Sudoku

Goal

Fill the 9×9 grid so that every row, column, and 3×3 box contains the digits 1 through 9 exactly once.

Rules

• Each row must contain the digits 1 through 9 with no repeats.
• Each column must contain the digits 1 through 9 with no repeats.
• Each of the nine 3×3 boxes must contain the digits 1 through 9 with no repeats.
• Some digits are pre-filled as clues (called givens) to get you started.

Basic Techniques

• Scanning. Pick a digit and scan each row, column, and box to see where it can and cannot go. When only one spot remains, fill it in.
• Elimination. For an empty cell, check which digits already appear in its row, column, and box. Cross those off. If only one possibility is left, fill it in.
• Pencil marks. When a cell has two or three candidates, note them lightly. As you fill in other cells, revisit your marks to narrow them down.

Tips

• Start where the most clues are. Look for rows, columns, or boxes that already have five or more digits filled in. Fewer empty cells means easier deductions.
• Work one digit at a time. Pick a number and trace it across the entire grid before moving on. This helps you spot placements you might otherwise miss.
• Never guess. Every digit can be placed through logic. If you feel stuck, try a different row, column, or box. A fresh angle usually shakes something loose.
• Watch for chain reactions. Placing one digit often reveals the answer for nearby cells. After each placement, check the affected row, column, and box for new singles.