# Finishing the Sudoku Puzzle

#### Description

Mathematician Laura Taalman demonstrates how to finish solving the Sudoku puzzle.

#### 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 discussing how to solve Sudoku puzzles. In this clip we will use the techniques of one choice, one place and scanning to finish the puzzle that we have been working one. If you like to try to finish solving this Sudoku puzzle yourself before I intimate the solution, now is the time to print the puzzle from brainfreezepuzzles.com. I don't recommend writing on your computer screen to finish this Sudoku puzzle. In a minute, I am going to go step by step through one possible way of solving this puzzle. Of course, there is only one solution to the puzzle, but there are many different paths to that solution depending on the order and type of technique that you use and where you use these techniques. At each step in the solution that follows I will suggest a certain technique to apply, pause for a second to give you a chance to press pause and try it on your own if you want to and then show the result of applying that technique. First, there are two very obvious one choices that you can fill in. Can you find them? There is a six you can fill it in the middle block and a nine you can fill in, in one of the rows. Now, try scanning for fours; you should be able to get all of the remaining fours in this Sudoku puzzle. We have a four in the top middle block and another one we can place in the lower right block and in the lower left block; that's all the fours. Now, scan for eights, this time you won't be able to find all of them, only two. Now, scan for nines; you should be able to find all of the nines by scanning. I should point out that the order in which you scan for the nines matters. Sometimes you can't scan for a nine in a certain block, but once you place a nine in a different block you can. So, try looking around the puzzle a few times when you try scanning. There are now two very obvious one choices to fill in. Since one of the numbers we just found was a two, let's try scanning for twos; you should find two of them. There is now another very obvious one choice to fill in and since we just filled in a seven, let's scan for rest of the sevens. Notice that most of the solving we are doing is just repeated scanning and let's try scanning for sixes; you should find two of them. We are almost done with this puzzle. If you apply just the techniques of one choice and one place you should find at least eight new entries in the Sudoku puzzle. You might try to press pause and see if you can find them yourself. Here are the eight entries that you can find. Finding them in the order they appear here is possible. It may now be possible to find them in some different order. Now, we have six cells left open; use scanning to place an eight and the rest shall fall into place. There is our eight and by just one choice and one place we can quickly get the remaining five cells of the puzzle. Now, that we are done let's sit back and admire the fruits of our labor. Notice, that each number one through nine is arranged in a non-attacking pattern on the board. We did it. This is the one unique solution to the puzzle we have been working on, the only way to have one through nine in each row, each column, and each block, given the initial clues that we started with. Today we discussed how to play Sudoku. We learned the one rule of Sudoku, look for the patterns in the solution to a Sudoku puzzle and we learn the techniques of one choice, one place, scanning and double scanning, with those four techniques we solved an entire Sudoku puzzle and those same four techniques should help you to solve most moderate difficulty Sudoku puzzles. Thanks for watching and happy Sudoku puzzling.

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