How to solve Sudoku: from your first puzzle to the X-Wing
9 min read ·
Sudoku looks like a maths puzzle, but there's no arithmetic in it at all. It's pure logic: every digit you write down follows from the digits already on the grid. Once you know a handful of patterns, puzzles that looked impossible start falling apart one cell at a time.
This guide walks through those patterns in the order you'll need them, from the scanning that solves most easy puzzles to the X-Wing that cracks hard ones. Every diagram is a real position from a puzzle on Puzzimo, so you'll meet these exact situations when you play.
The rules in thirty seconds
A Sudoku grid has 9 rows, 9 columns and 9 boxes of 3×3 cells. Some cells start with a digit (the givens). Fill every empty cell with a digit from 1 to 9 so that each row, each column and each box contains every digit exactly once.
A well-made puzzle has exactly one solution, and every puzzle on Puzzimo is checked for that before you see it. That matters: it means you never have to guess. If you're stuck, there's always a logical next step, and the techniques below are how you find it.
Scanning: find a hidden single
Start every puzzle by scanning (also called cross-hatching). Pick a digit and a box that doesn't contain it yet, then look along the rows and columns that pass through the box. Each copy of that digit outside the box rules out a whole row or column inside it.
That cell could hold several digits as far as its own row and column are concerned, but it's the only place in the box where 8 can go. That's a hidden single: the digit is hidden among other possibilities until you look at it from the box's point of view.
Last candidate: the naked single
The opposite view is to pick an empty cell and ask which digits it can't be. Collect every digit already in its row, its column and its box. If eight different digits are there, the missing ninth one is the answer.
This is a naked single: once you look closely, only one candidate is left in plain sight. Cells with many filled neighbours, in crowded rows, columns and boxes, are the best places to look.
Notes: keep track of the candidates
On medium and harder puzzles, scanning eventually dries up. That's the time to write notes (pencil marks): the small digits that could still go in each empty cell. On Puzzimo, switch on Notes with the button under the grid or the N key, then tap digits to add or remove them.
- Fill in notes box by box, so you don't miss a cell.
- Every time you place a digit, it leaves the notes of every cell in the same row, column and box. Puzzimo clears those notes for you; on paper, do it by hand.
- A cell whose notes shrink to one digit is a naked single; a digit that appears in the notes of only one cell of a row, column or box is a hidden single.
Notes take a minute to write, but they turn the more advanced techniques below from guesswork into something you can simply see.
Naked pairs
When two cells in the same row, column or box have the same two candidates and nothing else, those two digits must go in those two cells, in one order or the other. You don't know which is which yet, but you know that no other cell in that unit can have either digit.
The same idea extends to naked triples: three cells in a unit whose candidates, together, are only three digits. They're rarer and harder to spot, but they work exactly the same way.
Pointing pairs
Sometimes all the places for a digit inside a box line up in a single row or column. The digit must go somewhere in that line inside the box, so it can't appear anywhere else in that line, in the other two boxes.
The reverse also works (it's called box/line reduction): if, in a row, a digit can only go in cells that belong to one box, it can be removed from the rest of that box.
The X-Wing
The X-Wing is the first truly advanced technique, and it's often what separates a hard puzzle from an expert one. Look for a digit that, in two different rows, fits in exactly two cells, and in the same two columns in both rows.
The four cells form a rectangle. Whichever diagonal turns out to be right, each of the two columns gets its copy of the digit inside the rectangle, so you can remove that digit from every other cell of those columns. The same works with rows and columns swapped.
A solving routine that works
- Scan every digit across every box, then across rows and columns, until no more hidden singles appear.
- Look for naked singles in the most crowded rows, columns and boxes.
- When you're stuck, write full notes for the whole grid.
- Look for naked pairs and pointing pairs, and clean up the notes they remove.
- Go back to step 1: every elimination can create new singles.
- Still stuck on an expert grid? Check each digit for an X-Wing.
Resist the urge to guess. A guess that turns out wrong can stay hidden for a long time and quietly break the rest of the grid. If nothing seems to work, the step you need is almost always a pair or a single you haven't spotted yet.
Practise on the right level
Puzzimo's Sudoku has four levels, and each starts with fewer givens: Easy 40, Medium 33, Hard 28 and Expert 24. Fewer givens generally means fewer singles to start with, so you'll lean on notes and on the pair techniques more often.
- Learning the basics: play Easy and solve it with scanning only, without notes.
- Getting faster: move to Medium and use notes only when scanning stops.
- Learning pairs and X-Wings: Hard and Expert, with full notes.
Every grid is free, with no sign-up. Notes, undo and hints are built in (a hint adds 30 seconds to a ranked time), and a wrong digit counts as a mistake: the third one ends the round, so it pays to check before you commit. A new daily challenge appears every day.
Frequently asked questions
Do you ever need to guess in Sudoku?
No. A proper Sudoku has exactly one solution, so it can always be solved by logic alone. When you feel you have to guess, there's a single, a pair or an X-Wing you haven't found yet. Every Sudoku on Puzzimo is checked to have exactly one solution.
What's the best technique for beginners?
Scanning for hidden singles. Pick a digit, look at each box that's missing it, and use the copies of that digit in nearby rows and columns to rule out cells. Most easy puzzles can be finished with scanning and naked singles alone.
How do I get faster at Sudoku?
Scan in a fixed order (digits 1 to 9, box by box) so you don't look in the same place twice, and only write notes once scanning stops working. Playing a puzzle at your level every day helps more than occasional long sessions.