Sudoku techniques from beginner to expert: singles, locked candidates, pairs
Updated · Applies to Sudoku in MindGlyph and to the puzzle type in general.
Sudoku is solved with a short ladder of techniques, and each rung only matters when the one below it has run out. Naked singles (a cell with one possible digit) and hidden singles (a digit with one possible cell in a row, column or box) solve every easy and medium puzzle. Locked candidates — a digit confined to one row or column within a box, or to one box within a row or column — solve most hard puzzles. Naked and hidden pairs solve the rest. A well-made sudoku never requires a guess; a stall means a technique was skipped, not that the puzzle is unfair.
The rules, and what they imply
Every row, every column and every 3×3 box must contain the digits 1 to 9 exactly once. Everything in sudoku follows from that single rule. A digit that already appears in a row cannot appear again in that row; a cell that sees a 4 in its row, its column and its box cannot be a 4. Solving is the process of listing, for each empty cell, which digits it can still be — the candidates — and then finding cells or digits with only one option left.
Naked singles and hidden singles
A naked single is a cell with exactly one candidate: every other digit is already present in its row, column or box. Fill it. A hidden single is a digit that has only one possible cell within a row, column or box, even though that cell has other candidates too. Scanning for hidden singles is the workhorse of sudoku: pick a digit, look at each box, and ask where the digit can still go. If the answer is one cell, place it. Easy and medium puzzles fall entirely to these two techniques, applied in a loop until the grid is complete.
Cross-hatching is the fastest way to find hidden singles by hand: for a digit, imagine lines through every row and column that already contains it; the cells not crossed by any line inside a box are the digit's only options in that box.
Locked candidates: pointing and claiming
When a digit's candidates within a box all lie in one row (or one column), the digit must go in that row within that box — so the digit can be removed as a candidate from that row everywhere OUTSIDE the box. This is a pointing pair or triple. The reverse also holds: when a digit's candidates within a row all lie in one box, the digit can be removed from the rest of that box. This is claiming, or box–line reduction. Neither technique places a digit directly; both eliminate candidates, which then exposes new singles. A hard puzzle is usually one that needs a single locked-candidate step to unlock a chain of singles.
Naked pairs and hidden pairs
A naked pair is two cells in the same row, column or box that each contain exactly the same two candidates, say {2, 7}. Between them they must take 2 and 7, so both digits can be removed from every other cell in that unit. A hidden pair is two digits that appear as candidates in only two cells of a unit; those two cells must hold those two digits, so every other candidate can be removed from those cells. Pairs are the first technique most solvers find hard to see, because they require the candidate list to be written out; on a screen, use pencil marks, and on paper, write small digits in the cell corners.
Why guessing is never required
A properly constructed sudoku has exactly one solution and can be solved by logic alone. Guessing — filling a cell with one of two candidates and seeing whether the grid breaks — works, but it is not solving, and on an extreme puzzle a wrong guess can be twenty moves deep before it contradicts. If a puzzle stalls, the correct move is to go back down the ladder: re-scan for hidden singles (they are missed constantly), then look for locked candidates in every box, then for pairs. MindGlyph grades each board by the hardest technique its solver actually needed — singles, locked candidates or pairs — so an Easy label means the grid falls to singles, and a Hard label means a locked-candidate or pair step is waiting somewhere.
Sudoku tips, in order
- Scan digit by digit, not cell by cell. Pick a digit, cross-hatch every box for its remaining cells. Hidden singles appear this way.
- Write candidates on hard boards. Locked candidates and pairs are invisible without pencil marks.
- Start with the most-filled digits and units. A digit placed seven times has two left, and a box with six givens has three cells to think about.
- Look for a digit confined to one line in a box. Remove it from that line outside the box — a pointing pair.
- Look for two cells sharing two candidates. A naked pair clears those digits from the rest of the unit.
- Never guess; go down the ladder. A stall is a missed single or a missed elimination, not a missing technique.
- Re-scan after every placement. Each digit placed creates new singles in three units.
Practise it
Sudoku is one of the nine games in MindGlyph, free on Android and iOS. How Sudoku works in the app — including a new shared puzzle every day and an archive of every past one.
Questions about Sudoku strategy
What is the easiest sudoku technique to learn first?
Hidden singles found by cross-hatching: pick a digit, rule out every row and column that already contains it, and look for a box where only one cell remains. Easy and medium puzzles are solved entirely this way.
What are locked candidates in sudoku?
A digit whose possible cells within a box all lie on one row or column (pointing), or whose possible cells within a row or column all lie in one box (claiming). The digit can then be eliminated from the rest of that line or box.
Is it ever necessary to guess in sudoku?
Not in a well-made puzzle. Every board with a unique solution can be solved by logic. A stall almost always means a hidden single or a locked-candidate elimination was missed.
How does the app decide a sudoku's difficulty?
MindGlyph solves each generated board with a human-technique solver and labels it by the hardest technique the solve needed — singles, locked candidates, or pairs — rather than by counting blank squares.