# The One Place Technique in Sudoku

#### Description

Mathematician Laura Taalman demonstrates the one place technique 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 discussing how to solve Sudoku puzzle. In this clip we'll talk about a basic Sudoku solving technique called One Place . In the last clip we saw that we could sometimes find cells in the puzzle for which only one choice of number was possible. Now, we will see that sometimes we can find rows or columns in the Sudoku puzzle for which there is only one place where certain number can go. For example, look at the center column of the puzzle. There must be a one somewhere in this column. There are five open cells in this column where the one could potentially go, but which one is right? Well, there is already a one in the second row, so we know there can't be a one where that row intersects our column. There are also already ones is in the third row, the sixth row, and the eighth row of the Sudoku puzzle. This leaves only one cell in our column where the number one could be placed. There is only one place for the one in this column. Now, our job is to look for other rows or columns, where you might find a one place situation. Let's try the third row and see if we can place a nine in this row. There are seven open cells in this row. Four of these open cells are in columns that already contain nines. There is also a nine in the upper right block of the puzzle and this block intersects our row. Now, we know there are just two locations that the number nine could be placed in this row; but, at this point we can't be certain which of these locations is the one correct place for the nine in this row. So we can't use the method of One Place here. This is going to happen to you a lot as you solve Sudoku puzzles. You try something, see if it works and if doesn't then you move on and try something else. Can you find another row or column where one place might work? Let's try to use one place to fill in a four in the first column. Notice that the upper left block already contains a four. This means that none of the cells in our column that intersect this block can contain the number four. This leaves only one place in our column for the four. We now know how to find rows and columns in the Sudoku puzzle for which there is only one place for a given number; but, what about the blocks of the puzzle? In the next clip, we'll extend the concept of one place to a very powerful Sudoku solving technique known as Scanning.

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