Solve your 3rd easy Sudoku for beginners
Learn how to play Sudoku from scratch by playing the third Easy Sudoku for beginners. Step by step solution of the game follows the very basic techniques.
After going through the last session, we hope that you have successfully solved the Sudoku game we have given you at the end as an exercise.
But remember, playing only one or two Sudoku games is not enough. You have to play enough number of easy games even at this starting level so that finding a valid cell by row column scan or by exception becomes a part of reflex.
In this third session also we would have a recap on how to play Sudoku, but we will keep it brief. To skip and go straight to the solutions, click here.
Recap on How to play Sudoku in brief
Today we will play the following game of easy Sudoku for beginners.
This is the game we left you to solve in the last session. We hope some of you have solved it already. In today's session we will move a bit faster than before as you have already experienced Sudoku game playing to some extent.
The 81 cell board above is a specific Sudoku game board with some cells filled up with digits from 1 to 9. These are the valid digits that you can use to fill up any empty cell.
While filling up any empty cell you must follow the Sudoku game rule:
You must not repeat any digit in any column, in any row or in any 9-cell medium sized square bordered by thick lines.
The whole board has 9 such 9 cell squares with thick borders.
Ultimately your job is to fill up all the empty cells with digits 1 to 9 but without breaking the Sudoku game rule not even once. Then only we would say you have successfully completed the game.
For convenience, we will use the labels C1, C2, C3......C9 for identifying the 9 columns and labels R1, R2, R3....R9 for 9 rows.
We will refer to a cell by its row label suffixed with column label. For example top left corner cell is R1C1 and bottom right corner cell is R9C9.
Each of the 9-cell groups we will call a 9-cell square or major square.
The nine major squares are identified as top left, top middle, top right, left middle, central middle, right middle, bottom left, bottom middle and lastly bottom right.
A row, a column or a major square each has 9 cells and broadly referred to as a Zone.
Primary objective at each step
The only objective at each step is to find a cell in which one and only one digit can be placed. This is what we call a valid cell.
As you go on filling up empty cells, the number of empty cells gets reduced and it gets more and more easy to find a valid square with only one digit placement possibility. Near the end suddenly you can fill up all the remaining cells one after the other quickly, as possibility of digit placement in each cell is highly reduced at this stage.
Generally the more a Sudoku game board has cells filled up already, the easier it is to solve it. Conversely if you attempt a Sudoku game with lots of empty cells, finding a valid cell at each step may be very difficult.
But at this beginning stage we won't worry about that, as we know each game that we will solve, should not pose great difficulties.
Once you get fully comfortable with the basic techniques and strategies of finding a valid cell and valid digit, you would be ready for the next stage of difficulty. We will mention when we try a game of higher level of difficulty.
Valid cell and Valid digit
We would repeat the definition of valid digit and the valid cell.
We define a VALID digit as the digit you write in an empty cell so that,
It is the only possible digit which you can put in the cell following the rules of the game.
It means, the valid cell and its valid digit have the characteristics that, the digit you are considering does not appear at all in any of the row, column and the 9-cell square that contain the valid cell. The valid cell is the only place where you can put the digit. Additionally, you can't put any other digit in the valid cell. This situation is unique for the particular digit placement.
As before, the most important objective is, how to find out the cell in which you can put one and only one digit out of the digits 1 to 9.
In Sudoku game playing, the start may always give you some trouble.
The first basic technique that we will have to apply constantly is the row-column scan or horizontal-vertical cross-scanning.
Row-column scan or Cross-scanning
We look at contiguous (adjacent) three rows (or columns) of a 9-cell square zone (say R1, R2, R3 or C4, C5, C6 but not C3, C4 and C5 as the columns in this case cross over two sets of 9-cell squares) and if in any such three rows (or columns) we find a digit to have appeared twice then these two rows (or columns) are technically invalid zones for the particular digit.
You can place the digit then only in the third row (or column) unoccupied.
We have thus narrowed the possibility of the particular digit placement to one row.
But again, as the other two appearances of the digit are in two 9-cell squares, the digit can only appear in the third 9-cell square, thus leaving only three possible cells for it. We have narrowed the possibility of placement to three cells.
Now we change direction of scanning by 90 degrees and scan those three columns or rows for occurrence of the digit.
This is why we call this cross-scanning or row column sweep. If you scanned three rows first, finally you have to scan three columns.
If you are lucky you will eliminate by this process two out of three cells for placing the digit leaving a single valid cell where without any shred of doubt you can put the digit under consideration.
By this cross scanning you have not only been able to find the valid cell, but also ensured that the row, column or the 9-cell square containing the valid cell does not have any single occurrence of the digit you are considering to put in the valid cell.
A favorable zone may be a column or a row or a 9-cell square with high digit occupancy so that possibilities of filling up the empty cells in the zone is much less and so getting a valid cell is high.
On the other hand, as a particular digit can appear in the whole board only 9 times, a digit with high occurrence in the board has a higher chance of helping you to find its rest of the valid cells (each digit finally has a particular valid cell in a row or a column or a 9-cell square). We call a digit with a high number of occurrence as a favorable digit.
For convenience let's repeat the game we are going to solve.
Following our systematic primary strategy of valid cell search for easy Sudoku games, we start with R2C6 1 by row column for digit 1 in C4, C5 and that was the only success with digit 1.
Five major squares without a 1 couldn't be cracked. So we take up row column scan for 2 and quickly take up scanning for digit 3 because of too few numbers of digit 2 and no success with it.
This time with 3, there has been three consecutive successes: R9C5 3 by column scan in C4, C6 -- R8C1 3 by row scan for 3 in R7, R9 -- R2C2 3 by row column scan for 3 in R3, C1. That's the end of success on digit 3.
Two major squares without 3 couldn't be breached.
The empty cells in the major squares influenced by 1 and 3 for the valid cells for these two digits are shaded yellow.
Following is the status at the end of stage 1.
Solution to the third Sudoku for beginners: Second stage
Take up row column scan for next larger digit 4 for the two successes remaining to complete all 9 numbers of 4s.
But the first is by largest scan of 2 rows and 2 columns: R1C9 4 by row column scan for 4 in R2, R3, C7, C8 -- R5C5 4 by row column scan for 4 in R4, C4, C5. That completes 9 numbers of 4.
From previous scan of 3 we remember the failure to get a valid 3 in top right major square by a whisker. With R1C9 filled with 4, we take up strategy variation to return to scanning for 3. This is an opportunistic easy valid cell hit that is to be grabbed without hesitation.
First success with 3 is in R1C7 3 by row column scan for 3 in R2, R3, C8 followed by the ninth and last digit 3: R5C9 3 by R4, R6, C7, C8.
In the meantime a very favorable zone is created as row R1 with only two empty cells left with digits [6,8] left.
Success with digit 8 that would otherwise have been far in future: R1C8 8 by column scan for 8 in C5 on two empty cells of top row R1 AND NOT ON EMPTY CELLS OF A MAJOR SQUARE.
This is the second type of equally effective scan.
So only cell left in R1, the cell R1C5 gets 6, the only digit left in R1.
Exploring the same avenue of incomplete smaller digits success with 2: R5C5 2 by row column scan for 2 in R4, C4.
Empty cells blocked by the row column scans are shaded yellow.
Status till now shown.
Solution to the third Sudoku for beginners: Third stage
We remember that while scanning for 4 we went back for scanning for 3.
Coming back to track, we'll now take up row column scan for 4 with immediate success of the ninth 4: R9C1 4 by row column scan for 4 in R7, C2, C3.
Digit 4 is fully filled along with digit 3.
This last 4 has created a very favorable row R9 with only two cells left with digits [2,9] left -- success with column scan for 2 on empty cells of row R9 -- R9C3 2 by 2 in C2 -- R9C2 9 by exception in row R9.
The other very favorable zone top middle major square with 2 empty producing no success we'll return to primary scan.
Which digit will it be?
As 3 and 4 are fully filled we'll dutifully scan for digit 5 and we get one success: R5C7 5 by row column scan for 5 in R4, R6, C8.
Trying to get more valid cells for 5 and next for 6 both attempts fail in quick time.
This is how we realize that this game is though an easy Sudoku for beginners, it still not as easy as the two earlier games.
Cells blocked for valid digit scans are shaded yellow.
Status till now shown below.
Solution to the third Sudoku for beginners: Fourth stage
Continuing with primary strategy we try for digit 7 scan and fail again.
But scan for next larger digit 8 gives you success: R6C9 8 by row column scan for 8 in R4, C8.
Going back to digit 1 scan with no success, we get our breakthrough with digit 2: R2C1 2 by scan in R2, C3 -- opportunistic valid digit in R3C3 7 by scan in C2 -- R2C1 8 by exception in top left major square.
A simple valid cell: R3C4 8 by scan for 8 in R2 -- R2C4 5 by exception in top middle major square -- R2C9 6 by exception in R2 -- R5C8 6 by scan for 6 in C9 -- R4C9 1 by exception in left middle major square.
Opportunistic valid cell R3C9 5 by scan for 5 in C7, C8 -- R3C8 9 by scan for 9 in C7 -- R3C7 1 by exception in top right major square.-- R7C7 6 by exception in C7 -- R8C8 1 by exception in C8.
Status till now is show below.
Solution to the third Sudoku for beginners: Final fifth stage
Breakthrough at this stage with the new type of scan on empty cells of a zone: R4C1 6 by scan for 6 on empty cells R4C1, R4C6 and 6 in C6.
R4C6 9 by exception in R4 -- opportunistic R8C4 9 by scan for 9 in C6 -- R7C9 9 by scan for 9 in R8 -- R8C9 2 by exception in bottom right major square -- R8C6 8 by exception in R8 -- R7C6 2 by exception in C6.
With scan for 6 on two empty cells of column C4, R6C4 6 -- R5C4 7 by exception in central middle major square -- R6C1 7 by scan for 7 in R5 -- R7C2 7 by scan for 7 in C1, C3 -- R5C2 8 by exception -- R7C3 8 by scan for 8 in C1 -- R5C3 1 by exception in C3 -- R5C1 9 by exception in left middle major square -- R7C1 1 by exception in the whole game.
In beginner level Sudoku, you should be able to solve every game with these simple most basic techniques and strategies based on row column scan for hidden singles.
Final solved game shown below.
We would repeat now our recommendation regarding playing medium.
Should you play Sudoku using pen and paper, in a mobile or using something else? Our strong recommendation is,
Always play Sudoku in a spreadsheet program, if possible, at least at the beginning stage. We are not aware of any better medium of Sudoku game solving, be it an easy game like we have solved just now or the reportedly hardest Sudoku game in the world.
Lastly we leave a game for you to solve.
A game for you to solve
We leave you here with a new game for you to solve. In our next session we will present its solution and another new game.
Sudoku for beginners learning and practice sessions
Sudoku for beginners 3 - Learn and practice Sudoku level 1
Assorted Interesting Sudoku game plays
These Sudoku game solutions are collected from various sources and are found to be interesting. You can get these Sudoku solutions at Interesting Sudoku not classified at any hardness difficulty level.
Second and Third level Sudoku games
You will get links to all the 2nd level Sudoku game solutions at Second level Sudoku.
Links to third level Sudoku you will get first at 2nd level game solutions and links to fourth level Sudoku you will get in the 3rd level solutions.
It is recommended that without jumping over any of the hardness levels, one should progress through solving higher level Sudoku games strictly step by one step up. For example, you shouldn't play a 3rd level Sudoku game without being comfortable in solving 2nd level games.