How to solve Sudoku step by step
Sudoku is solved by a loop, not one trick. Check the simplest facts across the whole grid, make one proved change, then begin the loop again. Move to a stronger technique only after a complete simple pass finds nothing.
Definition
To solve Sudoku, repeatedly find a digit or candidate that the current row, column, and 3×3 box force, apply that deduction, and restart the search on the changed grid.
When to use it and what to verify
When to move to a stronger technique
Escalate only after a complete pass with the current technique family finds no valid placement or elimination.
What counts as progress
A candidate elimination is useful even when it does not place a digit immediately. It changes the grid and can expose a simpler move.
Common mistake
Do not continue searching at the same difficulty after the grid changes. Restart with scanning and singles, where the next proof is usually cheaper.
Use this order: rules → scanning → candidates → singles → box–line interactions → groups → one-digit patterns → wings and chains.
- 1. Apply the three Sudoku rulesEach row, column, and 3×3 box must contain digits 1 through 9 once. A legal move must satisfy all three units.
- 2. Scan for missing digitsStart with nearly complete rows, columns, and boxes. List what is missing, then test the crossing units before placing anything.
- 3. Add complete candidate notesWhen scanning stalls, write every digit still allowed in each empty cell and update those notes after every placement.
- 4. Place naked and hidden singlesA naked single leaves one candidate in a cell. A hidden single leaves one possible cell for a digit inside a row, column, or box. The example proves 4 at R1C3.
- 5. Use box–line interactionsPointing and claiming candidates remove a digit when all of its positions in a box or line stay inside their overlap.
- 6. Reserve candidate groupsCheck naked and hidden pairs before triples. A group is valid only when the number of reserved digits matches the number of cells.
- 7. Follow one digit across the gridUse X-Wing or Swordfish only after mapping every relevant position for one candidate across the selected rows or columns.
- 8. Use wings and chains last, then restartCheck two-candidate pivots, coloring, and chains only after simpler families fail. After any elimination, return to step 2.
At R1C3, the row rules out 3, 5, and 6; the column rules out 2, 8, and 9; and the box rules out 1 and 7. Therefore 4 is forced.
A reference verified by Doku.su
Doku.su checks every placement or elimination in this example with its deterministic Sudoku engine. Illustrative candidates are labelled when they do not represent a complete puzzle state.
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