Basic Rules of Sudoku

    Published: 06-16-2009
    Views: 78,805
    Mathematician Laura Taalman demonstrates the basic rules of Sudoku.

    Laura Taalman

    Laura Taalman is an Associate Professor of Mathematics at James Madison University. She received her Ph.D in mathematics from Duke University, and her undergraduate degree from the University of Chicago. Her research includes singular algebraic geometry, knot theory, and the mathematics of puzzles. She is the author of Integrated Calculus, a textbook that combines calculus, pre-calculus, and algebra into one course, and a recipient of the Trevor Evans Award and the Alder Award from the Mathematical Association of America.  As part of Brainfreeze Puzzles, she is an author of the puzzle book Color Sudoku.  Laura lives in Harrisonburg, Virginia where she spends way too much time playing and making puzzles.

    Laura Taalman: Hi! I am Laura Taalman with Brainfreeze Puzzles. Today, we'll be discussing how to solve Sudoku puzzles. In this clip, we'll talk about the basic rules of Sudoku, examine some of the patterns in Sudoku solutions and find a good puzzle to play. Here is an example of a Sudoku puzzle; notice that there are some numbers placed on the board. The object of the game is to fill in the rest of the board with the numbers one through nine. There will be only one way to do this correctly, provided that you follow the one rule of Sudoku. One through nine must appear exactly once in each row, in each column and in each block. Using basic logic in solving techniques, you can fill in all the numbers on the board one by one. Each new number you place on the board becomes yet another clue that can help you determine the remaining numbers. Looking at the solution to this puzzle, notice the positions of the ones. Each one sits in its own block; each one sits in its own column and in its own row. None of the ones attack each other horizontally or vertically and no two ones are ever in the same block. The same is true for the set of twos in the solution, the set of threes in the solution and so on. In general, each cell on the board has its own territory, determined by its row, block and column. Now let's take away the solution so we can work on finding it ourselves. The Sudoku puzzle that we'll be working with today has 29 clues given to start with. So there are 52 numbers that we need to fill in. This is an easy to moderate puzzle with difficulty Level 2 or 5, where I am considering Level 1 to be extremely easy and Level 5 five to be more difficult than what you would find in most books or newspapers. This puzzle is solvable using only the basic techniques we'll cover in this series of clips. If you want to play along as we step through the puzzle, you can print a copy of the Sudoku puzzle at or you can just follow along with the video. You might also want to press pause when I ask questions in the video to see if you can find the answers before I reveal them. Now, that we understand the rules of Sudoku puzzles, how do we go about solving them? In the next clip we will talk about, whether or not you should guess when you try to solve the Sudoku puzzle.