The rule, restated precisely
Fill the 9×9 grid so that every row, every column and every 3×3 box contains the digits 1 to 9 exactly once. That is the entire rule, and everything below is just a way of applying it efficiently.
Step one: scanning
Scanning is the technique you will use more than any other, and it is free. Pick a digit and read the whole grid for it. Because that digit already appears once in some rows, columns and boxes, it cannot appear again in those. Where the remaining possibilities line up, you have a placement.
- Look for a box that does not yet contain your chosen digit.
- Check which rows and columns already have it — those cells are ruled out.
- If only one cell in the box remains possible, place the digit.
Scanning is not a beginner technique you graduate from. Strong players scan constantly and consider it the backbone of the whole game.
Step two: naked singles
A naked single is a cell that has only one possible value left after eliminations. It is the easiest pattern to spot once you get into the habit of asking "what can go here?" rather than "where can this digit go?". Novice solvers look for digits; experienced solvers also look at cells.
Step three: hidden singles
A hidden single is subtler. A cell may have several possible values, but one of those values can go nowhere else in its row, column or box. When that happens, the digit must go in this cell — it is hidden because the cell itself looks ambiguous until you check the constraint from the digit side.
Hidden singles are where most medium puzzles are solved. When you are stuck, do not stare at cells. Pick a digit you have not placed in a while and hunt for it across the whole board.
Step four: pairs
Once you can find singles reliably, the next leap is elimination. If two cells in the same box can each hold only the same two digits, those two digits are locked to those cells — and you can remove them from every other cell in that box, row or column.
- Naked pair: two cells, same two candidates, nothing else. Remove those candidates elsewhere in the unit.
- Hidden pair: two digits that can only go in the same two cells of a unit. Those cells can hold nothing else.
How to practise
- Note candidates lightly. Writing small possible values in each cell turns sudoku from a memory game into a visual one.
- Finish every easy puzzle before moving up. Speed on simple grids comes from scanning skill, which carries over completely.
- When stuck on a hard grid, switch technique rather than staring. Move from cells to digits, or from rows to boxes.
- Never guess. If you cannot prove the next move, there is a technique you have not applied yet — guessing only teaches you to guess.
Put it into practice on Sudoku — start on easy, and move up a difficulty only when you can finish without marking candidates. If you enjoy logic grids generally, Nonogram is a good companion puzzle, and the wider puzzle games guide explains what each type asks of you.
