The rule
A sudoku is a 9×9 grid split into nine 3×3 boxes. Some cells are given. Fill the rest so that every row, every column and every box holds the numbers 1 to 9 exactly once.
That is all. There is no arithmetic: the numbers could just as well be nine colours. A proper sudoku has exactly one solution, and you can reach it by logic alone.
Start with the last free cell
The easiest move of all: a row, column or box with eight numbers already in it. The missing number goes in the empty cell. Players call it a full house.
Scan for hidden singles
Pick a number, say 5, and a box that does not have it yet. Every 5 elsewhere in the grid rules out its whole row and column. If those lines cover all the empty cells of the box but one, the 5 goes there. This is called cross-hatching, and it solves most easy puzzles on its own.
Work through the numbers one by one, 1 to 9, and through the boxes one by one. Each number you place opens new lines for the next scan.
Use notes: naked singles
When scanning stalls, write the candidates of each empty cell: the numbers its row, column and box still allow. A cell with a single candidate takes it. That is a naked single.
Keep notes small and tidy, and erase a candidate the moment a number lands in the same row, column or box. Sudowick does that erasing for you.
Pointing and claiming
If, inside one box, a number can only go in cells of the same row, that number must be in that row within this box. So you can cross it out of the rest of the row, in the other two boxes. That is a pointing pair (or triple).
The mirror move is claiming: if within a row a number can only go in cells of one box, cross it out of the other cells of that box.
Naked and hidden pairs
Two cells of the same row, column or box that both hold exactly the same two candidates, say 3 and 8, take those two numbers between them. No other cell of that line can be 3 or 8. That is a naked pair; the same works with three cells and three candidates.
A hidden pair is the reverse: two numbers that fit only in the same two cells of a line. Those cells can hold nothing else, so clear their other candidates.
The X-wing and beyond
Expert puzzles need a look across lines. If a number can go in exactly two cells in each of two rows, and those cells sit in the same two columns, the number fills one corner of that rectangle in each row. Either way it uses up both columns, so cross it out of the rest of those two columns. That is the X-wing.
The swordfish is the same idea with three rows and three columns. XY-wings chain three two-candidate cells. You rarely need them, but a fair expert puzzle will ask for one at its hardest step.
Habits that help
- Never guess. If you are stuck, look for a technique you have not tried yet; a fair puzzle always has a next step.
- Fill the easy numbers everywhere before going deep in one corner.
- Check a placed number against its row, column and box before you move on: one wrong number spoils everything after it.
- Stuck on a printed puzzle? Type it into the solver and ask for one hint instead of the answer.
Questions
- How many numbers does a sudoku need to have one solution?
- At least 17 givens. With 16 or fewer, a puzzle always has more than one solution. Most published puzzles give between 22 and 36.
- Do I need to be good at maths?
- No. Sudoku uses numbers only as symbols. You never add or multiply anything.
- What makes a sudoku hard?
- Not the number of givens but the techniques it needs. An easy puzzle falls to singles; an expert one needs pairs, X-wings or a swordfish at some step.
