Sudoku Solver

Sudoku is a logic puzzle played on a 9×9 grid divided into nine 3×3 boxes. The goal is to fill every row, every column, and every 3×3 box with the digits 1 through 9, with each digit appearing exactly once in each row, column, and box. Sudoku requires no mathematics — the digits are used as symbols only, and the entire puzzle is solved through logical elimination. A valid puzzle always has exactly one solution and provides 22-30 starting digits as clues. Click any cell and type a number 1-9 to enter the digits you already know, leaving unknown cells empty, then hit Solve to complete the puzzle instantly. You can also use Photo Scan to take a picture of your puzzle — the AI reads every digit automatically and fills the grid for you before solving.

Disclaimer: PuzzleUnlock is an independent puzzle help site and is not affiliated with The New York Times, Wordle, Connections, Spelling Bee, Strands, Scrabble, Hasbro, Boggle, or any other puzzle publisher. All trademarks belong to their respective owners.

About Sudoku

Sudoku is a logic-based number placement puzzle that became one of the biggest global puzzle phenomena of the 21st century. Despite its Japanese name — which roughly translates to "single number" or "digits must remain single" — Sudoku was originally created by American architect Howard Garns in 1979. Garns published it in Dell Pencil Puzzles & Word Games magazine under the name "Number Place." The puzzle was discovered by Japanese publisher Nikoli in 1984, renamed Sudoku, and refined with stricter rules requiring rotational symmetry and a minimum number of given clues.

Sudoku's international explosion began in 2004 when The Times of London began publishing daily Sudoku puzzles. The format spread rapidly to newspapers worldwide, and within two years virtually every major newspaper in the developed world carried a daily Sudoku. The puzzle's genius lies in its universality — it requires no language, no mathematics, and no cultural knowledge. The same grid with the same numbers works identically in Tokyo, Paris, São Paulo, or New York. This linguistic neutrality made Sudoku uniquely suited for global syndication.

The standard Sudoku grid is 9×9, divided into nine 3×3 boxes. The solver must fill every row, column, and box with the digits 1 through 9, with no digit appearing more than once in any row, column, or box. A valid puzzle has exactly one solution and typically provides 22-30 given digits as starting clues. Difficulty is determined not by the number of givens but by which solving techniques are required — easy puzzles yield to simple scanning, while expert puzzles require advanced techniques like X-Wings, Swordfish, and forcing chains.

Competitive Sudoku has a thriving international scene. The World Sudoku Championship has been held annually since 2006, featuring solvers who can complete expert-level puzzles in under two minutes using pattern recognition and intuition that goes far beyond what most players develop. The NYT Sudoku alone draws millions of daily solvers, and dedicated Sudoku apps have been downloaded billions of times worldwide. The puzzle appears in hospital waiting rooms, airplane seat pockets, and school classrooms across every continent.

Begin with rows, columns, and boxes that already contain the most given digits. A unit with seven or eight givens has only one or two open cells — these are trivial to complete and provide anchor digits for adjacent units. Working from the most constrained areas outward is the most efficient approach for any difficulty level.

For each digit from 1 to 9, scan across rows and down columns to find boxes where that digit can only fit in one cell. When a digit has been placed in two of the three rows (or columns) passing through a box, it can only go in the remaining row (or column) within that box — often in only one cell. This cross-hatching technique solves most easy and medium puzzles entirely.

A naked single is a cell where only one digit is possible after eliminating all digits already present in the same row, column, and box. Go through every empty cell and count how many digits are still possible. Cells with only one possibility are immediate placements. Filling naked singles often creates more naked singles in a chain reaction.

For medium and hard puzzles, write small candidate digits in each empty cell showing all possibilities. As you place digits, erase them from affected cells' candidate lists. This transforms the puzzle from a memory challenge into a pure logic exercise. Most serious Sudoku players use pencil marks for anything harder than an easy puzzle.

PuzzleUnlock's photo scanner reads Sudoku grids directly from images. Take a straight-on photo with good lighting and the AI reads every digit automatically, filling the grid without any manual entry. This works on newspaper puzzles, puzzle books, magazine features, and digital screenshots. The solver then completes the puzzle instantly.

Start with the most constrained units

Master the scanning technique

Find naked singles first

Use pencil marks for harder puzzles

Use the photo scanner for print puzzles

Q: Does Sudoku involve mathematics?

No. The digits 1-9 function as symbols only — they could be replaced with any nine distinct symbols and the puzzle would work identically. There is no arithmetic, no addition, no multiplication. Sudoku is pure logic and spatial reasoning.

Q: How many valid completed Sudoku grids exist?

Exactly 6,670,903,752,021,072,936,960 — roughly 6.67 sextillion. Of these, considering symmetry and relabeling equivalences, there are approximately 5.47 billion essentially different puzzles. The number of valid puzzles with unique solutions is estimated in the billions.

Q: What is the minimum number of given clues for a unique solution?

The mathematical minimum is 17 given digits. Any puzzle with 16 or fewer givens has either no solution or multiple solutions. Most published puzzles provide 22-30 givens for playability, though expert puzzles sometimes use as few as 17-20.

Q: Can the solver handle any difficulty level?

Yes — PuzzleUnlock uses a backtracking algorithm combined with constraint propagation that solves any valid Sudoku puzzle regardless of difficulty. Diabolical and expert puzzles requiring advanced human techniques like X-Wings, Swordfish, and Unique Rectangles are solved instantly.

Q: What if the solver says 'no solution found'?

This means the puzzle as entered has no valid solution — usually due to a data entry error. Double-check that no digit appears twice in the same row, column, or box in your given digits. Even one incorrectly entered digit typically makes a Sudoku unsolvable.

Q: How does the photo scanner work?

The photo scanner sends your image to Claude AI, which reads the grid visually and identifies each digit's position. The AI is trained to handle various fonts, lighting conditions, and image angles. For best results, photograph the puzzle straight-on with even lighting and no shadows across the grid.