remove that digit's candidates from everywhere else in those two columns. The same logic works with rows and columns swapped.

The X-Wing is the moment sudoku stops being local. Nothing in a single row, column, or box reveals it; you have to track one digit's pattern across the entire grid. Our Master-level puzzles are built to require moves of this rank.

Swordfish — the X-Wing's bigger sibling

A Swordfish extends the X-Wing from two lines to three: one digit confined, across three rows, to cells that fall in only three columns. The digit must appear once in each of those rows, distributed across those three columns — so each of the three columns gets it from within the pattern, and you erase the digit from every other cell in those columns. As with the X-Wing, rows and columns are interchangeable.

Swordfish patterns are rare and genuinely hard to see; finding one unaided is a milestone. If an expert-grade puzzle has stalled completely and every simpler technique is exhausted, a fish hunt is usually what the puzzle is asking of you.

XY-Wing — chaining three cells

The XY-Wing uses three cells, each holding exactly two candidates, in a pivot-and-wings arrangement: a pivot cell with candidates [X, Y] that shares a unit with two wing cells, one holding [X, Z] and the other [Y, Z]. Whichever value the pivot takes, one of the wings is forced to be Z. Z is therefore certain to land in one wing or the other — so any cell that shares a unit with both wings can never be Z. Strike it.

This is your first taste of chain logic — "if this, then that, then therefore" — which is the engine behind everything at Grandmaster level. It rewards tidy notes above all: the pattern is invisible unless your two-candidate cells are accurately maintained.

Practicing the techniques

Reading about a technique and spotting it cold on a real board are different skills. The app's Learn tab includes a Technique Trainer with short, hand-built exercises — each one a board positioned so that a specific technique is the move, with a hint highlighting where to look if you stall. Progression is linear: finish a technique's exercises and the next unlocks, so the curriculum carries you from your first Naked Single toward the patterns above at your own pace. Then pick a real puzzle one notch above your comfort level — see Difficulty Levels for which techniques each level expects — and let the puzzle make you use what you've learned.