your query is: # sudoku solver python

Algorithm for solving Sudoku - Stack Overflow

stackoverflow.comHere is my sudoku solver in python. It uses simple backtracking algorithm to solve the puzzle. For simplicity no input validations or fancy output is done.

Sudoku Solver in Python - AskPython

www.askpython.comSteps to solve the sudoku puzzle in Python. In this method for solving the sudoku puzzle, first we assign the size of the 2D matrix to variable M (M*M).

Solve Sudoku using Linear Programming (Python — PuLP)

towardsdatascience.comHere we will try to create one such Sudoku solver. This article aims at exploiting the concepts of linear programming to solve a Sudoku puzzle. We will start ...

Sudoku Solver in Python - Lior Sinai

liorsinai.github.ioThis post describes a Sudoku solver in Python. Even the most challenging Sudoku puzzles can be quickly and efficiently solved with depth ...

Python Sudoku Solver w/ Backtracking - techwithtim.net

www.techwithtim.netThis tutorial will show you how to create a sudoku solver using python and the backtracking algorithm. We will compare this against what is known as the ...

Sudoku | Backtracking-7 - GeeksforGeeks

www.geeksforgeeks.orgRecommended: Please solve it on “PRACTICE ” first, before moving on to the solution. Method 1: Simple. Approach: The naive approach is to ...

Solving Every Sudoku Puzzle - Peter Norvig

norvig.comWe can implement the notions of units, peers, and squares in the programming language Python (2.5 or later) as follows: def cross(A, B): "Cross product ...

Sudoku Solver: A Brute Force Approach Using Python - Better ...

betterprogramming.pubSudoku Solver: A Brute Force Approach Using Python. A complete guide to solving a Sudoku puzzle with a recursive method.

Solving Sudoku in Seconds (or Less!) With Python

medium.datadriveninvestor.comSolving Sudoku in Seconds (or Less!) With Python · A function to check the row for possible values · A function to check the column for possible ...

Building a Simple Sudoku Solver in Python with numPy

medium.comThe logic · Go through each empty cell (0) from the top left · Set possible values for that cell as a list of numbers from 1–9, the first time we ...

Sudoku Solver-Python using Backtracking - Level Up Coding

levelup.gitconnected.comSudoku Solver-Python using Backtracking · sudoku = input("Enter Soduku") · sudoku = input("Enter Soduku") · puz = [[int(sudoku[(i+j)-1]) for i in ...

Sudoku Solver - LeetCode

leetcode.comWrite a program to solve a Sudoku puzzle by filling the empty cells. A sudoku solution must satisfy all of the following rules:.

GitHub - dhhruv/Sudoku-Solver

github.comThis Script is a Sudoku Solver that solves almost any Sudoku Puzzle by visualizing through the Backtracking Algorithm which is made using the PyGame Library in ...

How to build an AI algorithm that solves Sudoku puzzles

www.activestate.comFrom creating the Python environment to building the algorithm, follow along step by step to learn how to use Python to solve Sudoku ...

Create your own Sudoku Solver using AI and Python - Coursera

www.coursera.orgDefine the idea of a Constraint Satisfaction Problem · Implement how to obtain the candidate solutions in the Sudoku game · Implement the Backtracking algorithm ...

Python Programming Challenge 11: Sudoku Solver in Python

learncodingfast.comPython Programming Challenge 11: Sudoku Solver in Python · Step 1: Create and print board · Step 2: Write a function to check if a number is valid ...

OpenCV Sudoku Solver and OCR - PyImageSearch

www.pyimagesearch.comFigure 2: Our OpenCV and OCR Sudoku solver uses a number of open source Python packages including TensorFlow/Keras, OpenCV, scikit-image, and ...

Using PyEDA to Solve Sudoku — Python EDA Documentation

pyeda.readthedocs.ioAccording to Peter Norvig in his fantastic essay on solving every Sudoku puzzle using Python, security expert Ben Laurie once stated that “Sudoku is a ...

How To Solve A Sudoku Puzzle Using Python And Linear ...

www.realpythonproject.comStuck on a Sudoku Puzzle? Python can solve it for you! · Each box must have a digit between 1 to 9 (inclusive) · Each row should contain all the ...

Deep Sudoku Solver (Multiple Approaches) | Kaggle

www.kaggle.comThis tutorial is beginner friendly so anyone with a basic understanding of python and neural nets(convnets) can proceed. What is a sudoku?¶. Sudoku is a logic- ...

A Sudoku solver using Python - One Step! Code

onestepcode.comNote: This solver is a simplified implementation. It will take too long to solve difficult Sudoku puzzles. For a more efficient solution based ...

Valid Sudoku in Python - Tutorialspoint

www.tutorialspoint.comValid Sudoku in Python · create some empty dictionary called row, col and block, row_cube := 3 * (i / 3), and col_cube := 3 * (i mod 3) · for j in ...

Simple Sudoku Solver in Python - Code Review Stack Exchange

codereview.stackexchange.comThe challenge description is: Write a function that will solve a 9x9 Sudoku puzzle. The function will take one argument consisting of the 2D ...

Solved *****Python-3 Code*********SUDOKU | Chegg.com

www.chegg.comPlease Complete the following Sudoku Puzzle using the given starter code. Please Write this Python Code using Backtracking to solve an unsolved 9x9 Sudoku Board.

Sudoku solver Python |Backtracking|Recursion

copyassignment.comBacktracking involves inserting a possible number in the nearest empty box and going to the next unsolved box. This will go on until we run into ...

How to make a sudoku solver with Backtracking Algorithm in ...

articlearn.idThis article explains how to code a simple sudoku solver using a backtracking algorithm in Python. What is backtracking and how does that work?

Solving Sudoku puzzles with Python - University of Warwick

warwick.ac.ukMy Python Sudoku solver is available to download here. Neil reported it took him about three hours to write his solver, mine took a similar time ...

Solve a Sudoku Puzzle Using Backtracking in Python

python.plainenglish.ioA backtracking algorithm builds up a solution incrementally. Checking every step. If the step leads to a valid solution it continues. If the ...

jonathanmartinnyc/python-sudoku-solver-assignment - Jovian

jovian.aiSolving a Sudoku: To solve a Sudoku, you must fill all the blank spaces in the above 9x9 grid with digits so that each column, each row and each of the nine 3x3 ...

Sudoku Solver in Python w/ Backtracking - CSEStack

www.csestack.orgHow does Backtracking Algorithm Work? Backtracking Problem Example | Sudoku; Python Program to Solve Sudoku Problem. Optimizing Sudoku Solver in Python. How ...

ShortestSudokuSolver

blog.singleton.ioThe current shortest Python sudoku solver program is 169 bytes long. This program is clean, in that it does not use any unusual features such as outputting ...

What are some good intermediate Python projects? I have ...

www.quora.comI have done a sudoku solver, checkers game with AI and more. ... I am damn excited to share with you all my first Python project in which I have made a ...

Sudoku Solver using OpenCV & Python - DataFlair

data-flair.trainingBuild a sudoku solver algorithm using Machine Learning with OpenCV in Python. It detects sudoku board from an image and then solves it.

Coding a Sudoku Solver in Python using recursion/backtracking

morioh.comLearn how to code a Sudoku puzzle solver in Python! In this tutorial, I explain how recursion/backtracking work in order to solve a Sudoku puzzle input.

Part 3: Solving the Sudoku. Sudoku Solver AI with OpenCV

becominghuman.aiWe will be creating a Sudoku Solver AI using python and Open CV to read a Sudoku puzzle from an image and solving it.

Sudoku solver using backtracking with python

pythonawesome.comSudoku solver using backtracking with python ... Basically in sudoku, we want to be able to solve a sudoku puzzle given an input like this, ...

codewars -- Sudoku Solver （python） - Programmer Sought

www.programmersought.comcodewars -- Sudoku Solver （python）, Programmer Sought, the best programmer technical posts ... Write a function that will solve a 9x9 Sudoku puzzle.

[LeetCode in Python] 37 (H) sudoku solver - Programmer All

www.programmerall.com[LeetCode in Python] 37 (H) sudoku solver, Programmer All, we have been working hard to make a technical sharing website that all programmers love.

The Top 5 Python Sudoku Solver Depth First Search Open ...

awesomeopensource.comThe Top 5 Python Sudoku Solver Depth First Search Open Source Projects on Github. Topic > Depth First Search. Categories > Programming Languages > Python.

A Nature Inspired Sudoku Solver - LinkedIn

www.linkedin.comThis Python project aims to the development of an open-source experimental prototype for solving and generating Sudoku puzzles by using only the ...

Python Code Examples for solve sudoku - ProgramCreek.com

www.programcreek.com15 Python code examples are found related to "solve sudoku". These examples are extracted from open source projects. You can vote up the ones you like or vote ...

Algorithm for solving Sudoku - Stack Overflow

stackoverflow.comHere is my sudoku solver in python. It uses simple backtracking algorithm to solve the puzzle. For simplicity no input validations or fancy output is done.

Sudoku Solver in Python - AskPython

www.askpython.comSteps to solve the sudoku puzzle in Python. In this method for solving the sudoku puzzle, first we assign the size of the 2D matrix to variable M (M*M).

Solve Sudoku using Linear Programming (Python — PuLP)

towardsdatascience.comHere we will try to create one such Sudoku solver. This article aims at exploiting the concepts of linear programming to solve a Sudoku puzzle. We will start ...

Sudoku Solver in Python - Lior Sinai

liorsinai.github.ioThis post describes a Sudoku solver in Python. Even the most challenging Sudoku puzzles can be quickly and efficiently solved with depth ...

Python Sudoku Solver w/ Backtracking - techwithtim.net

www.techwithtim.netThis tutorial will show you how to create a sudoku solver using python and the backtracking algorithm. We will compare this against what is known as the ...

Sudoku | Backtracking-7 - GeeksforGeeks

www.geeksforgeeks.orgRecommended: Please solve it on “PRACTICE ” first, before moving on to the solution. Method 1: Simple. Approach: The naive approach is to ...

Solving Every Sudoku Puzzle - Peter Norvig

norvig.comWe can implement the notions of units, peers, and squares in the programming language Python (2.5 or later) as follows: def cross(A, B): "Cross product ...

Sudoku Solver: A Brute Force Approach Using Python - Better ...

betterprogramming.pubSudoku Solver: A Brute Force Approach Using Python. A complete guide to solving a Sudoku puzzle with a recursive method.

Solving Sudoku in Seconds (or Less!) With Python

medium.datadriveninvestor.comSolving Sudoku in Seconds (or Less!) With Python · A function to check the row for possible values · A function to check the column for possible ...

Building a Simple Sudoku Solver in Python with numPy

medium.comThe logic · Go through each empty cell (0) from the top left · Set possible values for that cell as a list of numbers from 1–9, the first time we ...

Sudoku Solver-Python using Backtracking - Level Up Coding

levelup.gitconnected.comSudoku Solver-Python using Backtracking · sudoku = input("Enter Soduku") · sudoku = input("Enter Soduku") · puz = [[int(sudoku[(i+j)-1]) for i in ...

Sudoku Solver - LeetCode

leetcode.comWrite a program to solve a Sudoku puzzle by filling the empty cells. A sudoku solution must satisfy all of the following rules:.

GitHub - dhhruv/Sudoku-Solver

github.comThis Script is a Sudoku Solver that solves almost any Sudoku Puzzle by visualizing through the Backtracking Algorithm which is made using the PyGame Library in ...

How to build an AI algorithm that solves Sudoku puzzles

www.activestate.comFrom creating the Python environment to building the algorithm, follow along step by step to learn how to use Python to solve Sudoku ...

Create your own Sudoku Solver using AI and Python - Coursera

www.coursera.orgDefine the idea of a Constraint Satisfaction Problem · Implement how to obtain the candidate solutions in the Sudoku game · Implement the Backtracking algorithm ...

Python Programming Challenge 11: Sudoku Solver in Python

learncodingfast.comPython Programming Challenge 11: Sudoku Solver in Python · Step 1: Create and print board · Step 2: Write a function to check if a number is valid ...

OpenCV Sudoku Solver and OCR - PyImageSearch

www.pyimagesearch.comFigure 2: Our OpenCV and OCR Sudoku solver uses a number of open source Python packages including TensorFlow/Keras, OpenCV, scikit-image, and ...

Using PyEDA to Solve Sudoku — Python EDA Documentation

pyeda.readthedocs.ioAccording to Peter Norvig in his fantastic essay on solving every Sudoku puzzle using Python, security expert Ben Laurie once stated that “Sudoku is a ...

How To Solve A Sudoku Puzzle Using Python And Linear ...

www.realpythonproject.comStuck on a Sudoku Puzzle? Python can solve it for you! · Each box must have a digit between 1 to 9 (inclusive) · Each row should contain all the ...

Deep Sudoku Solver (Multiple Approaches) | Kaggle

www.kaggle.comThis tutorial is beginner friendly so anyone with a basic understanding of python and neural nets(convnets) can proceed. What is a sudoku?¶. Sudoku is a logic- ...

A Sudoku solver using Python - One Step! Code

onestepcode.comNote: This solver is a simplified implementation. It will take too long to solve difficult Sudoku puzzles. For a more efficient solution based ...

Valid Sudoku in Python - Tutorialspoint

www.tutorialspoint.comValid Sudoku in Python · create some empty dictionary called row, col and block, row_cube := 3 * (i / 3), and col_cube := 3 * (i mod 3) · for j in ...

Simple Sudoku Solver in Python - Code Review Stack Exchange

codereview.stackexchange.comThe challenge description is: Write a function that will solve a 9x9 Sudoku puzzle. The function will take one argument consisting of the 2D ...

Solved *****Python-3 Code*********SUDOKU | Chegg.com

www.chegg.comPlease Complete the following Sudoku Puzzle using the given starter code. Please Write this Python Code using Backtracking to solve an unsolved 9x9 Sudoku Board.

Sudoku solver Python |Backtracking|Recursion

copyassignment.comBacktracking involves inserting a possible number in the nearest empty box and going to the next unsolved box. This will go on until we run into ...

How to make a sudoku solver with Backtracking Algorithm in ...

articlearn.idThis article explains how to code a simple sudoku solver using a backtracking algorithm in Python. What is backtracking and how does that work?

Solving Sudoku puzzles with Python - University of Warwick

warwick.ac.ukMy Python Sudoku solver is available to download here. Neil reported it took him about three hours to write his solver, mine took a similar time ...

Solve a Sudoku Puzzle Using Backtracking in Python

python.plainenglish.ioA backtracking algorithm builds up a solution incrementally. Checking every step. If the step leads to a valid solution it continues. If the ...

jonathanmartinnyc/python-sudoku-solver-assignment - Jovian

jovian.aiSolving a Sudoku: To solve a Sudoku, you must fill all the blank spaces in the above 9x9 grid with digits so that each column, each row and each of the nine 3x3 ...

Sudoku Solver in Python w/ Backtracking - CSEStack

www.csestack.orgHow does Backtracking Algorithm Work? Backtracking Problem Example | Sudoku; Python Program to Solve Sudoku Problem. Optimizing Sudoku Solver in Python. How ...

ShortestSudokuSolver

blog.singleton.ioThe current shortest Python sudoku solver program is 169 bytes long. This program is clean, in that it does not use any unusual features such as outputting ...

What are some good intermediate Python projects? I have ...

www.quora.comI have done a sudoku solver, checkers game with AI and more. ... I am damn excited to share with you all my first Python project in which I have made a ...

Sudoku Solver using OpenCV & Python - DataFlair

data-flair.trainingBuild a sudoku solver algorithm using Machine Learning with OpenCV in Python. It detects sudoku board from an image and then solves it.

Coding a Sudoku Solver in Python using recursion/backtracking

morioh.comLearn how to code a Sudoku puzzle solver in Python! In this tutorial, I explain how recursion/backtracking work in order to solve a Sudoku puzzle input.

Part 3: Solving the Sudoku. Sudoku Solver AI with OpenCV

becominghuman.aiWe will be creating a Sudoku Solver AI using python and Open CV to read a Sudoku puzzle from an image and solving it.

Sudoku solver using backtracking with python

pythonawesome.comSudoku solver using backtracking with python ... Basically in sudoku, we want to be able to solve a sudoku puzzle given an input like this, ...

codewars -- Sudoku Solver （python） - Programmer Sought

www.programmersought.comcodewars -- Sudoku Solver （python）, Programmer Sought, the best programmer technical posts ... Write a function that will solve a 9x9 Sudoku puzzle.

[LeetCode in Python] 37 (H) sudoku solver - Programmer All

www.programmerall.com[LeetCode in Python] 37 (H) sudoku solver, Programmer All, we have been working hard to make a technical sharing website that all programmers love.

The Top 5 Python Sudoku Solver Depth First Search Open ...

awesomeopensource.comThe Top 5 Python Sudoku Solver Depth First Search Open Source Projects on Github. Topic > Depth First Search. Categories > Programming Languages > Python.

A Nature Inspired Sudoku Solver - LinkedIn

www.linkedin.comThis Python project aims to the development of an open-source experimental prototype for solving and generating Sudoku puzzles by using only the ...

Python Code Examples for solve sudoku - ProgramCreek.com

www.programcreek.com15 Python code examples are found related to "solve sudoku". These examples are extracted from open source projects. You can vote up the ones you like or vote ...

Algorithm for solving Sudoku - Stack Overflow

stackoverflow.comHere is my sudoku solver in python. It uses simple backtracking algorithm to solve the puzzle. For simplicity no input validations or fancy output is done.

Sudoku Solver in Python - AskPython

www.askpython.comSteps to solve the sudoku puzzle in Python. In this method for solving the sudoku puzzle, first we assign the size of the 2D matrix to variable M (M*M).

Python Sudoku Solver w/ Backtracking - techwithtim.net

www.techwithtim.netThis tutorial will show you how to create a sudoku solver using python and the backtracking algorithm. We will compare this against what is known as the ...

Sudoku Solver in Python - Lior Sinai

liorsinai.github.ioThis post describes a Sudoku solver in Python. Even the most challenging Sudoku puzzles can be quickly and efficiently solved with depth ...

Solve Sudoku using Linear Programming (Python — PuLP)

towardsdatascience.comStep 1: Define the Linear Programming Problem · Step 2: Set the Objective Function · Step 3: Define the Target Variables or the Decision Variables · Step 4: Set ...

Sudoku | Backtracking-7 - GeeksforGeeks

www.geeksforgeeks.orgAlgorithm: Create a function that checks if the given matrix is valid sudoku or not. Keep Hashmap for the row, column and boxes.

Solving Every Sudoku Puzzle - Peter Norvig

norvig.comWe can implement the notions of units, peers, and squares in the programming language Python (2.5 or later) as follows: def cross(A, B): "Cross product ...

Solve a Sudoku Puzzle Using Backtracking in Python

python.plainenglish.ioOne of them was backtracking. Backtracking is not a specific algorithm, rather it is a problem-solving technique. A popular practice problem of ...

Sudoku Solver-Python using Backtracking - Level Up Coding

levelup.gitconnected.comSudoku Solver-Python using Backtracking · sudoku = input("Enter Soduku") · sudoku = input("Enter Soduku") · puz = [[int(sudoku[(i+j)-1]) for i in ...

GitHub - dhhruv/Sudoku-Solver

github.comThis Script is a Sudoku Solver that solves almost any Sudoku Puzzle by visualizing through the Backtracking Algorithm which is made using the PyGame Library in ...

Create your own Sudoku Solver using AI and Python - Coursera

www.coursera.orgIn this project, You will use the Backtracking algorithm to solve CSPs, in a Sudoku game. Backtracking is a recursive algorithm that tries to build a solution ...

Python Programming Challenge 11: Sudoku Solver in Python

learncodingfast.comPython Programming Challenge 11: Sudoku Solver in Python · Step 1: Create and print board · Step 2: Write a function to check if a number is valid ...

Algorithm X in 30 lines!

www.cs.mcgill.caHome · CV · Projects · Python Fun. Algorithm X in 30 lines! If you were ever interested in writing a Sudoku solver, then you probably heard about the exact ...

How to make a sudoku solver with Backtracking Algorithm in ...

articlearn.idThis article explains how to code a simple sudoku solver using a backtracking algorithm in Python. What is backtracking and how does that work?

Sudoku Solver - LeetCode

leetcode.comSudoku Solver. Hard ... Write a program to solve a Sudoku puzzle by filling the empty cells. A sudoku solution must satisfy all of the following rules:.

Sudoku Solver in Python w/ Backtracking - CSEStack

www.csestack.orgHow does Backtracking Algorithm Work? Backtracking Problem Example | Sudoku; Python Program to Solve Sudoku Problem.

Sudoku solver python - Pretag

pretagteam.comIn this method for solving the sudoku puzzle, first we assign the ... same algorithm using backtracking:,I also wrote a Sudoku solver in ...

How to make my backtraching sudoku solving algorithm in ...

codereview.stackexchange.comYour sudoku solver is missing a crucial part: the one that fills ... it should be pretty fast, even when you translate it back to Python.

Generating and solving Sudoku puzzles with Python - lvngd

lvngd.comSteps to generate a Sudoku puzzle · Start with an empty grid. · Generate a complete solution using backtracking that fills up the grid. · Remove ...

Sudoku Generator Algorithm | 101 Computing

www.101computing.netYou can find an example of such an algorithm by investigating the code provided in this Python Challenge: Sudoku Solver using a Backtracking ...

A Sudoku solver using Python - One Step! Code

onestepcode.comImplementing a recursive Sudoku solver in Python. The first step is to generate possible candidates for each empty cell by scanning rows, ...

Solving Sudoku with Backtracking | C, Java and Python

www.codesdope.comExplanation and code of Sudoku-solving algorithm using backtracking. A little introduction about Sudoku and how we can use backtracking to ...

What algorithmic knowledge is required to build a sudoku ...

www.quora.comOriginally Answered: Wha algorithmic knowledge is required to build a sudoku generator, solver, and checker in Python? Backtracking comes to mind right off the ...

Just Another Sudoku Solver in Depth First Search (and ...

helloacm.comJust Another Sudoku Solver in Depth First Search (and BackTracking) Algorithm. March 7, 2021 No Comments algorithms, c / c++, games, python ...

Solved using python, code a simple sudoku solver with - Chegg

www.chegg.comusing python, code a simple sudoku solver with the backtracking algorithm and explain exactly what the backtracking algorithm is doing in the code. Taking the ...

Deep Sudoku Solver (Multiple Approaches) | Kaggle

www.kaggle.comThis tutorial is beginner friendly so anyone with a basic understanding of python and neural nets(convnets) can proceed. What is a sudoku?¶. Sudoku is a logic- ...

How I came back to an old problem and finally wrote a Sudoku ...

www.freecodecamp.orgSo coding was brand new to me when I took that Python class in college. ... I decided to retry implementing the Sudoku solving algorithm to ...

Hard Sudoku Solver Algorithm - Part 1 - Hexadix

hexadix.comHow fast is your sudoku solver algorithm? Can it beat the time limit on this Codewars ... The following sample code is written in Python.

Coding a Sudoku Solver in Python using recursion ... - Morioh

morioh.comLearn how to code a Sudoku puzzle solver in Python! ... Check out this wiki page for some more info about sudoku algorithms that are more intelligent than ...

Sudoku Solver: Python algorithm explained

www.eddaardvark.co.ukThe algorithm works by writing out all the possible answers and then eliminating those that are incompatible with the numbers published in the puzzle. The ...

[LeetCode in Python] 37 (H) sudoku solver - Programmer All

www.programmerall.com[LeetCode in Python] 37 (H) sudoku solver, Programmer All, ... tags: Algorithm Python LeetCode. topic. https://leetcode-cn.com/problems/sudoku-solver/.

[LeetCode] 37. Sudoku Solver Problem Solving Report (Python)

www.programmersought.com[LeetCode] 37. Sudoku Solver Problem Solving Report (Python), Programmer Sought, the best programmer technical posts sharing site.

sudoku-solver · GitHub Topics

hub.fastgit.orgA Sudoku Solver implemented using Python and PyGame Library by visualizing the Sudoku Board using Backtracking Algorithm. game python shell cli library games ...

Python Sudoku Solver - Derek A. Moore

www.derekamoore.comThe goal of this project was to develop a Sudoku Solver in Python to further my Python programming abilities. I made use of a backtracking algorithm for ...

Sudoku solving algorithms - Wikipedia

en.wikipedia.orgSudoku solving algorithms · A typical Sudoku puzzle · A Sudoku (top) being solved by backtracking. Each cell is tested for a valid number, moving "back" when ...

A sudoku solver in Python | Larsblog

www.garshol.priv.noWriting a sudoku solver, however, sounded like it might be fun. ... the difference between optimizing the code and optimizing the algorithm.

The Top 5 Python Sudoku Solver Depth First Search Open ...

awesomeopensource.comSudoku game generator and solver in Python 3+ · Sudokusolver ⭐ 1 · Implementation of Depth-First Tree Search algorithm for solving a sudoku puzzle.