From the rulebook
How to Solve Sudoku
Sudoku is a pure logic puzzle. Every grid has exactly one solution you can reach without guessing, as long as you know what to look for. This guide takes you from the rules to the techniques that crack medium and hard puzzles.
The rules of Sudoku
A standard Sudoku is a 9 by 9 grid split into nine 3 by 3 boxes. Some cells start filled with given digits. Your job is to fill every empty cell so that each row, each column and each 3 by 3 box contains the digits 1 through 9 exactly once.
That single constraint, no repeats in any row, column or box, is the whole game. Every deduction you make comes from ruling out digits that would break it.
Start by scanning
The fastest opening move is scanning. Pick a digit, say 5, and look across the rows, columns and boxes where a 5 already appears. Those lines and boxes cannot take another 5. Often that leaves only one empty cell in a box where a 5 can legally go, so you can place it with certainty.
Work digit by digit through the grid. Scanning alone solves most easy puzzles and gives you a strong head start on medium ones.
Use pencil marks for candidates
When scanning stops finding placements, switch to pencil marks. In each empty cell, note the small candidate digits that could still legally go there. As you fill cells, erase candidates that are now blocked. A cell left with a single candidate is a forced placement.
Pencil marks turn a hard puzzle into a bookkeeping exercise. The patterns you need next are all easier to spot once candidates are written down.
Naked pairs and hidden pairs
A naked pair is two cells in the same row, column or box that share the same two candidates, for example both holding only 3 and 7. One of them must be the 3 and the other the 7, so you can remove 3 and 7 from every other cell in that line. This often unlocks new single candidates.
A hidden pair is the same idea in reverse. If two digits can only go in the same two cells of a unit, those cells must hold exactly those digits, so you can erase every other candidate from them.
Pointing pairs and box-line reduction
Sometimes a digit is confined to a single row or column within one box. If the only candidates for 4 in a box all sit in its top row, then the 4 for that box must be in that row, so you can remove 4 from the rest of that row outside the box. This is a pointing pair, and with box-line reduction it is the main tool for hard puzzles.
Apply these techniques in order, easy scans first, then pencil marks, then pairs and pointing pairs. On Puzzle Lair every Sudoku is guaranteed solvable by logic alone, so if you are stuck there is always a deduction waiting, never a guess.
Frequently asked questions
- How do you solve Sudoku for beginners?
- Start by scanning one digit at a time. For each number, find the rows, columns and boxes that already contain it, then look for a box where only one empty cell can legally hold that number and place it there. Scanning alone solves most easy puzzles. When it stalls, write candidate pencil marks in each empty cell and look for cells with a single candidate.
- What is the hardest part of Sudoku?
- The jump from scanning to candidate-based logic. Easy puzzles fall to scanning, but medium and hard puzzles need pencil marks plus techniques like naked pairs, hidden pairs and pointing pairs to eliminate candidates and force placements.
- Does solving Sudoku ever require guessing?
- No. A well-made Sudoku has exactly one solution reachable by pure logic. Every Puzzle Lair Sudoku is generated and verified to be solvable without guessing, so being stuck means there is a deduction you have not spotted yet.
- What is a naked pair in Sudoku?
- A naked pair is two cells in the same row, column or box that each have the same two candidates and no others. Since those two digits must occupy those two cells between them, you can safely remove both digits from every other cell in that unit.
- How long should a Sudoku take to solve?
- It depends on difficulty and experience. An easy Sudoku often takes a few minutes, while a hard one can take fifteen minutes or more. Puzzle Lair tracks your solve times so you can watch yourself get faster and compare with the leaderboards.