# Guessing in Sudoku

#### Description

Mathematician Laura Taalman discusses guessing in Sudoku.

#### Expert

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.

#### Transcript

Laura Taalman: Hi! I am Laura Taalman from Brainfreeze Puzzles. Today, we are talking about how to solve Sudoku puzzles. In this clip, I am going to talk about whether or not it's a good idea to guess when solving a Sudoku puzzle. First, some beginning Sudoku players are tempted to guess numbers when they get stuck solving a puzzle. For example, if we didn't have any idea what number should be placed in the board here in this example, we might be tempted to guess a number for the top left cell of the board. Maybe it's a one, that wouldn't immediately cause a problem in the puzzle, so maybe it's okay. In this case that would be a lucky guess because the number that goes in that cell is indeed a one; but of course, we have no way of knowing that at this point of the puzzle. We could just have easily guessed a seven for that cell, which would be wrong. Although seven here will not cause an immediate problem with this puzzle, it will eventually lead to an impossible situation and an unsolvable board followed by a lot of erasing on your part. This is because every Sudoku puzzle has just one solution. There is only one way to fill in the board and satisfy the one rule of Sudoku, that each number appear exactly once in each row, column and block. Each guess you make has a good chance of putting you on a path that can never lead to that one solution. In fact there are over 6.67 sextillion possible Sudoku solution grids. That number is larger than all of the number of grains of sand on all the world's beaches combined. Unless you use logic every step of the way you when solving a Sudoku puzzle, coming across the one solution to a puzzle is going to be like finding a needle in a haystack. Luckily, there are many techniques you can use to determine without a doubt what numbers have to be placed in the Sudoku puzzle. In this series of clips, we will be discussing four of these techniques, one choice, one place, scanning, and double scanning. These four techniques alone are enough to solve most moderate difficulty Sudoku puzzles. There are many other most advanced techniques for solving Sudoku puzzles, many with crazy names like X-wings, Swordfish, Naked Pairs and Forcing Chains, but that's another video. Some puzzles are so deviously difficult that you might need to go beyond even these advanced techniques and do some sort of guessing, but even in those cases it would be a very targeted kind of guessing and a very advanced technique. For most of the Sudoku puzzles that you find in newspapers and books, you should definitely not be guessing. So, if you are not supposed to guess, what you are supposed to do? In the next clip we will talk about the most basic Sudoku solving technique, One Choice.

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