Sudoku

What is Sudoku?

Sudoku is a logic puzzle played on a 9×9 grid divided into nine 3×3 boxes. The grid starts partially filled, and your task is to place the digits 1 through 9 so that each row, each column, and each 3×3 box contains every digit exactly once. No arithmetic is involved — the puzzle is solved entirely by deductive reasoning. A well-formed Sudoku has exactly one solution and can always be reached without guessing.

A brief history

The modern Sudoku was popularised by Japanese publisher Nikoli in 1986 under the name Sūji wa dokushin ni kagiru — roughly "the digits must remain single." The puzzle's mathematical roots trace back to Latin squares studied by Leonhard Euler in the eighteenth century, and a precursor called Number Place was published in an American puzzle magazine in 1979. Sudoku became a global phenomenon after The Times of London began printing it in 2004, rapidly spreading to newspapers worldwide and spawning dedicated puzzle books, apps, and competitions.

Core techniques

The most fundamental technique is elimination: if a digit already appears in a row, column, or box, it cannot appear again in that unit. By scanning all three constraints at once — the row, the column, and the box of each empty cell — you can often identify cells where only one digit is possible. This is called a naked single and requires no sophistication beyond counting.

When naked singles are exhausted, look for hidden singles: a digit that can only go in one cell within a given row, column, or box, even if that cell appears to have multiple options. Beyond singles, pairs and triples of candidates that are confined to the same cells within a unit allow you to eliminate those digits from other cells in the unit. Most daily puzzles at easy and medium difficulty yield entirely to these three techniques. Hard puzzles may require more advanced chains, but the principles remain the same: constrain, eliminate, confirm.

Notes and perfect wins

The notes mode lets you pencil in candidate digits — small numbers that might belong in a cell. Good players maintain their notes meticulously: every time you place a digit, remove it from the notes of all cells in the same row, column, and box. This keeps the candidate list accurate and turns the puzzle into a visible constraint-satisfaction problem rather than a memorisation exercise. A perfect win requires solving the puzzle with no mistakes and without using the hint system, so notes discipline is the most reliable path to one.

Difficulty levels

Easy puzzles are solved almost entirely with naked and hidden singles. Medium puzzles require pairs and occasional forward-looking deductions. Hard puzzles demand chains and more deliberate candidate management, with few naked singles available at the start. All three difficulties use the same rules and the same grid — only the number of givens (pre-filled cells) and the techniques required to resolve the rest change. Best times are recorded separately for each difficulty so progress in each track is meaningful on its own terms.

Tips for beginners

Start with the digit that appears most often in the given cells — if seven nines are already placed, finding the remaining two is straightforward. Work through each digit in turn before moving to open-ended scanning. When you feel stuck, switch to notes mode and mark every possible candidate for every empty cell; the pattern of candidates often reveals a hidden single or pair that was invisible without the visual. Never guess: if you cannot find a logical deduction, you have missed something. Step back, verify your notes are up to date, and scan again.