Sudoku Puzzle Solving – A Beginner’s Guide

April 24th, 2009 | By Balasingam

SUDOKU Puzzle Solving – A Beginners’ Guide. This guide is for the absolute beginner who has difficulty in getting started with Sudoku Puzzles. In this Part One of the tutorial, we will take you through the simple steps of scanning to begin filling in as many cells as you can. Once you get the idea of how to solve the initial steps, you will be able to continue and solve the demo puzzle. We shall avoid all the buzz words used to explain various steps and go by pure logic based on the Sudoku Rule. This is possible for the Easy Puzzles.

Sudoku is a Numbers Puzzle played by millions of children and adults, world-wide, from below age 7 to above age 70. The History of Sudoku is posted elsewhere in the website under Articles.

The Classic Sudoku Puzzle, which is the most popular, has a 9 x 9 grid with nine rows, nine columns and nine 3 x 3 sub-grids, containing a total of 81 cells with about 25 to 35 given numbers. To solve the puzzle, the player is required to complete all the remaining blank cells based on one simple rule.

Rule: Complete all the blank cells in the 9 x 9 Grid so that each row, each column and each 3 x 3 box (sub-grid) contains all the digits 1 to 9 without repetition.

Sudoku puzzle solving does not require any mathematical or language skills, or general knowledge; just logic, and lots of patience for the puzzles graded difficult. It is fun, challenging and good for a mental workout. It will enhance the development of Logic and Deductive ability in children and has been acclaimed to be beneficial in delaying the onset of Alzheimer’s among the elders, if prone.

Solving a simple sudoku puzzle – A Step By Step Guide – Part One

In the Sudoku Grid below, the nine rows and nine columns are indicated by R1 to R9 (row 1 to row 9) and C1 to C9 (column 1 to column 9). The nine sub-grids are designated as Box 1 to Box 9 from left to right.

Please print the Demo Puzzle, below, or copy the given numbers on to a Blank Grid. (You can download and print an A4-size blank grid on this website)

As you follow the Steps One to Eight, fill in the blank cells on the Demo Puzzle to give you a hands-on feeling of solving the puzzle. As you go through the Steps, read C1 as Column 1 and R2 as Row 2 and so on.

The following Steps are illustrated with arrows showing the Rows or Columns in which a particular digit cannot be placed because the digit is already present in that Row, Column or Box (Sudoku Rule). You will observe that it is partly a process of elimination. To determine where a particular digit can be placed, we have to first identify in which cells in a Row, Column or Box the digit cannot be placed.

The Blank Cells solved are added progressively in each subsequent Step. The original given numbers are in Black. In each Step below, all previously solved cells are in Red and the current solved cell(s) is [boxed in Red]

To solve a sudoku puzzle, we first scan the puzzle to identify the digits that occur more frequently. In this puzzle, there are more of the digits 1,4,5,7 and 9 than the others, within the given numbers.

We will scan three rows or three columns of three boxes at a time, (horizontally or vertically).

Step One: Taking the first three boxes, there is a 7 in Row 3 of Box 1 and a 7 in Row 2 of Box 2 as shown by the arrows. There is no digit 7 in Box 3. Digit 7 cannot be in Row 2 or Row 3 as per the sudoku rule. It can then only be in Row 1. There is only one blank cell left in Row 1 of Box 3, i.e. position R1-C8, (between the digits 9 and 4).

So we are sure that the digit 7 can only be placed in R1-C8 in Box 3. You can now write the digit 7 in your Demo Puzzle as in Step One above.

Congratulations! You have placed your first digit.

Step Two: We now look at Columns 1, 2 and 3. We observe that the digit 9 appears in Boxes 4 and 7 but not in Box 1. The digit 9 cannot be in Columns 1 and 2 of Box 1 as shown by the arrows.

It can only be placed in Column 3. There is a blank cell R2-C3 between the digits 8 and 3. So this is the only location for the digit 9 in Box 1. Now you can put the digit 9 in R2-C3 on your Demo Puzzle.

(Note that the same result would have been derived, as above, for digit 9 if Rows 1, 2 and 3 had been scanned as shown by the arrows in Row 1 and 3.

Step Three: As in Step 2, we observe that the digit 4 appears in Boxes 4 and 7 but not in Box 1. The digit 4 cannot be in Column 1 or 3 of Box 1. It can only be placed in Column 2.

There are two blank cells in Column 2 of Box 1. Now the digit 4 could possibly be in either of these cells (R1-C2 and R2-C2). Now we have to see if the digit 4 appears anywhere along R1 and R2. There is a digit 4 in R1-C9; so it cannot be placed in R1-C2. Therefore the only position for digit 4 is in R2-C2 in Box 1.

We have now completed three of the blank cells. As each additional cell is completed, we will find it easier in our progress in solving this puzzle.

Step Four: Having completed Step 3 for the digit 4, we can find the cell for digit 4 in Box 2. We can see that R3-C4 is the correct blank cell for the digit 4 as it cannot be in R1, R2, C5 and C6.

Step Five: The digit 5 is placed in R4-C6 of Box 5, as it is the only blank cell in Column 6 in Box 5 for the digit 5, as indicated by the arrows from the digit 5 in Boxes 2, 6 and 8.

Step Six: Having solved Step 5, it is now easy to place the digit 5 in R5-C2 in Box 4, as it cannot be in Row 4 or Row 6 or in Boxes 5 and 6 as indicated by the arrows from the digit 5 in Boxes 5 and 6.

Step Seven: Based on the previous steps, try to deduce the positions of the digits 4 and 7 as shown. The arrows from the digit 4 in Boxes 3 and 4, and the digit 7 from Boxes 4 and 5 will fix the placement of 4 and 7.

Step Eight: The digits 9 and 4 are shown solved in Boxes 8 and 9. The digit 9 in Box 8 is solved here with the placement of 9 in Boxes 2, 5 and 7 as indicated by the arrows. Similarly the digit 4 in Box 9 is solved with the help of the arrows from the digit 4 in Boxes 3, 7 and 8.

By now, you should have a pretty good idea of solving a simple Sudoku Puzzle (classified as “Easy”). Try solving the rest of the puzzle and you can check your progress against the Solved Puzzle.

The Sudoku rule is so simple. All you have to do in the initial stages is to remember that every Row, Column and Box must have the digits 1 to 9. The rule itself is the clue to solving Sudoku Puzzles.

We would greatly appreciate any constructive feedback on whether the guide is clear and easy to follow, and suggestions on how to improve the presentation.

Please email to balasingam@sudoku.com.my or use the ‘Contact Us’ link to submit your comments

Have Fun.