Learn how to play Sudoku - Solve your 4th game of Sudoku for beginners
Follow the step by step solution to the Sudoku for beginners game 4 and learn how to play Sudoku. Solve the bonus Sudoku exercise for practice.
In this fourth session, with brief recap on Sudoku basics, we will directly take up step by step solution of the Sudoku game that was the exercise in the last session.
If you want to skip the brief recap on Sudoku basics and go straight to the solution of game 4, click here.
Brief recap on Sudoku basics
The following is the game board we would solve in this session.
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 a 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.
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 put 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.
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.
We have used the most basic technique of row column scan or horizontal-vertical cross-scanning.
We have used the concept of a favorable zone as a column or a row or a 9-cell square with high digit occupancy so the number of digits possible to fill up the empty cells in the zone is much less and so by eliminating the few other contenders getting only a single digit for a single cell is that much higher.
We also have used digits with high occurrence in the board, that is, the favorable digits to our advantage.
For a favorable digit that has appeared, say, in 7 cells out of maximum 9 possible all over the board, finding the rest of the two valid cells for this favorable digit by row-column scan is generally very easy because of elimination of a large part of the board by its occurrence in most zones.
For convenience let's show again the game we are going to solve.
By primary strategy of row column scan we'll start the game play by scanning for digit 1 with the results: R6C5 1 by scan for 1 in R4, R5, C6 -- R3C4 1 by scan for 1 in C5, C6 -- R2C1 1 by scan for 1 R1, R3 -- lastly R9C2 1 by scan for 1 in R7, R8, C3. All 9 number of 1s are filled.
Taking up scan for next larger digit 2, the single success we get is: R6C9 2 by scan for 2 in R4, R5, C8.
But three successes by row column scan for the next larger digit 3: R4C5 3 by scan for 3 in C4, C6 -- R5C9 3 by scan for 3 in R4, R6 -- R7C7 3 by scanning for 3 in R8, R9, C9 -- lastly R3C8 3 by scanning for 3 in R1, R2, C7. Digit 3 is over.
Changing strategy to focus on most favorable zone of right middle major square with only two empty cells and two missing digits [5,9], R6C8 5by scan for 5 in C7 -- R4C7 9 by exception in right middle major square.
Obtain an opportunistic easy hit in R3C9 5 by column scan for 5 in C7, C8.
Returning back to digit 2 scan for another opportunistic hit: R7C2 2 by scan for 2 in R8, C3 -- R9C5 2 by row scan for 2 on R7, R8.
For both 2 and 3 two numbers of major square cells are left to be filled.
Following is the game status at this point.
Solution to the Sudoku for beginners game 4 Second stage
So digit 1 and 3 are over and two number of 2s are left.
With next larger digit 4, only success is at R1C8 4 by scanning for 4 in R2, C7 and no success with digit 5 by row column scan.
With 6 we get only an easy valid cell hit and no more: R3C6 6 by scan for 6 in C5. An easy valid cell for next larger digit 7 : R1C5 7 by scan for 7 in R2 -- R4C4 7 by scan for 7 in R5, R6 -- R7C6 7 by scan for 7 in C4, C5 -- R9C7 7 by scan for 7 in C8, C9 -- lastly R8C3 7 by scan for 7 in R7, R9, C2.
All 9 number of 7s filled.
R2C5 5 by exception in top middle major square -- R8C5 8 by exception in C5 -- R7C4 9 by exception in bottom middle major square -- R5C4 5 by exception in C4.
Game status at this stage is shown below.
Solution to the Sudoku for beginners game 4 Third stage
First come first served valid cell in this stage with R6C3 9 by scan for 9 in R4, C1 -- R6C6 8 by exception in R6 -- R5C6 9 by exception C6 -- R1C2 9 by scanning for 9 in C1, C3 -- R2C8 9 by scanning for 9 in R1, R3, C7.
And the last R9C9 9 by scanning for 9 in R7, R8, C8 -- R2C7 6 by exception in R2. R8C9 6 by scanning for 6 in R7, C8 --R9C8 8 by exception in C8 -- R9C3 6 by exception in R9.
R2C7 6 by exception in R2.
Game status at this point is shown below.
Solution to the Sudoku for beginners game 4 Final fourth stage
R1C1 6 by scanning for 6 in R3, C3 -- lastly R8C9 6 by scanning for 6 in R7 -- R7C9 4 by exception in C9 -- R8C2 4 by exception in R8.
R4C2 5 by exception in C2.
R3C1 2 by scanning for 2 in C3 -- R1C7 2 by scanning for 2 in R3 -- R3C7 8 by exception in C7 -- R3C3 4 by exception in R3 -- R1C3 5 by exception in R1 -- R7C3 8 by exception in C3 -- R7C1 5 by exception in left bottom major square -- R5C1 8 by exception in R5 -- R4C1 4 by exception R4.
For no valid cell, we have used the more advanced Digit Subset Analysis technique.
Systematic use of row column scan has been sufficient.
Final solution 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 4 - Learn and practice Sudoku level 1
Second and higher level Sudoku games
You will get links to all the 2nd level Sudoku game solutions at Second level Sudoku.
Links to third and higher level Sudoku game solutions are available in the main Sudoku page.
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.