Sudoku looks like a maths puzzle, but there is no arithmetic in it at all. It is a puzzle of pure logic: every number you write can be proved from the numbers already in the grid. Once you know where to look, most easy and medium puzzles fall to the same handful of techniques.
This guide explains the five techniques that matter most for beginners. Learn these and you will be able to finish every Monday to Thursday case on Daily Whodunit, and make real progress on the harder ones.
The rules and a few words you need
A sudoku grid has 81 cells arranged in nine rows, nine columns and nine 3×3 boxes. The goal is to fill every empty cell so that each row, each column and each box contains the numbers 1 to 9 exactly once. A well-made puzzle has only one possible solution, and you never need to guess.
- Givens are the numbers printed in the grid at the start. They never change.
- A unit is any row, column or box. Every unit must end up holding 1 to 9.
- Candidates are the numbers a cell could still be. Writing them small in the corner of a cell is called pencil marking, or taking notes.
1. Scanning (cross-hatching)
Scanning is the first technique everyone learns, and it solves a surprising amount of every puzzle. Pick one number and one box that does not have that number yet. Then look along the rows and columns that pass through the box.
Say you are looking for a 7 in the top-left box. Row 1 already has a 7 further along, so the 7 cannot go anywhere in the top row of the box. Row 3 also has a 7, so the bottom row of the box is ruled out too. That leaves only the middle row. If column 2 already contains a 7 lower down the grid, and the middle-left cell is filled, there is only one cell left. The 7 goes there.
Work through the numbers 1 to 9 this way, box by box. Start with the numbers that appear most often among the givens, because they block the most cells.
2. The last free cell
This one is almost too simple to call a technique, but beginners miss it constantly. Whenever a row, column or box has eight numbers filled in, the last cell must be the one number that is missing. Count from 1 to 9, see which one is absent, and write it in.
Get into the habit of checking any unit that is nearly full every time you place a number. One placement often completes a row, which completes a box, which completes a column: a chain reaction that can fill a dozen cells in a minute.
3. Naked singles
Scanning looks at one number and asks where it can go. A naked single turns the question around: it looks at one cell and asks which numbers it can be.
Choose an empty cell and list every number that already appears in its row, its column and its box. If eight different numbers are ruled out, the ninth is the only candidate left, and the cell is solved. Cells where a row and a column are both busy, inside a crowded box, are the best places to try this.
4. Hidden singles
Sometimes a cell still has several candidates, yet one of those numbers has nowhere else to go. Look at a single unit, for example one row, and ask where the number 4 could go in it. If only one cell in the whole row can take a 4, then the 4 belongs in that cell, even if the cell could in theory also hold a 2 or a 9.
Hidden singles are where pencil marks start to pay off. With candidates written in, you can spot a number that appears only once in a row, column or box at a glance.
5. Naked pairs
When you are stuck, look for two cells in the same unit that share exactly the same two candidates, for example both can only be 3 or 8. You do not yet know which cell is the 3 and which is the 8, but you do know that those two numbers are used up in that unit. Remove 3 and 8 from the candidates of every other cell in the unit.
That small elimination often creates a new naked single or hidden single elsewhere, and the puzzle starts moving again. The same idea works with three cells that share three candidates, called a naked triple, but pairs are far more common.
A simple routine to follow
- Scan for each number from 1 to 9 across all nine boxes.
- Fill any unit that has only one empty cell left.
- When scanning stops working, pencil in the candidates for every empty cell.
- Look for naked singles and hidden singles.
- Still stuck? Hunt for naked pairs, remove those candidates, and go back to step 4.
Each time you place a number, remove it from the pencil marks in the same row, column and box. On Daily Whodunit this happens automatically when you play online, which saves a lot of rubbing out.
Mistakes that trip up beginners
- Guessing. A guess that turns out wrong can leave errors hidden for twenty moves. If you cannot prove a number, do not write it.
- Out-of-date pencil marks. Notes are only useful if you update them after every placement.
- Checking only rows. Every number must satisfy its row, its column and its box. It is easy to forget the box.
- Rushing the end. Most errors happen in the last few cells, when the grid feels nearly done. Slow down and check each one.
Practise with a story
The best way to improve is a little practice every day. Daily Whodunit gives you a new murder mystery sudoku each morning: solve the grid, then read three marked evidence cells to find the killer, the weapon and the room. Monday and Tuesday cases are gentle and perfect for practising scanning and singles. By Friday and Saturday you will need pairs.
Every earlier case is also waiting in the case archive, free to play online or print.