How to Play Sudoku

Sudoku is a great mental game that stimulates your mind and is fun to play. It's a game that once you know how to play, is very easy to pick-up-and-play and can be stopped at any time, and then re-continued at any time.

This post is merely to show you the basic rules of how to play a simple game of Sudoku and will not include advanced tips and tricks for those more challenging puzzles. This post is aimed at those of you who don't know how to play Sudoku and so I won't bog you beginners down by giving you more information than is necessary for you at the moment.

The sudoku board (as seen above) is made up of 9 squares creating a 3 x 3 grid. You will also notice that each of these 9 squares are further divided into 9 smaller squares which are called cells, creating smaller 3 x 3 grids. Each and every cell holds a value from 1 - 9, and it is up to you to determine what values they are - this is the whole concept of the game.

There are restrictions however to what number can be placed in what cell as every square (that is also a 3 x 3 grid) must contain all numbers 1 - 9, and as there are only 9 cells in each square - you've most likely realised that you can not have two of the same number if you are to include all the numbers 1 - 9. For example: a grid containing numbers 1, 2, 3, 4, 4, 5, 6, 7, 8 would not be allowed. There are 9 numbers granted, however there contain two number fours and so would be incorrect.

Also that is not the only restriction to where a number can be placed. You may or may not have noticed but each column and row contain 9 cells (not by coincidence), and each of them must also contain the numbers 1 - 9. This means that each column and row (if done correctly) will never have the same number in twice.

You will need to look at every cell and see if a number can go there, you will be able to see if a number goes there as other numbers (in columns/rows/square) will rule out possibilities.

Have a look at the top-left square from the images that are present. You will see that it contains numbers 3, 5, 6, 8, and 9. This means that these numbers will not be able to be included in this large square as you must have all of the numbers 1 - 9. This means the numbers 1, 2, 4, and 7 are the only possibilities for the remaining four cells in that square. You must look at each of those cells and determine if numbers in other cells (from rows/columns) rule out possible cells for that number to go until you are left with only one possible cell for it to go.

You won't be able to determine where numbers can go straight-away and will require you to travel around the sudoku board searching.

Let's number every cell in each square A - I just so I can show you some examples. We're number them A - I as you would read a book. So looking at the first square; cell A contains the number 5, cell B contains the number 3, cell C is empty, cell D contains the number 6, cell E is empty, cell F is also empty, cell G is also empty, cell H contains the number 9, and cell I contains the number 8.

Let's try looking for the number 1 in the top-left square. The only other number 1 that would have an impact to our square is the top-middle square that contains the number 1 in cell D. This rules out the possibility of the number 1 being in cells E and F in our top-left square, and leave us with two possibilities to where the number 1 could be: cells C or G. We don't have enough numbers to determine which one so we'll have to come back to that later.

Some people like to pencil in small the possible numbers which could occupy that cell.

Now let's try looking for the number 2 in the top-left square. You will notice that there is not a single number 2 that is in a line or column that affects our top-left square, so at the moment the number 2 could potentially occupy any of the four cells (C, E, F, or G)  in our top-left square.

Now let's try looking for the number 4 in the top-left square. You will notice that there is a 4 in the middle-left square (cell D) that does affect us, and it rules out cell G in the top-left square to where the number 4 could appear. However it is the only cell that does affect us and so the number 4 could potentially still be in any of the cells C, E, or F.

I'll quickly do the number 7 for the top-left square too. The number 7 appears in the top-middle square and rules out cell C in the top-left square to where 7 can appear - this leaves us with cells E, F or G.

There is also a number 7 however in the middle-left square and that rules out cell G in the top-left square. Now only cells E and F remain to where the number 7 can appear. We don't have any more information at the moment so we'll have to move onto another square.

I'll now show you an example where a number can be found. Look at the bottom-left square. It only contains the number 6 and so can still house the numbers 1, 2, 3, 4, 5, 7, 8, and 9.

Let's try looking for the number 8. The number 8 can appear in any of the cells A, C, D, E, F, G, H, or I. You will see however that there is a number 8 in the top-left square and that rules out cells C, F, and I straight away, leaving cells A, D, E, G, and H.

Then you will see another number 8 in the middle-left square and that rules out cells A, D, and G in our bottom-left square - and that now leaves us with cells E and H, both of which could potentially hold the number 8.

There is also another 8 in the bottom-middle square and that rules out cell H for us, which only leaves cell E. As there is only one possibility for where the number 8 can go (cell E) that means that the number 8 HAS to go there. It doesn't make any difference that there is a number 8 in the bottom-right square as that rules out cells A and C that the previous number eights did (in top-left and middle-left squares.

You just work your way around the board doing this and you will eventually have yourself a completed board. The 2 images below are of a sudoku board before and after completion. There are sudoku puzzles however where this very basic method is not nearly enough and where other techniques will be needed to be incorporated to complete them. For example the X-Wing and Jellyfish techniques.

 

Credit: Cburnett