## Let's play Sudoku - Game 5

In this fifth session we will solve the Sudoku game we left as exercise in the last session.

In this session we will spend little time on what is Sudoku and what are its rules of play and so on. If you want to know please refer to any of our * session 1*,

*or the*

**session 2***.*

**session 3****Links for all our Beginner level Sudoku game plays is available at the end.**

It is recommended that you solve at least a few easy Sudoku games at this level by yourself before graduating to the second or higher level of games.

The following is the game board we would solve in this session.

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 select the valid cells sequentially and in five lots of step sequences we will solve the game completely.

In each valid cell step, we will first mention **the cell number** (by row number appended by column number, rows are numbered R1 to R9 and columns C1 to C9), then the **valid digit for the selected cell**, followed by the **scan row-column set** or if **by Exclusion technique** just 'Exclusion' and if by Digit Subset Analysis technique by '**DSA**'. We will leave a **remark** also in a step if required.

*After each set of steps*, **the result of our selection will be shown** and then the next set of steps will follow. This will **continue till we completely solve the game.**

If you feel any difficulty at any point, please refer back to our earlier sessions, **session 1,*** session 2*, or

*.*

**session 3**Before starting just remember once again, the 81 cell board above is a specific Sudoku game board with some cells filled up with valid digits from 1 to 9 and while filling up any empty cell you must follow the **Sudoku game rule:**

You

must not repeat any digitin any column, in any row or in any 9-cell mediumsized square bordered by thick lines.

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 and specify by the three row labels suffixed by three column labels. For example the top right **9-cell square is R1R2R3-C7C8C9.**

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.**

**Aside:**

**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 mot basic technique of row column sweep or horizontal-vertical cross-scanning and also the more powerful technique of digit subset analysis. We have used Exclusion technique wherever we found it possible.*

*We 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 have also 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 sweep is generally very easy because of elimination of a large part of the board by its occurrence in most zones.*

### Let's find the batch of valid cells - first stage

Valid cell **R6C5 for digit 9** by scan R4, R5, C6 –- **cell R2C4, digit 9**, scan C5, C6 – **cell R3C3, digit 9**, scan R1, R2 -- **cell R9C1, digit 9**, scan R7, R8, C2 : digit 9 over -- **cell R6C7, digit 1**, scan R4, R5, C9 : existing -- **cell R2C6, digit 5**, scan C4, C5 : existing -- **cell R9C5, digit 1**, scan C4, C6, R7 : existing – **cell R4C5, digit 2**, scan C4, C6 – **cell R5C7, digit 2**, scan R4, R6.

Freezing the board at this stage, as usual we copy it to a new place in our spreadsheet, and start analyzing fresh for finding the next valid cells.

Observe that in this play session, we have not colored the cells except coloring the **starting cell with green.** Later when we may have to use **Digit subset analysis technique**, we will **color the first result out of the analysis with light blue**.

But we will **always color the digits that we fill in the empty cells with red**. This way, after every stage removing the shading won't be required. Whichever row or column scan is mentioned you have to carry those out in your mind.

### Second batch of steps to find valid cells

Valid **cell R1C5 for digit 8** by scan R2, R3: existing – **cell R3C5, digit 7**, exclusion – **cell R7C5, digit 4**, exclusion -- **cell R4C4, digit 8**, scan R5, R6 -- **cell R5C4, digit 7**, scan C6 -- **cell R8C6, digit 8**, scan C4 – **cell R9C8, digit 8**, scan C7, C9, R8 – **cell R7C2, digit 8**, scan R8, R9, C1 : digit 8 over – **cell R8C4, digit 3**, exclusion.

We will freeze the board at this stage and go over to the next stage.

### Third batch of valid cells

Valid **cell R8C8 for digit 2** by scan R7, R9, C7 – **cell R2C9, digit 2**, scan R1, R3, C7, C8 – **cell R2C8, digit 4**, scan R1, R3, C7 -- **cell R9C9, digit 4**, scan C7 -- **cell R3C8, digit 5**, DSA -- **cell R3C9, digit 3**, exclusion – **cell R6C9, digit 7**, scan C8 – **cell R1C9, digit 6**, exclusion – **cell R4C8, digit 3**, exclusion 9-cell square.

We freeze the board here and go over to the next stage.

**Fourth batch of valid cells**

Valid **cell R1C8 for digit 1**, exclusion – **cell R2C7, digit 7**, exclusion 9-cell square – **cell R9C7, digit 3**, scan R7, R8 -- **cell R7C7, digit 5**, scan R8 -- **cell R8C7, digit** **6**, exclusion 9-cell square -- **cell R7C1, digit 6**, exclusion – **cell R9C2, digit 5**, exclusion – **cell R1C3, digit 5**, C1, C2, R2 – **cell R2C3, digit 1**, R1, C2.

**Fifth batch of valid cells**

Valid **cell R2C2 for digit 6**, exclusion – **cell R4C3, digit 6**, scan C1, C2, R5 – **cell R4C1, digit 7**, exclusion -- **cell R1C2, digit 7**, scan C1 -- **cell R1C1, digit 3**, exclusion -- **cell R8C1, digit 1**, exclusion – **cell R8C3, digit 7**, scan C2 – **cell R8C2, digit 4**, exclusion 9-cell square – **cell R6C2, digit 3**, exclusion -- **cell R5C3, digit 4**, exclusion -- **cell R6C6, digit 4**, exclusion -- **cell R5C6, digit 3**, exclusion.

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.

Enjoy.

### Other Sudoku game plays at absolute beginner level

**Sudoku beginner level game play 11**

**Sudoku beginner level game play 10**

**Sudoku beginner level game play 9**

**Sudoku beginner level game play 8**

**Sudoku beginner level game play 7**

**Sudoku beginner level game play 6**

**Sudoku beginner level game play 5**

**Sudoku beginner level game play 4**

**Sudoku beginner level game play 3**

**Sudoku beginner level game play 2**

**Sudoku beginner level game play 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.