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## The Basic Sudoku Rules

- A Sudoku game is played in a 9×9 grid.
- Within the grid are 9 large squares (3×3 each), 9 rows (9×1 each), and 9 columns (1×9 each).
- Each row, column, and square (of 9 blocks each) needs to contain the numbers 1 through 9 without repeating any numbers within that same row, column, or square.

## Logic & Reason

- Sudoku is not a guessing game!
- Logic and reason should be used to determine the number that goes in each space.
- I’ll be demonstrating how to solve a sudoku puzzle using this example:

## Solving Methods for Sudoku

There are several methods you can use to solve a sudoku puzzle.

### Solving for Each Number

- Start by choosing a number (I like to choose one that has a lot of the number on the board already).
- Find all the numbers already given.
- Eliminate everywhere that number cannot go.
- Now, are there any obvious blocks you can fill in your number? If yes, do it!
- If you add numbers, repeat steps 4 and 5. Once you don’t add anything, it’s time to move on.
- Optional: mark any potential numbers (more on this next).

In this example, we’re going to try to fill out all the 2’s.

- First, we found all the existing 2’s (circled in orange).
- Then, we eliminated all the places a 2 cannot go (orange lines).
- Next, we filled in two 2’s (orange, upper right and bottom left squares).
- Then, we repeated in blue (which gave us one more 2).

### Optional: Mark Potential Numbers

- When you go through a number, you may want to mark off where that number could
*potentially*go. - You can do this for any method of solving a sudoku puzzle.

For our example, we need two more 2’s and there are only 4 blocks that they could potentially go into. I’ve added small 2’s to the top of those boxes in green.

### Solving by Square

One method to solve a sudoku puzzle is to do it one square at a time.

- Start by choosing a square (I like to choose one that only needs a few numbers).
- Determine which numbers you need.
- Look in the columns and rows for those numbers.
- Fill out numbers where possible.
- Once you can’t add any more numbers, it’s time to move on.
- Optional: mark any potential numbers.

This is easier to see with an example. We’re going to do the bottom left square.

- First, we selected the square (bottom-left).
- Then we determined the missing numbers (6, 8, 9)
- I started with the column furthest to the left.
- Does it have a 6, 8, or 9? YES, it has a 9 which means there is only one place I can put a 9 in my square. (orange)

- There are no more columns I can check, so I’ll look in the top row next.
- Is there a 6 or an 8? YES! The top row has an 8, so my top block must have a 6. (blue)

- This leaves me with only one free block in the square, which has to contain an 8. (purple)
- This square is completely filled out! YAY!

### Solving by Row

Another method when playing sudoku is to solve by row.

- Start by choosing a row (I like to choose one that only needs a few numbers).
- Determine which numbers you need.
- Look in the columns and squares for those numbers.
- Fill out numbers where possible.
- Once you can’t add any more numbers, it’s time to move on.
- Optional: mark any potential numbers.

Let’s check out our example. We’re going to do the third row from the top.

- First, we selected the row (third from the top).
- Then we determined the missing numbers (4, 5, 9)
- I started with the column furthest to the left. Does it have a 4, 5, or 9?
- YES, it has a 5 and 9 which means the block must have a 4. (orange)

- I’ll check the next column over that needs a number. Does the column have a 5 or 9?
- No. Does that square have a 5 or 9?
- Yes, it has a 5 so we’ll put a 9 in this block. (blue)

- This leaves me with only one free block in the row, which has to contain a 5. (purple)
- This row is completely filled out! YAY!

### Solving by Column

You can also try to solve a sudoku puzzle by column.

- Start by choosing a column (I like to choose one that only needs a few numbers).
- Determine which numbers you need.
- Look in the rows and squares for those numbers.
- Fill out numbers where possible.
- Once you can’t add any more numbers, it’s time to move on.
- Optional: mark any potential numbers.

Let’s check out our example. We’re going to do the column furthest to the left.

- First, we selected the column (furthest to the left).
- Then we determined the missing numbers (1)
- There’s only one missing number, so we’ll just fill it out. (orange)

That was too easy! Let’s do another column example (the middle column).

- First, we selected the column (middle column).
- The we determined the missing numbers (3, 5, 6, 9)
- I’m going to start from the top and work my way down, doing both the row and square at the same time.
- The top empty block cannot have a 3, 5, or 9 so it must contain a 6. (blue)
- The second empty block doesn’t have a 3, 5, or 9 in the square or in the row so it could be any of them.
- The third empty block has a 5 and a 9 in the row, so it must be a 3. (purple)
- The fourth empty block has a 9 in the row, so it must contain a 5. This means our second empty block must contain the 9. (pink)
- This column is completely filled out!

## Can You Finish the Example?

We’ve done a lot of our sudoku example. Try to finish it up yourself (click here for a printable version)!

You can use the number, square, row, or column method (or a combination of all the methods).

### There’s One More Method

But what about those potential numbers you’ve been (optionally) marking? Let’s see how those can helpful by filling out the middle square.

- First, we selected the square (center).
- Then we determined the missing numbers (2, 5, 6, 7)
- A quick look shows me that the bottom two rows of the square both contain a 5 which means our 5 must go in the top right block. (orange)
- The right column cannot be a 6 (because there’s one in the column) or a 2 (because we’ve already marked any potential 2’s), so it must be 7. (blue)
- Now we know that the remaining two boxes must be 2 and 6, but we don’t know which is which (yet).

Let’s checkout the 6th row from the top (or 4th row from the bottom).

- First, we selected the row (4th from the bottom).
- Then we determined the missing numbers (2, 4, 6)
- The furthest column contains a 4, which means that block must be a 2 or a 6. We also know that the blank left block must contain a 2 or a 6. This means the middle block can only be a 4.
- The right column cannot be a 6 (because there’s one in the column) or a 2 (because we’ve already marked any potential 2’s), so it must be 7. (blue)
- Now we know that the remaining two boxes must be 2 and 6, but we don’t know which is which (yet).

## Let’s Finish the Example

I’m going to work (mostly) by square because that’s my preferred method. But, you could start wherever you wanted (by row, column, or number).

**The Top-Left Square**

- Missing: 5, 7, 8
- There’s a 5 in the right-most column, which leaves only one block free for a 5.
- There’s a 7 in the top row, which leaves only one block free for a 7.
- With the 5 and 7 filled out, we know where the 8 goes.

**The Top-Middle Square**

- Missing: 1, 4, 8
- There’s an 8 in the top row, which leaves only one block free for an 8.
- There’s a 1 in the right column, which leaves only one block free for a 1.
- With the 1 and 8 filled out, we know where the 4 goes.

**The Top-Right Square**

- Missing: 3, 6, 9
- There’s a 3 in the top row, which leaves only one block free for a 3.
- But, we don’t know where the 6 and 9 will go so we’ll mark them as potentials.

**The Third-Column From the Right**

- Missing: 1, 6, 7, 9
- There’s a 9 in the bottom square and a 9 in the middle row, so the only block that can be a 9 is the top one.
- There’s a 1 and a 7 in the bottom row, so the block must be a 6. (blue)
- There’s a 1 in the middle square, so that block must be a 7.
- With the 6, and 7, and 9 filled out, we know where the 1 goes. (pink)

**BONUS! The potential numbers we’ve marked down can be really helpful here.**

- Top-Right Square: We’ve filled out the 9, so we know the top corner block must be the 6. (orange)
- Middle-Right Square: we see one block that must be a 2 or a 6. Since we’ve added a 6 to that column, it must be a 2. (blue)
- Center Square: we know the bottom block must be a 6 (because we just filled out the 2 in this row). (purple)
- Finally, we can fill out the remaining middle square block with a 2. (pink)

**The Middle-Left Square**

- Missing: 3, 4, 6, 7
- There’s a 7 in the top row and a 7 in the right column, which leaves only one block free for a 7. (orange)
- There’s a 6 in the right column, which leaves only one block free for a 6. (blue).
- There’s a 4 in the middle row, which leaves only one block free for a 4. (purple)
- With the 4, 6, and 7 filled out, we know where the 3 goes. (pink)

**The Middle-Right Square**

- Missing: 3, 6, 9
- There’s a 9 in the middle column, which leaves only one block free for a 9. (orange)
- There’s a 6 in the top row, which leaves only one block free for a 6. (blue)
- With the 6 and 9 filled out, we know where the 3 goes. (purple)

**The Bottom-Right Square**

- Missing: 4, 5, 7
- There’s a 7 in the bottom row, which leaves only one block free for a 7. (orange)
- There’s a 4 in the right column, which leaves only one block free for a 4. (blue)
- With the 4 and 7 filled out, we know where the 5 goes. (purple)

**The Bottom-Middle Square** (LAST ONE!)

- Missing: 3, 4, 7, 9
- There’s a 7 in the bottom row & top row, which leaves only one block free for a 7. (orange)
- There’s a 9 in the top row, which leaves only one block free for a 9. (blue)
- There’s a 3 in the left column, which leaves only one block free for a 3. (purple)
- With the 3, 7, and 9 filled out, we know where the 4 goes. (pink)

## The Completed Sudoku Puzzle

I’ve given every number a unique color so that you can see the number patterns. Every single square has 1-9, every single row has 1-9, and every column has 1-9.

## Get Sudoku Puzzles

Now that you know how to solve a sudoku puzzle, it’s time to grab some puzzles & get solving!

Feeling ready to move on to harder or different puzzles? Check out