The three Sudoku rules
- Each row contains 1–9. No digit can appear twice in the same horizontal row.
- Each column contains 1–9. The same no-repeat rule applies vertically.
- Each 3×3 box contains 1–9. The heavier grid lines divide the board into nine boxes.
The numbers printed at the start are called givens or clues. They stay fixed. A well-formed puzzle can be completed by logic, so guessing should not be necessary.
A practical solving routine
1. Scan for nearly complete areas
Look across each row, down each column, and through every 3×3 box. If an area is missing only one digit, that answer is immediate. Write it in, then scan again because one new digit often unlocks another.
2. Cross-check rows and columns
Choose a digit—perhaps 7—and find where it already appears in neighboring rows or columns. Those existing 7s eliminate squares in the box you are studying. If only one square remains available, place the 7 there. This technique is often called crosshatching.
3. Add small candidate marks
When a square has two or three possible digits, write them lightly in the corners. Remove a candidate whenever that digit is placed in the same row, column, or box. If only one candidate survives, it becomes the answer.
Three beginner techniques
Naked single
A square has only one legal candidate after checking its row, column, and box. Because every other digit is excluded, the remaining candidate must be correct.
Hidden single
A row, column, or box may have several empty squares, but a particular digit can fit in only one of them. The square may show several pencil marks; the important fact is that no other square in that area can hold that digit.
Naked pair
If two squares in one row, column, or box contain the same two candidates, those digits must occupy those two squares in some order. You can remove both candidates from every other square in that area.
Common mistakes to avoid
- Guessing too early: a wrong guess can create a contradiction many moves later. Return to scanning first.
- Checking only one direction: every entry must satisfy its row, its column, and its box.
- Using permanent pencil marks: candidates change as the puzzle develops, so keep them small and easy to erase.
- Rushing after a breakthrough: one incorrect digit can spoil the whole grid. Verify each placement.
How to use a printable Sudoku sheet
Choose one large puzzle per page if you want generous writing space. Two per page is a comfortable everyday format; four per page saves paper and works well for experienced solvers. Keep the answer key enabled when teaching or learning, and print puzzles only when you want to share a challenge without revealing the solution.
Start with Easy until scanning feels natural. Move to Medium when you can reliably find singles and pairs, then try Hard when you enjoy maintaining a larger set of candidates. Speed is optional—the real goal is a clean chain of deductions.