In the example below, the two yellow highlighted squares must contain 1 and 8 because all the other digits have been eliminated since they already appear in the column, row, or box of the square. That means to find a square that can only be one possible number. Most people will determine the possible number for one box at a time, instead of for the full grid.Īfter you eliminate numbers, you can look for single candidates. The possible numbers were determined by eliminating all digits that occur in the same column, row, or box. In the example below, the possible numbers for each square are noted in a smaller font. The second thing you should do is to look for a single candidate. The first thing you should do is to eliminate numbers from rows, columns, and boxes (3x3 subgrids). When solving a Sudoku puzzle, you should be constantly doing two things. In the image below from a Sudoku game, the number that should go in the blue highlighted square cannot be in any of the yellow squares corresponding to the column, row, and 3x3 box. The puzzles start with some numbers already on the grid and it's up to you to fill in the other numbers. The objective is to fill a 9x9 grid with digits (1-9) so that each column, row, and each of the nine 3x3 subgrids (also called boxes) all contain each of the digits from 1 to 9. This article is about the most popular type. Sudoku is a number-placement puzzle and there are a few different types. After reviewing Sudoku and some strategies, I will break down Norvig's code step-by-step so you can understand how it works. Norvig's solution is considered a classic and is often referred to when people develop their own code to play Sudoku. Peter Norvig developed an elegant program using Python to win sudoku using constraint propagation and search. Who needs thinking when you can let the computer think for you. But more importantly, you will learn how to use machine learning to easily solve every Sudoku puzzle. In this article, you will learn how to play and win Sudoku. Now we have computers! (Ok, so most people still just use their minds.) When it first came out people had to actually solve the puzzles using only their minds. You can find many more puzzles on the internet, in a whole range of difficulty levels.Sudoku (and its predecessors) has been played for over a hundred years. If you reach a contradiction (a repeated digit in a row, column, or block), you should retrace your steps and undo what you've done until you have no contradiction.Įxercise: Here is a Sudoku puzzle for you to try: Continue playing, using the strategies above and any other ones you discover. If no entries are forced, try to pick a box with the fewest number of possibilities and pick one of them. Similarly, a triple of cells having only three possibilities of entries between them will eliminate these entries in all other cells in a neighborhood of this triple. This will decrease the number of possibilities for the other cells in the neighborhood and help you get closer to a solution. What you can still gain from this observation is that those pair of numbers cannot occur anywhere else in the neighborhood. You might find that a pair of cells has only two options of entries, but don't know which goes where. One more complicated strategy is to look at pairs or triples of cells within a row, column, or block. You often need more complicated analysis methods to make progress, and sometimes you need to make a guess and proceed, backtracking if the guess results in a conflict. These two strategies are usually not enough to completely fill in a Sudoku grid. Once you've done this, the chosen number can be eliminated from being a possibility for any other cell in the neighborhood. If the digit can only be placed in one cell in the neighborhood, you should fill that cell in. Note all the cells in the row, column, or block in which the number can be placed without violating the One Rule. If a cell ends up having only one possible entry, it is a "forced" entry that you should fill in.Īnother way to proceed is to pick a number and a row, column, or block. The most basic strategy to solve a Sudoku puzzle is to first write down, in each empty cell, all possible entries that will not contradict the One Rule with respect to the given cells. In fact, mathematical thinking in the form of logical deduction is very useful in solving Sudokus. Any nine symbols would serve just as well to create and solve the puzzles. The puzzle does not depend on the fact that the nine placeholders used are the digits from 1 to 9. When one hears that no math is required to solve Sudoku, what is really meant is that no arithmetic is required.
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