## Let's play Sudoku - Game 7

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

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

*or the*

**session 2***.*

**session 3**You may also refer to **all our beginner level Sudoku game plays using links given at the end.**

In today's session we will select the valid cells step by step and in one sitting will list out all the steps through which we have solved the game completely.

*Having gained good experience in playing six games at this level already*, we have decided at the start of game play itself that **we would use only the most basic technique of finding a valid cell and valid digit, that is, the column row cross-scanning**.

We *won't use any other more advanced technique such as digit subset analysis* in any of the steps.

**Note:** Sudoku concepts in brief are in Aside 1 and Aside 2. You may skip if you feel it is not required by you.

**Aside 1:**

**A Sudoku game board of 81 square cells** comes with a few of the cells already filled up with **valid digits 1 to 9.** The *objective of the game is to fill up rest of the empty cells* following the * basic Sudoku rule of NOT using any of the digits 1 to 9 more than once in any row, column or 9-cell square* (identified by thick borders, there are 9 such 9-cell squares).

At each step when we locate a **valid cell** where **we can put one and only one digit**, we will **identify the cell** by its row number (R1 to R9) suffixed by column number (C1 to c9), mention **the digit**, and mention the **column row scan information** (**or exclusion** if the cell happens to be only one empty in the containing row, column or 9-cell square). Sometimes we will add a remark.

The final result will be shown at the end. If you feel any difficulty at any point, please refer back to our earlier sessions, **session 1,*** session 2*, or

*.*

**session 3**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 2:**

**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 sweep or horizontal-vertical cross-scanning mainly. 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 all the valid cells - the first and final stage

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

These are all the steps.

Valid cell **R7C6 2, **scan R9 – **R9C5 7, **scan C4 – **R9C4 4, **exclusion -- **R1C6 9, **scan C4, C5 -- **R1C5 3, **scan C4 -- **R3C4 1, **exclusion -- **R4C4 2, **scan R5, C6 –- **R5C4 6, **exclusion –- **R5C5 1, **exclusion -- **R6C2 9, **scan R4, R5 -- **R5C2 8, **scan R4.

We continue with, **R6C6 8, **scan R5 -- **R5C6 5, **exclusion -- **R5C8 7, **exclusion -- **R4C8 1,** scan R6 -- **R7C7 1, **scan C8, C9 -- **R7C9 8, **scan R8, R9, C8 -- **R8C9 7, **scan R9, C8 -- **R7C3 7, **scan R8, R9, C1 -- **R7C1 9, **scan R8, R9 -- **R7C8 3, **exclusion -- **R3C7 3, **scan R1, C8, C9 -- **R3C2 7, **scan R2, C1, C3 -- **R3C3 9, **scan C1, C2 -- **R2C9 9, **scan R1, R3, C8 -- **R1C8 4, **scan R2, C7, C9 -- **R3C1 4, **scan R1, R2 -- **R1C1 5, **scan R2 -- **R9C2 1, **scan R8, C3 -- **R2C1 1, **scan C2.

From this point on most of the valid cells will be identified by exclusion -- **R2C2 3, **exclusion -- **R8C1 3, **scan R9, C2 -- **R8C2 6,** scan C3 -- **R9C3 5, **exclusion -- **R9C9 6, **exclusion -- **R8C8 5, **exclusion -- **R1C7 6, **exclusion -- **R2C8 2, **exclusion -- **R3C9 5, **exclusion -- **R4C1 6, **exclusion -- **R4C2 5, **exclusion -- **R4C3 3, **exclusion -- **R6C7 5, **exclusion -- **R6C8 6, **exclusion -- **R6C9 2, **exclusion. End.

The game solved.

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.