Basic Sudoku Strategies: Solve with Clear Logic

Keep the three constraints in view

A standard Sudoku has nine rows, nine columns and nine bold 3 × 3 boxes. Each of these units must contain the digits 1–9 exactly once. A candidate is a digit that has not yet been ruled out for a particular empty cell. Check that cell's row, column and box together; checking only two of them can create a plausible but invalid entry.

Use row and column coordinates to keep explanations clear: r4c7 means row four, column seven. A candidate list is temporary working information, not a promise that every listed digit remains possible. Whenever you place a number, remove it from the notes of all other cells in its row, column and box.

Find naked singles by eliminating candidates

A naked single is a cell with exactly one remaining candidate. Start with rows, columns or boxes containing many filled cells: they require less checking. Write down the missing digits, then test those digits against the crossing units. If just one survives, enter it. Immediately inspect the affected units because one placement can create several more singles.

For example, suppose a row needs 2, 5 and 8. One empty cell already sees a 2 in its column and an 8 in its box. That cell must be 5. This is stronger than choosing 5 because it looks convenient: both alternatives have specific, visible reasons they cannot fit.

Find hidden singles by following one digit

A hidden single is the only possible location for a digit within a unit, even when that cell has other candidates. Choose a digit such as 7 and inspect a box missing it. Existing 7s in crossing rows and columns eliminate positions inside the box. If one position remains, place 7 there.

Change perspective when cell-by-cell checks stop working. Instead of asking what can enter a particular square, ask where a particular digit can enter this row, column or box. These two questions expose different deductions. A cell might have notes 3, 6 and 7, yet still be the only place for 7 in its column.

Work through a short deduction chain

Consider a row whose three empty cells are r4c2, r4c5 and r4c8. The row is missing 2, 5 and 8. After checking the crossing columns and boxes, the candidates below remain. This is a local example: the given candidate lists represent constraints already established elsewhere in the puzzle.

Only r4c8 can contain 5, so 5 is a hidden single in the row. Enter 5 in r4c8 and clear the remaining notes from that cell. The other two cells still form an unresolved 2/8 pair. Do not choose their order without another deduction. The useful result is one certain entry, even though the entire row is not finished.

Use naked pairs without overextending them

If exactly two cells in the same unit each have the same two candidates, those digits are reserved for those two cells. For instance, two cells in a column with notes 3/9 form a naked pair. You can remove 3 and 9 from every other empty cell in that column, even though you cannot yet tell which member is 3.

The shared unit matters. Two 3/9 cells scattered across unrelated parts of the grid do not form a useful pair. Nor do two cells containing 3/9/6: their third candidate prevents the reservation. Apply the elimination only within a unit containing both pair cells, and look for a single created by the change.

Connect boxes with rows and columns

Sometimes every candidate position for a digit inside a box lies on one row. That digit must occupy the box somewhere along that row, so it cannot appear elsewhere on the same row outside the box. The same reasoning works with columns. This deduction removes candidates without immediately placing a digit.

The reverse relationship is useful too. If every possible location for 4 in a row lies inside one box, remove 4 from the other cells of that box outside the row. Before acting, inspect every unsolved cell in the relevant unit. Missing one candidate can turn a sound technique into a false elimination.

Build a reliable solving routine

Progress comes from combining small checks, not constantly searching for a more advanced technique. After each placement, inspect its row, column and box before scanning the entire grid again. When a deduction produces no entry, retain the candidate removal: it may become useful after a later move.

1. Scan nearly complete units first and verify each proposed digit against all three constraints.
2. Update notes after every entry so later pairs and hidden singles use current information.
3. Switch between cell-focused scanning and following a single digit through the grid.
4. Check pairs and box-line relationships only after simpler placements stop appearing.
5. If a unit has nowhere for a required digit, review recent entries and eliminations before continuing.

Frequently asked questions