5 simple solutions for SUDOKU

Sudoku is an interesting logic game which is quite popular all over the world. The rules are simple,you will face a 9X9 quotation which has some numbers in some blanks. What you should do is to fill 1-9 in the other blanks to make every number in every row, column and 3X3 block which is divided by the thick lines appear only once.Every sudoku has and only has one solution, you can reasoning depend on it.

Heard about this game from Johny Bahra Koto few weeks ago,didn't really pay attention on it at that time.Out of curiosity,I started to try it this Saturday,and found out this is a real cool game,I have to admit. After a few counting,I summed up the following 5simple solutions to this game. You might find it hard at the first time you see all these number,but trust me,after reading this,SUDOKU is no difficult to you again. Everyone can be an expert in this game.

First,let me give an example for this studying.

At the right side,it's a picture of a typical SUDOKU problem. 

Here I will simply introduce the rules first in case this is the first time you see this game.

(You can also find the introduction about sudoku on Sudoku on wikipedia)

Rules:The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid (also called "boxes", "blocks", "regions", or "sub-squares") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which typically has a unique solution.

Now you know what you should do,it's very simple,right? Our job is only finding out all the numbers.

So,let's start our SUDOKU journey.

Solution 1,Exclusion the exit numbers.

According to the rules,no identical numbers in each row, each column,or each 3×3 box.

So you can see in number 2 in both row R1 and R2,it means,there must be a number 2 in R3.

As well,since each number can only exit once in each box,you can exclude number2 in Row R3C4-R3C9,then only have two possibilities left,block R3C1 and R3C3.

Now move your eyes to Row R9,you can see block R9C2 is number 2,so apparently block R3C2 is excluded.So the number in block R3C1 is definitely 2.

Now I believe you already have some clue about the exclusion,so let's move on.

After we fill in 2 in block R3C1,can you use the same solution to find out other numbers?

Let's see number 7 first,now it should be very clear for you. I will not explain the rest to you,now you need to work on it on your own.

Here's the numbers you need to find out: 7.

I believe now you are confused about 7 between block R3C4 and R3C6,R7C4 and R7C6.But why would you be stuck on these unsure blocks and ignore the ensure one? You might ask me,which one? Ok,let me ask you this,you know theres no 7 in block R1C5,R2C5,R4C5,R6C5,R8C5,R9C5,right?If until now,you still can't understand what I'm talking about,I can't help you anymore.

Anyway,the answer is, block R5C5 is the only one left which we can fill in number 7.

Tip: when you are confused about some blocks,do not be stuck on it,try the others,you might find something you need.

Okay,if you are continuing reading this,I'm sure now you are very happy with our first solution,Exclusion. And now you are trying to find out the next number which you can use this on,right? Unfortunately,there's no the other number in this game we can use Solution No.1 again. Feeling bad? Don't! Because now you can learn the next solution.

Solution 2,Remainder method

This sounds pretty mathematically,but I have to say,SUDOKU's originally based on mathematic counting theories. Each block is effected by the other related 20blocks.

What does this mean? It means,if in these 20blocks,there number 1-8 are already there,then we can ensure 9is the number we are looking for.

Look at the example on the right,block R7C8 is effected by Row R7,C8,and box R7C7-R9C9. You can find,1 is the only number missing in these 20blocks,so in block R7C8 is definitely number 1.

Very simple,right?

Now what can we do? Can you find out another block which can be used by our solution2? No.

So? Let's do some combination then.

Solution 3,Look for the triangle

This part is a little bit complicated,let me just explain it first with the picture.

First we can see block R1C2 and block R2C2,R2C3,their shape is like an triangle. As well,block R7C3 and block R8C2,R8C3.

Still remember our Solution 1? Now it's time for us to use it again. According to Solution 1,you can find,number 5 is for sure not at those blocks,R2C2,R2C3,R2C7,R8C2,R8C3,R8C7.

It leaves us 2options,neither 5 in R2C5 and R8C8 nor in R2C8 and R8C5.

Let's see it one by one,the first possibility,5 is at  block R2C5 and R8C8.

So all the blocks with Check Mark can not be filled in 5.

As well,let's see the second possibility,5 is at block R2C8 and R8C5. 

Same,the blocks with Check Marks are for sure not number 5.

Now what do u find? From Solution1, we know,in Row C5,C8,except for the 4blocks,there's no other block can be number 5,right?

Okay,it's time for us to leave it first and move on.

Still remember solution 2? Now can you do it on your own? Hint: R3C8

Find the answer? Very good! Yes,4 is the only number missing in the 20 related blocks. So we write 4 in R3C8.

Now can you find another number by yourself?

That's right,block R6C7 is 4.

Apparently it's time for us to work on number 2 now,but the range seems to be a little bit too big.

So we will need our 4th solution, Area Exclusion.

Solution 4, Box Exclusion

You can see block R6C9,R5C9,R4C9 are all possible to be number 2,and there's no 2 in box R7C7-R9C9. So clearly 2is only available for block R8C7,R9C7. Meanwhile,you can see 2 in Row R9,so it gives you the final result,Block R8C7 is 2.

If you don't understand this part,you can try to learn it from the picture on the right.

Now the problem's becoming much simpler. Use above 4solutions and try to practice,you will find out following numbers,

• step1：r7c6=2
• step2：r7c4=7
• step3：r3c6=7
• step4：r5c9=2
• step5：r6c9=1
• step6：r5c4=1
• step7：r7c2=4
• step8：r4c3=4
• step9：r6c3=2
• step10：r5c6=4
• step11：r4c5=2
• step12：r4c6=9

Try to solve the above blocks yourself before you look at my explanation picture. 

So now we already filled in half of the blocks.

Now check out the box R1C4-R3C6,you can find,number 1 and 9 can only be put in block R1C5 and R2C5. But we are not sure which block to fill in which number.

Now it's time for us to learn the 5th solution,Number Match.

Solution 5, Number Match

Before we make any more moves,can you use the solutions we already learned to find out one number in Box R1C4-R3C6? That's right,it's 4 in block R1C4.

As I said earlier,do not be stuck on the blocks which you cannot be sure or have too many possibilities.

Now why don't you just try to find out other numbers? Forget about block R2C5,R1C5 first for a second.

I think it's not hard to find out these numbers as below,

• Step1：r1c6=8
• Step2：r3c4=5
• Step3：r2c8=5
• Step4：r9c9=5
• Step5：r8c5=5
• Step6：r6c6=5

Now we can see how much problems we have solved so far. Pretty awesome,right?

I'm sure you are now starting to understand about SUDOKU,and if you come with me to so far and understand everything I just said,with some practice,you will be great at this popular game.

I'm not going to tell you how to find out the rest of the numbers,I think it's already too easy for you.

So let me just give you the result,

• Step1：r9c5=4 
• Step2：r9c4=6
• Step3：r6c5=6
• Step4：r1c9=3
• Step5：r5c8=3
• Step6：r4c9=8
• Step7：r8c8=8
• Step8：r6c4=8
• Step9：r6c4=8
• Step10：r4c1=5
• Step11：r6c1=3
• Step12：r2c7=8
• Step13：r9c1=8
• Step14：r5c2=8
• Step15：r5c1=6
• Step16：r3c2=6
• Step17：r3c9=9
• Step18：r1c7=6
• Step19：r7c9=6
• Step20：r9c7=9
• Step21：r9c3=1
• Step22：r7c1=9
• Step23：r1c1=1
• Step24：r1c5=9
• Step25：r2c5=1
• Step26：r2c2=9
• Step27：r2c3=3
• Step28：r8c2=3
• Step29：r8c3=6

So,did you do it all right? Ah,suddenly remember someone told me a lot before,PRACTISE MAKES PERFECT,I think now it's time to use this saying for encouraging everyone who's reading this blog:)

(You are more than welcome to share your experiences!)