## Let's play Sudoku - Game 10

In this session, just like the last session, we'll jot down the filling up of the empty cells sequentially, but this time we will look at a few cell choices analytically for understanding the routine method of row-column cross-scan better. Sometimes, special types of alternate choices are not easily visible.

To keep it clean, this time we will not mention a cell selection by "Exclusion". We will assume the selection to be obvious and will drop the word "Exclusion".

If you feel you *need to brush up the basics of how to play Sudoku*, please refer to any of our * session 1*,

*or the*

**session 2***.*

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

Like the last few sessions,* we will use only the most basic technique of choosing an empty cell for legally filling it up with a digit from 1 to 9, *that is,

**the row column scanning.**Additionally,**we will not scan more than three row-column combination to choose the right cell.****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 nothing 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 **R6C9 2, **scan R4, R5 -- R5C7 7, scan R4. We are not moving away from this favorable zone of the nearly filled up 9-cell square.

Continuing further, **R4C8 8** -- R8C7 1, scan C8, C9, R9 -- R7C1 1, scan R8, R9 -- R1C2 1, scan C1, C3, R3 -- R4C6 1, scan C4, C5 1 over. We have pursued this time the favorable digit 1 till it is completed. In the last selection, there was an alternative scan. Can you find it?

Still further, **R3C2 8,** scan C1, C3 -- R9C7 4, scan C8, C9 -- R9C2 6, scan C1, C3, R8 -- R6C5 6, scan R4, R5, C4 -- R1C9 6, scan C7, C8, R3 -- R2C6 6, scan R1, C5 6 over. Again we pursued favorable digit 6 till we got positive results.

Going ahead again, **R6C4 7**, scan R4, R5 -- R6C2 3 -- R5C3 9, scan R4 -- R4C1 4 -- R4C5 5 -- R5C5 4 -- R1C3 4, scan C1, R2 4 over -- R2C3 5, scan C1 -- R1C4 5, scan C5, C6 -- R3C9 5, scan R1, R2 -- R3C5 7 -- R2C5 8, scan C6 -- R1C6 2 -- R1C7 8, scan R2, C8 -- R2C7 3, scan C8 -- R2C8 2, scan R1 -- R1C8 7 -- R1C1 3 -- R2C1 7 -- R9C1 9 -- R8C2 7, scan C3 -- R7C8 9, scan R9, C9. This is a scan of one boundary row and its adjoining boundary column. Usually this escapes notice.

**There is another possibility for deciding cell R7C8 for 9**. Usually till now we have *targeted filling up a cell in a 9-cell square.* Accordingly we search for suitable scans. But notice the row R7. If we scan column C5 for 9, the cell R7C5 becomes invalid for digit 9 and only place left in the row R7 for 9 is the cell R7C8. This a different type of scan of the **target cell in the favorable row where only two empty cells are left.**

Continuing further, **R7C5 3** -- R9C8 5 -- R8C5 2 -- R9C6 7 -- R8C4 9, scan R9 -- R9C4 8 -- R8C9 8, scan R9 -- R9C9 3 -- R9C3 2 -- R8C3 3. End.

The game solved.

#### A special note for you

The cell choices at a stage may be more than one and it may very well be possible that **you may complete the game with lesser number of scanned rows and columns.**

At this level of the game, completing the game is not difficult, but **you may keep one more objective of improving upon our solution steps in total count of rows and columns scanned.**

Try once, you may surprise yourself!

Please remember, **optimization in general may be one objective** - optimization in terms of time and number of scans in this case.

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.