How to play Sudoku for Beginners Game 2
Learn how to play Sudoku and Solve your second Sudoku for beginners game all by yourself in no time. Just follow the step by step instructions to solve.
Content sections are,
- What is Sudoku and Recap of Sudoku game play in brief.
- Sudoku technique of Row column scan for finding a valid cell or valid digit.
- Favorable or promising zone and favorable or promising digit.
- Primary and modified strategy for finding valid cell in easy Sudoku for beginners.
- How to play Sudoku for beginners game 2 Stage 1 to final stage 7: Step by step explanation of finding valid digits for each empty cell.
- End note: Playing medium and Virtues of Sudoku.
- A new Exercise Sudoku for beginners for you to play and solve.
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What is Sudoku and Recap of Sudoku game in brief
Sudoku is a single player game where you have to fill up the empty cells of the given 9 by 9, that is, 81 cell large square. In a specific Sudoku game some of the 81 cells will have already filled digits.
The game we'll use to learn Sudoku is shown below.
This is the game we left you to solve in the last session as exercise. Hope some of you have solved it already.
In today's session we will fill up each empty cell and explain how and why we filled up the partular cell with the particular digit.
We will start with explaining the main technique of row column scan for filling up a valid digit and then the strategy we'll follow to fill all the empty cells systematically.
As a recap, this 81 cell board has some of the cells filled up with digits ranging from 1 to 9. In fact these are the only digits with which you can fill up an empty cell.
The binding compound rule is:
You must not repeat any digit in any column, in any row or in any 9-cell major square square bordered by thick lines.
Ultimately your job is to fill up all the empty cells with digits 1 to 9 but without breaking the compound rule not even once. Then only we would say you have successfully completed the game.
To follow the game play, you should draw the game with the filled in digits on paper, or better still, create it in a spreadsheet program.
At this point, you know what is Sudoku, and also the rules of the game. Before going ahead further, you should now try to complete filling up of all the empty cells of the given game with digits 1 to 9 without violating any rule. If you are really stuck, then refer to the solution. This is the best way to learn.
For convenience, we will use the labels C1, C2, C3......C9 at the top for identifying the 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 as a major square and specify by the names as: top left, top middle, top right, left middle, central middle, right middle, bottom left, bottom middle and bottom right major square.
Primary objective at each step
The final objective at each step is to find a cell in which one and only one digit can be placed. That is what we call a valid cell.
With Sudoku for beginners games such as this one, you will always be able to find a valid cell at each step easily.
When you fill up an empty cell by a single possible digit following the stringent Sudoku rules, the complexity of the game reduces by just a little bit.
In other words, if a game comes with many cells filled up already, its difficulty level is not high. Conversely if you find a game with very few cells filled up, finding the first valid cell itself may become a very difficult task.
We should mention here that this is a general criterion to measure the difficulty level of the game. It gives just an idea. It is not a metric or scientific measure of difficulty of a Sudoku game. And at this stage we should be aware of this general rule only.
Obviously, it should be easier to find a valid cell with a unique possible digit if the number of cells already filled up is more. As a particular digit may be placed only once in a row or column or a 9-cell major square, the more the number of filled up digits, the less are the possible number of digits in an empty cell.
In fact that is the whole objective - to reduce the number of possible digits that can be filled in a cell to exactly ONE.
Valid cell and Valid digit
We define a VALID digit as the digit you fill in an empty cell so that,
It is the only possible digit that you can place in the cell following the rules of the game.
- In the containing row, column and the 9-cell major square the chosen digit doesn't appear, and conversely,
- In the row, the column and the major square intersecting at the target cell should have all other digits except the one you are going to place in the cell. That leaves only one digit as valid for placement in the particular cell.
As before, the most important question is, how to find out the cell in which you can put one and only one digit out of the digits 1 to 9.
The first basic technique that we will have to apply constantly is the row column scanning.
Sudoku technique of Row column scanning for finding a valid cell and valid digit
Row column scan is the most basic and simple technique for finding a valid cell where a unique valid digit can be placed. In some Sudoku literature, it is also called as finding hidden singles.
Generally row column scan is done FOR A SPECIFIC DIGIT ON THE EMPTY CELLS OF A 9 CELL MAJOR SQUARE.
Three rows and three columns criss-cross at one particular 9 cell major square.
We will have a valid cell by row column scan when we discover that a specific digit is absent in a major square, but present in one or more than one row and/or column crossing the major square such that, only one cell in the major square is left where the specific digit can be placed.
All other cells of the major square will then be either already occupied or under the influence of the scanned digit present in the intersecting rows and/or columns.
An example of a valid cell by row column scan is shown below,
Row R1 and R3 have digit 1. It means, no other empty cells in these two rows can have digit 1. And same with 1 in column C9.
With this knowledge when the empty cells of top right major square R1R2R3-C7C8C9 are examined, you can see that by digit 1 in R1, R2 and C9 all cells in top right major square are disallowed for digit 1 EXCEPT CELL R2C8.
As the major square must have a digit 1 and as it can be placed only in R2C8, we get the valid cell as R2C8 1.
And this process we call as ROW COLUMN SCAN FOR DIGIT 1 ON TOP RIGHT MAJOR SQUARE.
Row column scan is usually done ON EMPTY CELLS OF A MAJOR SQUARE.
All cells in rows R1 and R3 and column C9 are lighted up by presence of digit 1.
With 1 already present, none of the empty cells of these three zones can have 1.
Lighting up cells means AFFECTED BY OR DISALLOWED FOR and this is indicated by yellow color shade.
Favorable or promising zone and favorable or promising digit
A favorable zone may be a column or a row or a major square with large number of cells already filled up (5 or 6) so that number of possible digits that can be placed in the few empty cells is low and so getting a valid cell out of the few by row column scan is high.
On the other hand, as a particular digit can appear in the whole board only 9 times, a digit with high occurrence in the board has a higher chance of helping you to find its rest of the valid cells (each digit finally has a particular valid cell in a row or a column or a 9-cell major square). We call a digit with a high number of occurrence as a favorable digit.
The puzzle game to be solved is repeated below for convenience,
We'll first put together the strategy of finding valid cells when solving an easy Sudoku beginner's game. If you remember, we have first formulated and used thids strategy with three variations to systematically solve a Sudoku beginner's puzzle game.
Primary Strategy for finding valid cells easy Sudoku
Row column scan starts with 1 as the digit scanned for. Scan for digit continued till all 9 number of 1s are filled it is no more possible to get a valid cell for 1. Scanning will be on next larger 2 and will be continued in the same way till stopped or number of 2s fully.
This process will be continued and repeated for gradually increasing digits 3, 4, 5, 6, 7, 8 and 9 as needed.
It is a good practice to do a quick scan all over the game on scopes for valid cells by row column scan (or hidden singles).
This is the primary systematic strategy we'll follow except for a few variations. But we do adopt three more variations to speed up the solution.
Variation 1 for valid cell search strategy for easy Sudoku game playing
Whenever a promising zone with six filled digits occur, valid cells are attempted on the two empty cells first.
Variation 2 for valid cell search strategy for easy Sudoku game playing
Whenever convenient, especially with some good progress in valid cell fills, process will return to the smallest digit that was not fully filled earlier.
Variation 3 for valid cell search strategy for easy Sudoku game playing
The first come first served strategy will randomly be used when much of the empty cells have been filled up.
By this variation, whichever valid cell seems easy to fix will be fixed. This is a fast process. As end approaches, most of the valid cells obtained will be by exception of the only digit left in a zone (column, row or major square).
Now that we are clear on how to proceed, let's draw the first blood.
Starting row column scan duly with smallest digit 1, first valid cell obtained is:
R2C7 1 by row scan of R1, R3 for 1 on top left major square. 1 in these two rows lights up all 3 out of 4 empty cells of the major square shown by yellow shading. The cell R2C7 unaffected and untouched by this scan gets 1 as the only cell in this major square where 1 can be filled.
With 5 number of 1s filled, 3 number of 1s are left, but none of these three are feasible at this moment.
Following our primary strategy, next attempt is on 2, but with only two number of 2s, no scan result on 2 is feasible.
Scanning for 3 next in all three major squares, top middle, central middle and bottom left fail to produce any positive results.
Scanning for the next larger digit 4 we get immediate positive results as:
R9C1 4 by scan for 4 in R7, C3 -- R8C8 4 by scan for 4 in R7, R9, C9 -- R5C7 4 by scan for 4 in C8, C9 -- R1C2 4 by scan for 4 in R2, C1, C3 -- R3C5 4 by scan for 4 in R1, R2, C5. And lastly, R4C4 4 by scan for 4 in R5, R6, C5, C6, the largest scan of four zones.
Note: You should take care to scan minimum number of row and columns combined for a valid cell hit.
The yellow shading indicates cells influenced by scan for 1 and 4. The valid cells found at this stage are shaded turquoise blue and the valid digits are colored red.
This is the convention of coloring we'll follow.
Results of actions taken in this first stage shown below.
Following primary valid cell search strategy, we'll have to go for scanning the next larger digit 5 in the second stage.
How to play Sudoku for beginners Game 2 Stage 2: Starting scan for the next larger digit
All 9 number of digit 4s are filled.
We'll scan next for digit 5, the next larger digit.
We get two successes with 5 and no more:
R7C9 5 by scanning for 5 in R8, R9, C7 -- R2C5 5 by scanning for 5 in R1, C6.
Scanning for next higher digit 6 in R9, C7 we get valid cell R8C9 6 and then, R7C3 6 by scanning for 6 in R8, C1.
With only two digits [1,3] left in bottom left major square we take up the first variation in strategy, we'll now try for valid cells for [1,3] in bottom left major square. And the decision has been right.
We get the valid cell R7C1 3 by scan for 3 in R8 -- R8C3 1 by exception as the only digit left for the zone of the major square.
Results at this second stage shown below.
How to play Sudoku for beginners Game 2 Stage 3: Coming back to track - finishing unfinished business
Coming back to track we'll finish the unfinished scan for 6. Successes are:
R2C2 6 by scanning for 6 in C1, C3 -- R1C4 6 by scanning for 6 in R2, R3 and lastly R5C6 6 by largest scan for 6 in R4, R6, C4, C5. All 6s are filled.
With these few hits we close this stage and show results below.
How to play Sudoku for beginners Game 2 Stage 4: Strategy variation 3 - first come first served
We'll now take up variation 3 of first come first served valid cell search.
Easy valid cell hits:
R3C7 7 by scanning for 7 in single column C9.
Two cells with two digits [8,9] left in top right major square, variation 1 is taken up to get R3C9 8 by scanning for 8 in R1 -- R1C9 9 by exception in top right major square -- R1C3 2 by exception in row R1 as the only digit left for the single empty cell -- R6C9 2 by exception in column C9.
Continuing first come first served strategy, R3C6 2 by scanning for 2 in R2 -- R2C6 3 by exception in top middle major square as the only digit left.
Last in this stage: R2C1 8 by exception in R2.
Results shown below.
How to play Sudoku for beginners Game 2 Stage 5: Strategy variation 2 - Going back to scanning for smallest unfinished digit
With a large number of empty cells filled we'll now take up variation 2 in primary strategy to scan for the smallest digit 1 that remained not fully filled.
And now successes are easy to get for digit 1: first R4C6 1 by scanning for 1 in R5, R6, C5 and lastly R7C4 1 by scanning for 1 in R8, R9, C5.
With digit 1 fully filled, continuing now with 2: R4C1 2 by scanning for 2 in C2, C3 -- R3C1 5 by exception in C1 -- R3C3 3 by exception in both row R3 and top left major square -- R5C3 5 by exception in C3.
Results shown below. End is near.
How to play Sudoku for beginners Game 2 Stage 6: Convenient zone of a major square with two digits left chosen first
For convenience we'll now first find missing digits in the left middle major square and then scan for either 3 or 7. R6C2 3 by scanning for 3 in R5 -- R5C2 7 by exception in both C2 and left middle major square.
Similarly by variation 1 in primary strategy we'll try for either of the two missing digits [5,9] in right middle major square: R4C8 5 by scanning for 5 in R5 -- R5C8 9 by exception in right middle major square -- R9C8 9 by exception in C8 -- R4C5 3 by exception in R5.
Now convenience scanning will be on most favorable zone of bottom right major square for the two missing digits [2,9]:
Unfortunately this fails to produce a result even at this late stage.
So we target two missing digits [2,9] in bottom row R9: Success: R9C7 2 by scanning for 2 in C6 -- R9C6 9 by exception in R9 -- R7C7 9 by exception in C7 -- R7C5 2 by exception in R7 -- R6C6 by exception in C6.
Results shown below.
How to play Sudoku for beginners Game 2 Final Stage 7: A formality but we stick to systematic approach
At this very late stage we'll just spot quickly any valid cell:
R6C4 5 by second type of scanning for 5 in C5 but not on empty cells of a major square, but on the two empty cells of row R6 -- R6C5 9 by exception -- R5C4 2 by scanning for 2 in C5 on empty cells of central middle major square -- R5C5 8 by exception in R5 -- R8C5 7 by exception in C5 -- R8C4 8 by exception in whole 81 squares game.
Final solution shown below.
We would repeat our recommendation regarding playing medium.
Should you play Sudoku using pen and paper, in a mobile or using something else? Our strong recommendation is,
If possible always play Sudoku in a spreadsheet program. 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.
We love spreadsheet because of its abilities:
- to form perfect looking 81 cell Sudoku game board with conveniently put digits in cells,
- to write and erase content in any cell painlessly,
- in undoing a series of steps, should you detect an error at any step, We assure you errors do happen. Erasing with pencil and erasure is painful, undoing is so much better
- in copying and pasting a whole game situation to a new place just by the side of the previous stage. Analysis of progress through the game is possible in doing this,
- write special comments below the game board of how you solved a special barrier in finding a valid cell. This may help you to build a complete structure of Sudoku game playing system,
- in coloring rows, columns or a group of cells to highlight them. This coloring regions is a great facility in a spreadsheet program,
- in one spreadsheet, you can place the stages of one game side by side, stages of second game below it, and this way, in one spreadsheet only you can keep record of a large number of Sudoku game playing sessions for same difficulty of game,
- you can play games of different difficulty level in another spreadsheet.
The virtues of spreadsheet for playing Sudoku are practically endless.
Virtues of Sudoku
We consider Sudoku as one of the best brain games for everyone with every ability because,
- Sudoku game boards are available in every level of difficulty, but at each level it poses enough challenge to the player at that ability level to keep itself interesting,
- it allows enhancement of mind power, especially in discovering new useful patterns that lies at the core of problem solving ability,
- it allows gradual progress through the level of difficulties,
- for even a child a new version of Sudoku game can be a great resource to teach the young the beauty of discovering new patterns and thus nurture creativity, We will present this version later,
- varieties of Sudoku game boards are inexhaustible, you can never finish it
- for the aged who still want to flex the muscles of their mind at their leisure, there is no friend like the Sudoku.
There are much more to Sudoku than this short list of pros of Sudoku playing that we could think of now.
The only con that we can think of is, the game is addictive, but what of it? Is there any great thing in this world that is not addictive?
Now 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 2 - Learn and practice Sudoku level 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.