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Solving Sudoku and the 8-Queens Puzzle as Constraint Satisfaction

Learn how to formulate and solve Sudoku and the 8-Queens puzzle as constraint satisfaction problems (CSPs) using Python.

Solving Sudoku and the 8-Queens Puzzle as Constraint Satisfaction

You will learn to:

Formulate Sudoku as a CSP.

Formulate the 8-Queens problem as a CSP.

Solve CSPs using Python.

Reduce one problem to another problem.


Data Visualization

CSP Formulation

Constraint Libraries


Intermediate knowledge of Python

Familiarity with constraint satisfaction problems

Basic understanding of Sudoku and the 8-Queens problems



Project Description

Constraint satisfaction problems (CSPs) are problems in artificial intelligence and computer science whose solution must satisfy a particular set of constraints. A constraint is a condition or restriction that a solution must meet. CSPs are often used to model problems associated with scheduling, planning, and resource allocation. These problems can be solved using various techniques, including search algorithms, constraint programming, and local search.

A Sudoku board is a 9x9 grid divided into 3x3 sub-grids called regions. The objective is to fill the grid with the digits 1–9 such that each digit appears in each row, column, and region just once. Sudoku is usually presented as a partially completed grid, and the player must fill in the blanks according to the rule above.

The 8-Queens problem is another classic example of a constraint satisfaction problem. The goal is to place eight queens on a chessboard such that no two queens threaten each other. This means that no two queens can be placed on the same row, column, or diagonal.

In this project, we’ll formulate both problems as CSPs and solve them using constraint programming in Python.

Project Tasks


Getting Started

Task 0: Getting Started

Task 1: Import the Necessary Modules


Solve the Sudoku Problem

Task 2: Generate a Sudoku Problem

Task 3: Define the Variables

Task 4: Create the CSP Instance and Add Variables

Task 5: Add the Constraints

Task 6: Satisfy the Constraints and Print the Solution


Solve the 8-Queens Problem

Task 7: Create a Problem and Add Variables with Domains

Task 8: Add Constraints to the Problem

Task 9: Satisfy the Constraints and Get the Solution

Task 10: Create a Board and Show the Solution