Lesson:The Core Rules
Look at the top row. It already has the numbers 1 through 8 filled in.
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💾 Saved locallyAbout This Lesson
The three core rules of Sudoku are deceptively simple: each row must contain the digits 1–9 exactly once, each column must contain the digits 1–9 exactly once, and each 3×3 box must contain the digits 1–9 exactly once. These three constraints, applied simultaneously across 81 cells, give rise to one of the most popular logic puzzles in the world.
What makes Sudoku compelling is that these three simple rules interact in complex and non-obvious ways. A single digit placement affects three units at once — its row, column, and box — and each of those effects can cascade through the rest of the grid, unlocking placements in cells that seem unrelated at first glance.
The rules also guarantee uniqueness: a properly constructed Sudoku puzzle has exactly one valid solution. This means that every logical deduction you make is necessarily correct — if your reasoning is sound, your placements are right. There is never any ambiguity in a well-formed Sudoku.
How It Works — Step by Step
Rule 1 — No duplicates in a row
Each of the nine horizontal rows must contain all digits from 1 to 9, each appearing exactly once. If a row already contains a 3, no other cell in that row may contain a 3. This rule immediately gives you candidate eliminations for every cell in a row as soon as its neighbors are filled.
Rule 2 — No duplicates in a column
Each of the nine vertical columns must also contain all digits from 1 to 9 exactly once. Column constraints work identically to row constraints but in the vertical direction. Because every cell belongs to both a row and a column, both constraints apply simultaneously.
Rule 3 — No duplicates in a 3×3 box
Each of the nine 3×3 boxes must contain all digits from 1 to 9 exactly once. The box constraint adds a third layer of restriction beyond rows and columns, making certain placements forced and others impossible in ways that pure row/column analysis would miss.
Combining the rules
The power of Sudoku comes from combining all three rules at once. When you place a digit, you should immediately think: what does this block in my row? In my column? In my box? The intersection of these three sets of blocked positions is what constrains the remaining empty cells.
When to Use This Technique
The core rules are always in use — every single technique in Sudoku, from the simplest Naked Single to the most complex AIC, is derived from applying these three rules logically. You never stop using them; you simply find more sophisticated ways to apply them.
Worked Examples
A cell in Row 4, Column 6 of the center box: Row 4 already has 1, 2, 4, 5, 8. Column 6 already has 3, 6, 7. The center box already has 1, 2, 5, 9. Combining all three: the cell cannot be 1, 2, 3, 4, 5, 6, 7, or 8. The only remaining digit is 9. Place 9 here — this is a Naked Single derived purely from the three core rules.
Frequently Asked Questions
Can 0 be used in Sudoku?
No. Standard Sudoku uses only digits 1 through 9. The digit 0 is sometimes used in notation to represent an empty cell (especially in string representations like "530070000..."), but it is never a valid placement.
What if a puzzle has no solution?
A Sudoku with no valid solution has a logical contradiction in its clues — at least two givens violate one of the three rules. Legitimate published puzzles always have exactly one solution.
What makes some Sudokus harder than others?
Difficulty is determined by which logical techniques are required to solve the puzzle. Easy puzzles can be solved with Naked Singles alone. Harder puzzles require Hidden Singles, Pairs, fish patterns, or chains. The number of clues provided also affects difficulty, though clue count alone does not determine it.
Related Lessons
Ready to test your knowledge? Try applying this technique in our Beginner level course, How to Play Sudoku or explore Easy Sudoku puzzles. Keep training to improve your solve times and master the grid!
Ready to Practice?
Apply this technique on a real puzzle from our daily or practice modes.