- The single rule: no digit 1–9 can repeat in any row, column, or 3×3 box
- Every valid Sudoku puzzle has exactly one solution
- You never need to guess — every correct placement follows from logic
- A cell belongs to three groups at once: one row, one column, one box
- The goal is to fill all 81 cells while satisfying the rule in all 27 units
The One Rule That Governs Everything
Sudoku has exactly one rule: each digit from 1 to 9 must appear exactly once in every row, every column, and every 3×3 box. That's it. There are no special cases, no exceptions, and no math involved — just that single constraint applied across 27 different groups of nine cells.
Because every cell belongs to a row, a column, and a box simultaneously, placing one number immediately eliminates it as a candidate in up to 20 other cells. That chain of eliminations is what makes Sudoku solvable by pure logic.
The Structure of the Grid
| Unit | How Many | Cells Each | Must Hold |
|---|---|---|---|
| Rows | 9 | 9 cells (horizontal) | Digits 1–9, each once |
| Columns | 9 | 9 cells (vertical) | Digits 1–9, each once |
| Boxes | 9 | 3×3 cells | Digits 1–9, each once |
| Total units | 27 | — | — |
What "Exactly One Solution" Means
A properly constructed Sudoku puzzle has one and only one valid solution. If you reach a point where two different digits could both complete the grid correctly, the puzzle itself is flawed — not your solving. This property is what allows you to prove every move through elimination rather than guessing.
When you use Naked Singles or Hidden Singles, you are exploiting this guarantee: if only one digit can legally go in a cell, that digit is correct by definition.
The Goal vs. the Method
The goal is simple: fill every empty cell. The method is where the skill lies. Beginners often confuse the two — they understand the goal but try to reach it by guessing rather than by systematic elimination.
Every technique in the techniques library is just a structured way to apply the one rule until no more candidates can be eliminated in an obvious way. Even the most advanced strategies like X-Wing and Swordfish are just the same rule applied to larger patterns.
Given Digits (Clues) vs. Solved Digits
The numbers printed in the grid at the start are called givens or clues. You cannot change them. The empty cells are what you fill in. A standard Easy puzzle typically has 36–46 givens; a hard puzzle might have as few as 24.
The number of givens determines difficulty — but only loosely. What actually matters is which cells are given and how they force the solution. Some 24-clue puzzles are easier than some 30-clue ones, depending on the pattern.
Why Logic Always Works
Because exactly one solution exists and the rule is applied globally, every empty cell's value is already determined the moment the puzzle is set. You are not creating the solution — you are discovering it. Every digit you place is a logical consequence of the givens and the rule.
This is why Sudoku rewards patience over speed. If you're stuck, the answer is always look harder, not guess. Read our guide on how to play for a walkthrough of the elimination process from your very first move.