Welcome to our comprehensive Sudoku tutorial! Whether you're a complete beginner or looking to improve your skills, this guide will teach you everything you need to know about solving Sudoku puzzles. From understanding the basic rules to mastering advanced techniques, we'll walk you through the entire journey of becoming a Sudoku expert.
Sudoku is a logic-based number-placement puzzle that has captivated millions of people worldwide since its rise to popularity in the mid-2000s. The name "Sudoku" comes from the Japanese phrase meaning "single number." Despite its Japanese name, the puzzle's roots can be traced back to 18th-century Swiss mathematician Leonhard Euler's work on Latin squares.
A standard Sudoku puzzle consists of a 9Ã9 grid divided into nine 3Ã3 sub-grids (also called "boxes," "blocks," or "regions"). Some cells are pre-filled with numbers from 1 to 9, called "givens" or "clues." The objective is to fill in the remaining empty cells following three fundamental rules.
Every Sudoku puzzle has only one correct solution that can be reached through logical deduction. You should never need to guess! If you find yourself guessing, you're likely missing a logical step or technique.
When you begin a Sudoku puzzle, you'll see a partially filled grid with numbers already placed (the givens). These numbers are fixed and cannot be changed. Your job is to use logic to determine where the remaining numbers belong.
Start by scanning the puzzle for cells where only one number can possibly fit. These are called "naked singles" or "lone singles." Look at each empty cell and ask yourself: "Which numbers are already present in this cell's row, column, and box?" If eight of the nine numbers are already placed in the cell's row, column, or box, then the missing number must go in that cell.
For cells where the answer isn't immediately obvious, write small "pencil marks" or "candidates" - the numbers that could potentially go in that cell based on the current state of the puzzle. Our solver tool includes a "Pencil Mode" feature that makes this easy. You can also enable "Auto-update candidates" to automatically calculate possible values.
Once you've identified candidates, you can apply various solving techniques to narrow down the possibilities. We'll cover many of these techniques in detail below.
What it is: A naked single occurs when a cell has only one possible candidate number. This is the most basic and common technique in Sudoku solving.
How to find it: Look at an empty cell and check which numbers are already present in its row, column, and box. If eight numbers are present, the ninth number is your answer.
Example: If a cell's row already contains 1, 2, 3, 4, 5, 6, 7, and 8, then that cell must be 9.
What it is: A hidden single occurs when a candidate number can only be placed in one cell within a row, column, or box, even though that cell might have other candidates.
How to find it: For each number (1-9), check each row, column, and box to see if there's only one possible position where that number can go. Even if that cell has multiple pencil marks, if it's the only place a specific number can go in that unit, you can place it.
Example: If the number 5 can only go in one cell within a particular box (even if that cell could also be 7 or 8), then that cell must be 5.
What it is: Cross-hatching or scanning involves systematically checking rows, columns, and boxes to find where numbers can be placed.
How to use it: Pick a number (like 5) and scan across all boxes to see where it's already placed. Then look at empty boxes and determine where that number must go based on the positions in other boxes.
What it is: When two cells in the same row, column, or box both have the exact same two candidates, those two numbers must occupy those two cells (though you don't know which number goes where yet).
Why it helps: You can eliminate these two candidates from all other cells in that same row, column, or box.
Example: If cells A and B in the same row both contain only the candidates {3, 7}, then 3 and 7 must go in those two cells. You can remove 3 and 7 from the candidates of all other cells in that row.
What it is: When two numbers can only appear in the same two cells within a row, column, or box (even if those cells have other candidates), those two cells must contain those two numbers.
Why it helps: You can eliminate all other candidates from those two cells, leaving only the pair.
Example: If numbers 2 and 9 can only appear in cells C and D within a box (and nowhere else in that box), then cells C and D must be 2 and 9, so you can remove all other pencil marks from those cells.
What it is: When a candidate number in a box is confined to a single row or column within that box, that number can be eliminated from the rest of that row or column outside the box.
Example: If the number 4 can only appear in the top row of a box (in two or three cells), then 4 can be eliminated from all other cells in that top row outside of that box.
What it is: If all candidates for a number in a row or column are confined to a single box, that candidate can be eliminated from other cells in that box.
Example: If all the 6s in a row must be in the same box, you can eliminate 6 from other cells in that box that aren't in that row.
What it is: An extension of naked pairs. When three cells in the same row, column, or box contain only three specific candidates (distributed among them), or four cells contain only four candidates, those candidates can be eliminated from other cells in that unit.
Example: If three cells in a column have candidates {2,5}, {2,7}, and {5,7}, then 2, 5, and 7 must occupy those three cells, so these numbers can be removed from other cells in that column.
What it is: When a candidate appears in exactly two positions in two different rows (or columns), and these positions line up to form a rectangle, that candidate can be eliminated from the intersecting columns (or rows).
Visual: If you drew lines connecting the four cells, they would form an X shape, hence the name "X-Wing."
Why it's powerful: This technique works across multiple units simultaneously and can unlock difficult puzzles.
What it is: A complex technique involving three cells that form a Y shape. One "pivot" cell has two candidates, and two "wing" cells each share one candidate with the pivot. If both wings contain the same additional candidate, that candidate can be eliminated from cells that see both wings.
Example structure: Pivot: {A,B}, Wing1: {A,C}, Wing2: {B,C}. Any cell that can see both wings cannot be C.
What it is: An extension of X-Wing involving three rows and three columns instead of two. When a candidate appears in exactly two or three positions in three different rows, and these positions align in three columns, eliminations can be made.
Our online Sudoku Solver is designed to help you learn and improve:
Now that you understand how to solve Sudoku puzzles, here are some resources to continue your journey:
Sudoku is a rewarding puzzle that combines logic, pattern recognition, and patience. With the techniques outlined in this tutorial and regular practice using our online solver, you'll progress from solving easy puzzles to tackling expert-level challenges. Remember that every Sudoku master started as a beginner - the key is consistent practice and a willingness to learn new techniques.
Happy solving!