Learn how to play beginner Sudoku from step by step easy solution of game 5
First solve the beginner Sudoku game 5 and then learn how to play beginner Sudoku from step by step easy solution of the game.
In this fifth 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 5, 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.
Starting with increasing value scan digit strategy starting with 1, success with 1: R9C5 1 by scan in R7, C4, C6 -- R6C7 1 scan in R4, R5, C9. With no more success with 1 next digit 2 taken up.
Next, success with 2: R4C5 2 scan in R6, C4, C6 -- R5C7 2 scan in R4, R6 - R8C8 2 scan in R9, C7 -- lastly R2C9 2 scan in R1, R3, C7, C8.
Digit 2 over.
Turning attention to the very favorable zone right middle major square with only two empty cells and two missing digits [3,7] -- Success: R6C9 7 by scan in C8 -- R4C8 3 by exception in right middle major square.
A quick opportunistic valid cell hit in the neighborhood: R2C7 7 by scan in C8, C9.
Followed by another opportunistic valid cell in the nearby area: R1C5 8 by scan in R2, R3. Continuing with same opportunistic first come first served strategy: R6C5 9 by scan in R4, R5, C6 -- R2C4 9 by scan in C5, C6 -- R3C3 9 by scan in R1, R2.
And the last 9: R9C1 9 by scan in R7, R8, C2.
Continuing opportunistic strategy of easy valid cell spotting: R4C4 8 by scan in R5, R6 -- R8C6 8 by scan in C4, C5. Now in most favorable zone top middle major square with two missing digits [5,7]: R3C5 7 by scan in R2 -- R2C6 5 by exception in the major square.
Following is the game status at this point.
Solution to the Sudoku for beginners game 5 Second stage
Opportunistic R5C4 7 by scan in C6.
R8C4 3 by exception in C4 -- R7C5 4 by exception in bottom middle major square.
Success in next very favorable zone bottom middle major square with two missing digits [3,4]: R8C4 3 by scan in R7.
R3C9 3 in very favorable top right major square with only two missing digits [3,5]: by scan in C8 -- R3C8 5 by exception in R3.
An immediate success with scan for 3: R9C7 3 by scan in R7, R8, C8, C9.
Two missing digits [5,6] in very favorable zone C7: R7C7 5 by scan in R8 -- R7C8 6 by exception in C7.
Two missing digits [4,8] in very favorable zone of bottom right major square -- R9C8 8 by scan in C9 -- R9C9 4 by exception in bottom right major square -- R9C2 5 by exception in R9 -- R1C3 5 by scan in R2, C1, C2.
The scan is automatic for the latest valid digit obtained. This is a major strategic variation to the primary scan strategy of scanning for gradually increasing digits.
Game status at this stage is shown below.
Solution to the Sudoku for beginners game 5 Third and final stage
An easy opportunistic valid cell hit: R1C9 6 by scan in C8.
In the same way, R7C2 8 by scan in R8, C1, C3 -- R7C1 6 by exception in R7 -- R4C3 6 by scan in R5, R6, C1 -- R4C1 7 by exception in R4 -- opportunistic scan R6C2 3 by scan in C3 -- R5C3 4 by exception in left middle major square -- R5C6 3 by exception in R5 -- R6C6 4 by exception in R6.
An opportunistic scan in very favorable zone top right major square with only two missing digits [1,4]: R2C8 4 by scan in R1 -- R1C8 1 by exception in top right major square.
Immediate scan opportunity: R2C3 1 by scan in R1, C2 -- R8C3 7 by exception in C3 -- R1C2 7 scan in R2, C1 -- R1C1 3 by exception in R1 -- R2C2 6 by exception in top left major square -- R8C2 4 by exception in C2 -- R8C1 1 by exception.
Avoided the more advanced technique of possible digit subset analysis DSA by spotting easy scan opportunities following no systematic strategy except an easy next valid digit by row column scan.
Final solution shown below.
We'll now leave you a new game to solve as exercise. You may look up its solution in the sixth session (link below) beginner Sudoku game play.
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 5 - 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.