What strategies help solve a Sudoku puzzle logically?

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To solve a Sudoku puzzle, it is important to clarify that the process relies entirely on logic rather than arithmetic. The objective is to fill a 9×9 grid so that every row, column, and 3×3 subgrid contains all the numbers from 1 to 9 exactly once.1

While specific advanced techniques exist, the fundamental logical strategy involves:

Elimination: By identifying which numbers are already present in a given row, column, or 3×3 subgrid, you can determine which numbers are missing and must be placed in the remaining empty cells.
Constraint Satisfaction: Because each number 1–9 can appear only once in its respective row, column, and subgrid, you can logically deduce the placement of a digit by observing where it is restricted from appearing in other cells.
Deduction: As you fill in cells, you create new constraints for the remaining empty spaces, allowing you to solve the puzzle step-by-step through systematic observation.1

The difficulty of the puzzle is determined by the quantity and initial positions of the numbers provided at the start.1