How to solve a sudoku

In this guide, I will show you how to solve a sudoku puzzle logically and simply.

Rules: In a sudoku puzzle, every row, column, and 3-by-3 square must contain the numbers 1-9 once and only once. For example, a row can look like 967485321, but not 118855662


Here we have an example puzzle

• 1. The first thing we do is to draw lines from numbers that we see often. In the first three rows, we notice that there are 2 8's, in the middle three rows, we notice 2 3's, and in the bottom 3 rows, we notice 2 6's
  
  
  
• 2. We have now limited the spaces where we can place these numbers. This next picture shows these spaces with circles
  
  
  
  In one of the first 2 circles, we must place an 8. We see an 8 already directly below one of the circles, so we know we cannot put another 8 there. Likewise, we see a similar situation for the number 3 in the middle rows. For the last rows, we are already limited to one choice for the number 6 to go.
  
  
  
• 3. Now we fill in our numbers and move on. I have gone ahead and filled in a few more numbers using only the step mentioned above and doing the same thing using columns as well. I have not done any other tricks to obtain these numbers, and without too much difficulty, you should be able to see how they were obtained.
  
  
  
• 4. The next trick is to locate rows, columns, and 3-by-3 squares that only have a few numbers missing. In the next picture, I have circled a few rows, columns, and a 3-by-3 square that have only a few blanks
  
  
  
  We then figure out what numbers are missing in each of these rows/columns/squares, and look around to see what cannot go in these spaces.
  
  For example, in the first column, we see that a 7 and a 9 are missing. Because a 9 is already in the 3rd row, the 9 must go in the 2nd-row spot and the 7 must go below it. Repeating this for the rest of the circled areas yields this:
  
  
  
• 5. Repeat these steps for the rest of the rows, columns, and squares. Using these steps, you will be able to solve most sudokus. However, I will detail one more step which you may need to solve harder puzzles.

THE METHOD OF GUESSING
In some puzzles, you may encounter a situation where you are simply stuck. Most sudoku puzzles state that they will not require guessing to solve completely, but this shouldn't stop you from using it if you need to.

Suppose you have a row which has 2 blank spaces, but you don't know what number goes where. If you are doing this on paper, grab a pen and trace over the numbers you know for certain. Then grab a pencil and guess where one of the numbers goes. Try to pick a row that you know will be useful to eliminating a lot of other options. Continue solving the puzzle in pencil until you either are forced into an impossibility, (suppose you are forced to place a 6 in a column where one exists already), you finish the puzzle, or you hit another dead end. If you reach an impossibility, erase everything you wrote in pencil and switch around the 2 numbers you placed before. You can use pen for this. If you solve the puzzle, great! If you hit a dead end, you may have to use the guess method again, and it gets pretty hairy by this point. You won't usually get this last unfortunate scenario unless you're attempting a very difficult puzzle, so don't worry too much about it.

If you want a good website to practice with, try www.websudoku.com, this is the site I used to grab the pictures. It tells you your time at the end once you finish, and it tells you if you mess up. Also it has billions of puzzles at 4 difficulties, start with easy until you feel comfortable moving onto medium, then hard, then insane.

Hope you enjoy the guide, if you have any comments or questions, please post them below. This is guide #4 in my application for UE.​

 

I never guese, very good guide, well put out. Well done.
8/10

 

Takes the fun out of it, but nice guide.

Well laid out and full of detail.

 

Helped me quite a lot, I've always been bad at Sudoku since when it was first introduced to me in primary school, I think I'm going to go and try one out.
8/10, some parts could have been clearer.