Sudoku Solve Walkthrough

How to solve a sudoku puzzle

Take a look at the following Sudoku puzzle:

The digits given at the beginning are the clues you would use to solve the puzzle. A properly formed puzzle has one (and only one) unique solution.

In order to solve the Sudoku puzzle, we must place the digits 1-9 in each row of the grid, each column of the grid, and in each of the 3x3 outlined blocks shown above. There must not be any duplicate numbers in a row, column, or any of the outlined 3x3 grids.

Let's start the solve by looking at the center square--it is currently empty and surrounded by 6, 8, 3, and 2. (Why am I starting with that square? Well, just looking at the puzzle I tried to find a square that has lots of surrounding digits. You'll see why in a moment.)

Step 1: Naked Singles

(Stop giggling, and do not google that!) This is a real Sudoku solving technique. By looking at the numbers in the row, column, and 3x3 grid surrounding that cell, we can determine that the only number that could possibly go into that cell is a 5. Why? Well, if we look at the numbers 1-9, we can eliminate them one-by-one until only a single number remains, 5. See, it can't be a 1 because there is already a 1 in the column (and in the row). It can't be a 2 because there is a 2 in the 3x3 cell. It can't be a 3 for the same reason. It can't be a 4 because there's a 4 in the row. It CAN be a 5. It can't be a 6 because there is a 6 in the 3x3 cell. It can't be a 7 because there is a 7 in the column. It can't be an 8 because there is an 8 in the 3x3 cell. And, it can't be a 9 because there is already a 9 in that column. Therefore, the only number left is a 5 which goes in the center cell of the puzzle.

Step 2: Eliminations

Now, let's look at the 3x3 grid in the bottom right corner. There are 4 open boxes in that 3x3 grid that need to be filled. Ask yourself where can a 1 go in that 3x3 grid? If we look at the rightmost column, we can see a 1 in there already (higher up in the puzzle), so you can't put a 1 in the upper right corner of that 3x3 grid–that eliminates one of the 4 possible open boxes. We can also see a 1 in the second to last row of the puzzle (middle column). Since you can't have a duplicate in that same row, that eliminates 2 of the remaining possibilities. That just leaves one empty box left that can take the 1. So, we place a 1 in the lower left corner of that 3x3 grid giving us “1-7-9” on the bottom row.

Now that we've SET two numbers in our puzzle, it should look like this:

Now use that same technique to determine where the 1 can to in the upper right corner of the puzzle. Currently, there's only one digit up there, a 6:

Oh, look! There's only a single square left that can have a 1 in it!

Let's keep going and see if we can place a 1 in the upper left 3x3 box:

Nice! We can place a 1 in that box now.

With that out of the way, let's look at the lower left corner of the puzzle. Where can we place a 1 in that 3x3 box?

Looks like there is only a single square available for the 1 in that box. Place that digit and now we'll check on a new technique:

Step 3: Pencil Marks

Looking at the middle 3x3 boxes, there are only two more 1's to be placed in the puzzle. Can we "SET" them now? Using the elimination technique, we see that there are two cells in each 3x3 box that can have a 1 in them. Oh, no! How do we decide which cell gets the number?

Until we know more information (fill in more surrounding cells) we don't know! Not to worry. We will simply mark those cells with "Pencil marks" for the time being.

These are small marks we leave as notes so we don't have to keep the entire puzzle in our heads during the solve. Later, when we determine one of those cells must be a 1, we automatically get the other for free.

If the upper right "1" turns out to be the valid one, then the lower left "1" is also valid. And, vice versa.

More elimination techniques

We can complete the bottom right box of the puzzle using elimination techniques. Then we'll get back to more Pencil Mark examples.

Looking at the lower right 3x3 box, we can see that it already has a 1, 2, 5, 7, 8, and 9. That only leaves a 3, 4, and 6 to complete that box. Using elimination techniques, we can see that there are currently two cells where the 3 can go--let's wait on that a bit.

There's only one cell the 4 can go, let's SET that number and look at the 6. There's only one cell the 6 can go, SET that number. Now, that leaves only one cell left for the 3!

Now, our solution should look like this:

Let's get back to pencil marks...

We still have those 1's penciled in the middle of our grid. What else can we place in that middle 3x3 grid?

Looking at the 4, we can eliminate two cells and we'll pencil in the 4 in the two remaining cells in the center 3x3 grid.

Step 4: Locked Pairs

Now that we have two cells in the sixth column that have marks of "14", this means that one of those two cells must have a 1 and the other must have a 4. This is very powerful information as that means that there can be no other 1's or 4's in that column!

If we consider where a 7 can go in the middle 3x3 box, we can eliminate two cells because of a 7 in row six... AND we can eliminate the cells with markings of "14" because that cell MUST have a 1 or 4 in it!

That leaves just one cell for the 7.

We can then place a 9 in that 3x3 box for the same reasons!

What's Next?

I'm going to end the lesson here. But, I would encourage you to finish off this puzzle using the techniques learned here.

For example, where can a 4 go in the top, middle 3x3 box? I'll give you a hint, you can eliminate two boxes because of a 4 and two boxes because of the "14" pair. That leaves only one spot left!

Using these techniques should allow you to solve most of the Easy and Medium puzzles in the application.

- Show me how the application can help me solve puzzles

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