🧩 Puzzles
9️⃣Sudoku Introduction
Rows, columns and boxes each hold 1–9 once — a quiet detective game of pure logic.
A 9×9 grid hands you barely a dozen digits, yet a single answer hides inside. Sudoku needs no arithmetic and no speed — it tests how well you can eliminate suspects like a detective.
Only three rules
- Every row must contain 1–9, no repeats;
- Every column must contain 1–9, no repeats;
- Every 3×3 box outlined in bold must contain 1–9, no repeats.
The digits printed at the start are the clues. A good puzzle has exactly one solution, reachable by pure reasoning — no guessing needed.
Place 1–9 so every row, column and diagonal sums to 15
Remaining
Warm up with the magic square to get a feel for placing digits in a grid: every row and column must sum to the same total. Once the grid feels familiar, sudoku adds just one more rule — the box — and the reasoning gets richer.
Elimination: the detective's first tool
A row already shows 1, 2, 3, 4, 5, 7, 8, 9. Who is missing? One glance says 6 — no repeats allowed. But does the column of that empty cell already hold a 6? Then 6 cannot enter either. Sweep the row, sweep the column, sweep the box, and the one surviving candidate is the answer. Nearly every sudoku is solved by squeezing cells out like this, one at a time. The whole mantra: shrink the suspect list until only one name remains.
Full reasoning on a 4×4
9×9 too big? Start with the mini version: a 4×4 grid using 1–4, where every row, column and 2×2 box holds no repeats.
| 1 | · | 3 | · |
|---|---|---|---|
| · | 4 | · | · |
| · | · | · | 3 |
| 4 | · | 2 | · |
Step by step:
- The top-left box already holds 1 and 4 and lacks 2 and 3; row 1 already has a 3, so row 1 column 2 takes 2, and row 2 column 1 takes 3;
- Row 1 is missing only a 4 — so column 4 gets it;
- Column 3 already holds 3 and 2, so row 2 column 3 can take neither; the row lacks 1 and 2, so it takes 1, and the last cell of row 2 takes 2;
- Column 1 already holds 1, 3 and 4, so row 3 column 1 must take 2; keep reasoning this way and the grid fills in quickly.
The solution:
| 1 | 2 | 3 | 4 |
|---|---|---|---|
| 3 | 4 | 1 | 2 |
| 2 | 1 | 4 | 3 |
| 4 | 3 | 2 | 1 |
What when you get stuck
When elimination runs dry, expert solvers pick the cell with the fewest candidates and assume one value: the moment a row or box shows a repeat or a dead end, the assumption was wrong — back up and try another. That is trial and backtracking, the same idea as search in programming. Remember, though: official sudoku puzzles are guaranteed solvable by reasoning alone, and guessing stays a last resort.
Ready for a real 9×9 board? Play Mini Sudoku on the games page. If the logic itch is not scratched yet, keep going with Logic Puzzles and Magic Square.
Check yourself
Quick quiz
1. In sudoku, what is a 'box'?
2. A row already holds eight different digits, 1 through 8. What goes in the last cell?
3. In a 4×4 sudoku, a cell's row already holds 1 and 2, and its column already holds 3. What can it be?