## Solve A Medium Sudoku – Part I

Whether you are traveling or recovering in a hospital, Sudoku is a perfect mental workout for you! It helps develop your logic thinking, patience, concentration to solve problems, and confidence.  In my earlier article “How to Design a Sudoku within minutes,” I talked about the idea of designing a Sudoku in the exact REVERSE WAY of solving a Sudoku. If you want to create a Sudoku, you must be able to solve a Sudoku! In this article, following earlier methods – OneChoice and Elimination, I am going to show you two advanced solving methods – Interaction and Subset that used in solving medium Sudoku puzzles.

Interaction

RowBox-Interaction/ColumnBox-Interaction: If a number in a row/column has to be in one box, this number cannot appear in other empty squares of that box.

BoxRow-Interaction/BoxColulmn-Interaction: If a number in a box has to be in one row/column, this number cannot appear in other empty squares of that row/column.

Interaction Example: In the second column, number 1 only appears in the fourth box so other empty squares in the fourth box cannot be number 1

In the second column, number 1 only appears in the fourth box, therefore, either R5C2 or R6C2 will be number 1. If we look at the fourth box, because either R5C2 or R6C2 will be number 1, therefore, all other empty squares in the fourth box will not be number 1. That is, in the fourth box, neither R4C1 nor R5C3 will be number 1. Note: R5C2 is the square at the fifth row and the second column. The fourth box is the intersection of the fourth row to the sixth row and the first column to the third column.

Subset

If the union of candidate values of two/three/four empty squares in a row/column/box are a set of two/three/four different numbers, other empty squares in this row/column/box cannot be any of these two/three/four numbers.

Subset Example: In the third row, the union of candidate values of R3C6 and R3C8 is 3 and 5. Other empty squares in the third row (R3C1, R3C5, R3C7) cannot be 3 or 5.

In the third row, R3C6 and R3C8, their candidate values, combined together, are 3 and 5. Therefore, all other empty squares, including R3C1, R3C5, R3C7 in the third row, cannot be number 3 or 5.

Try today’s medium Sudoku?

Today’s Medium Sudoku 今日数独（难度：中等）

## Solve An Easy Sudoku

Whether you are having a vacation or recovering from the hospital, Sudoku is a perfect number game for you! It develops your logical reasoning ability, patience, your concentration to solve problems, and helps you build confidence.

In my earlier blog “How to Design a Sudoku Within Minutes,” I talked about the idea of designing a Sudoku in the exact REVERSE WAY of solving a Sudoku. If you want to create a Sudoku, you must be able to solve a Sudoku! In this article, I am going to show you two basic methods to solve an easy Sudoku – OneChoice and Elimination.

OneChoice: An empty square can only be filled with a number because all other numbers are taken in its row, column, or box.

Use OneChoice method to infer the number for square R1C9

For the highlighted square, which number must it be? 1 is taken in the ninth column, 2 is taken in the first row, 3 is taken in the third 3×3 box, 4 and 5 are taken in the first row, 6 is taken in the ninth column, 7 and 8 are taken in the first row. Therefore, only number 9 is not taken. The empty square at R1C9 (first row, ninth column) must be filled with number 9.

Elimination: An untaken number in a row/column/box can only be filled in an empty square in that row/column/box because all other empty squares are ruled out.

Where do I put number 6 in the seventh box?  Elimination: In the 7th box, only R8C2 can be filled with number 6.

In the 7th box, number 6 is untaken. Where can we put it? The first column already contains number 6, therefore, R7C1, R8C1, R9C1 can not be filled with number 6. The seventh row already contains number 6, therefore, R7C2, R7C3 can not be filled with number 6. The third column already contains number 6, therefore R9C3 can not be filled with number 6. Therefore, in the seventh 3×3 box, number 6 can only be filled in R8C2.

How about practicing your skills of OneChoice and Elimination and solving today’s Sudoku from createclassicsudoku.com?

## How Can I Solve a Sudoku Puzzle Fast?

You are given a Sudoku with pre-filled numbers in a nine by nine grid.

Your task is to fill all empty squares in this nine by nine grid so that each row/column/box contains nine numbers 1 through 9.

And you know the methods to solve a Sudoku puzzle, including OneChoice, Elimination, Interaction, Subset, X-Wing, XY-Wing, XYZ-Wing, and guessing. You are able to solve Sudoku puzzles. Now, you wonder, how can I solve a Sudoku puzzle fast? What are good practices solving Sudoku puzzles FAST?

If you are in this phase, congratulations! You are exploring the efficiency of solving Sudokus to be an expert Sudoku solver.

When you solve a Sudoku puzzle, you are constantly checking which number should an empty square be, and where an untaken number in a row/column/box goes to.  If this does not work, you write down all the candidate numbers of each empty square and try to refine them using solving methods. To be efficient, you will need to form a routine of solving Sudoku, a routine that is most suitable for you! This routine includes but not limited to

• Form a routine how you scan the empty squares. Some people prefer checking the empty squares from the top to the bottom, then from the left to right; while others prefer checking empty square with most clues first. Choose the one you like the best.
• Form a routine how you examine an untaken number in a row/column/box. Some people prefer checking an untaken number that appears the most in the nine by nine grid; while others prefer checking an untaken number exactly from 1 to 9. Choose the one that works the best for you.
• Form a routine how you use the solving methods.  First, rank the solving methods. Some may think OneChoice is easier than Elimination. While others think Elimination is easier than OneChoice. You need to rank the solving methods based on your preferences.  After ranking the solving methods, you always use the easier solving methods first. An advanced method is used only when all easier methods do not work.
• Be careful not making mistake. Double check. Every time you fill a number in an empty square, double check. This way you are less likely making mistake.

If you develop a routine that works the best for you, you will certainly solve Sudoku puzzles faster.  For me, I like using OneChoice and Elimination first because these two methods do not need me to write any candidate numbers for each empty square. Only when these two methods do not work, I will write down candidate values for the empty squares. Using this routine, I solve Sudoku puzzles pretty fast!

## How do I solve a Sudoku puzzle?

Sudoku is a number game in which missing numbers are to be filled into a 9 by 9 grid of squares which are subdivided into 3 by 3 boxes so that every row, every column, and every box contains the numbers 1 through 9.

You are given a Sudoku puzzle, some of the squares are pre-filled with a number, and your task is to fill the remaining empty squares so that each row/column/box has nine different numbers 1 through 9.

How do I solve a Sudoku puzzle like this? Because this is a logical game, a lot of methods have been summarized to solve Sudoku puzzles, and more to come (you may be the one who will invent new solving methods). The most famous methods are OneChoice, Elimination, Interaction, Subset, X-Wing, XY-wing, XYZ-Wing, and guessing.

• Here are examples of using OneChoice and Elimination.
• Here are examples of using Interaction and Subset.

One book I like the most is Mensa Guide to Solving Sudoku by Peter Gordon. Almost all methods are summarized and plenty of exercises that will use certain methods are given.