11/19/2023 0 Comments Solving sudoku step by step![]() ![]() People however like to challenge themselves. It is enough to use the simplest of these strategies combined with depth first search to solve any Sudoku puzzle very quickly. I can solve these puzzles in 20-30 minutes. It is very easy to rediscover the other basic strategies: pairs, triples, pointing pairs and box-line reduction. To solve the rest of the puzzle, one should compare rows, columns and boxes to eliminate candidates. I can solve such a puzzle in 3-5 minutes. This will create other singles, until the very end of the puzzle. These are cells where there is a candidate that is unique to that row, column, or box. Here is an example of an easy puzzle (left) and a hard puzzle (right). The New York Times publishes daily Sudokus at There are three levels: easy, medium and hard. My solver can find all solutions for any given puzzle. This section only considers puzzles with a unique solution or no solution.Īny given Sudoku puzzle might have multiple solutions, but most published Sudokus only have one. For a computer, all puzzles can be described as “easy”. Because the solver uses search, these levels don’t affect its performance. I’ve gained an appreciation of them over the last few weeks. Difficulty levelsīefore describing my solver, I’d like to give a quick overview of difficulty levels in Sudoku. ![]() One of the more complex of these is Andrew Stuart’s solver which implements 38 different strategies for solving Sudokus.Ī major drawback of this type of solver is, despite the complexity, it cannot solve every type of Sudoku puzzle. There are many solvers which refrain from search or any other trial and error strategies. It does this by combining Norvig’s solver with a Convolutional Neural Network that can read pictures of numbers. This program solves and overlays solutions on pictures of unsolved Sudokus in real time. Raghav Virmani’s augmented reality solver is very cool. ![]() For example, he stores the board as a dictionary instead of a 9x9 array. However, I found his structure unintuitive. I used his set of 95 hard puzzles and 11 hardest puzzles to test my code. He uses a more comprehensive search and constraint propagation strategy and provides a thorough analysis with multiple puzzles. Her code however cannot solve hard puzzles because it only follows a simple constraint propagation strategy. I liked the overall structure of her code, and used it to refactor some of mine. There are two articles I would like to mention that were particularly helpful. I tackled this problem by myself, before comparing it to other online solvers. Other solversĪfter a few days of manually playing Sudoku, I naturally decided to write a solver for it. But all are remarkably easy to solve with computers. These puzzles range in difficulty, and some can be surprisingly hard to solve by hand. The goal of Sudoku is to full a 9x9 grid where each row, column and 3x3 region contains each of the numbers from 1 to 9. “Sudoku” is Japanese for “single number”. Introduction A 17-clue Sudoku puzzleĪccording to Wikipedia, this popular brain teaser puzzle rose to prominence in 2004. Also head over to his own website for a tutorial on Eel.Īs an example of the UI, here is the solution for the 13 March 2021 NY Time’s Hard puzzle: solution. You can download the solver and UI code from my GitHub repository. Update 13-03-2021: Erfan Paslar made a neat user interface for my solver using JavaScript and the Eel Python package. Even the most challenging Sudoku puzzles can be quickly and efficiently solved with depth first search and constraint propagation. Continue using logic and deduction until you have filled in all of the empty squares.This post describes a Sudoku solver in Python. Every Sudoku has one solution, so double check by making sure each column, row and square contains the numbers 1-9 with no duplicates or omissions. Next, you can start scanning each row for a certain number, like 1, to see where it should go. Then look for single empty squares in each row and column that you can fill in. If you see a single empty space in a larger square, fill that in first. For example, if a square already has 7 out of the 9 spaces filled in, you can figure out which 2 numbers are missing and use the numbers in the correlating rows and columns to determine which of the two missing numbers belongs in each space. Some squares already have numbers filled in, so begin by look for missing numbers in a row, column or square. To complete the grid, every column, row and square (each containing 9 spaces) needs to be filled in with the numbers 1-9 without repeating any numbers within the row, column or square. The grid is divided into 9 separate 3 x 3 squares. Sudoku is a game played on a 9 x 9 grid where the object of the game is to fill every space with the correct number. ![]()
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