Sudoku Puzzles -Worksheets Library - Free Printable

To solve the Sudoku puzzle, we need to fill in the grid such that every row, every column, and every 3x3 box contains the numbers 1 through 9. Let's go step by step.

Step 1: Understand the Rules

- Each row must contain the numbers 1 through 9.
- Each column must contain the numbers 1 through 9.
- Each 3x3 box must contain the numbers 1 through 9.

Step 2: Analyze the Given Puzzle

Here is the initial grid:

```
+-------+-------+-------+
| 7 | 3 | 5 6 |
| 5 1 | 6 7 2 | 4 3 8 |
| | 4 5 9 | 7 |
+-------+-------+-------+
| 9 2 | 8 5 | 3 7 4 |
| | 8 4 3 | 1 6 |
| | 6 9 2 | 7 1 |
+-------+-------+-------+
| 2 4 | 7 | 9 8 5 |
| 6 9 7 | | 8 5 3 |
| 1 8 5 | 2 4 3 | 9 6 7 |
+-------+-------+-------+
```

Step 3: Solve the Puzzle

We will solve it step by step, filling in the missing numbers while ensuring all rules are followed.

#### Row 1
- The first row is `7 _ _ _ 3 _ _ 5 6`.
- Missing numbers: 1, 2, 4, 8, 9.
- Check the 3x3 box and columns:
- The number 1 is already in the second column.
- The number 2 is already in the fourth column.
- The number 4 is already in the fifth column.
- The number 8 is already in the eighth column.
- The number 9 is already in the ninth column.
- Fill in the remaining numbers:
```
+-------+-------+-------+
| 7 8 9 | 1 3 4 | 2 5 6 |
```

#### Row 2
- The second row is `5 1 _ 6 7 2 4 3 8`.
- All numbers are already filled.

#### Row 3
- The third row is `_ _ 4 5 9 8 _ 7 _`.
- Missing numbers: 1, 2, 3, 6.
- Check the 3x3 box and columns:
- The number 1 is already in the first column.
- The number 2 is already in the second column.
- The number 3 is already in the eighth column.
- The number 6 is already in the seventh column.
- Fill in the remaining numbers:
```
+-------+-------+-------+
| 6 3 4 | 5 9 8 | 1 7 2 |
```

#### Row 4
- The fourth row is `9 2 _ 8 5 _ 3 7 4`.
- Missing numbers: 1, 6.
- Check the 3x3 box and columns:
- The number 1 is already in the first column.
- The number 6 is already in the sixth column.
- Fill in the remaining numbers:
```
+-------+-------+-------+
| 9 2 1 | 8 5 6 | 3 7 4 |
```

#### Row 5
- The fifth row is `_ _ 8 4 3 1 _ 6 _`.
- Missing numbers: 2, 5, 7, 9.
- Check the 3x3 box and columns:
- The number 2 is already in the first column.
- The number 5 is already in the third column.
- The number 7 is already in the eighth column.
- The number 9 is already in the ninth column.
- Fill in the remaining numbers:
```
+-------+-------+-------+
| 5 7 8 | 4 3 1 | 2 6 9 |
```

#### Row 6
- The sixth row is `_ _ 6 9 2 7 1 _ _`.
- Missing numbers: 3, 4, 5, 8.
- Check the 3x3 box and columns:
- The number 3 is already in the seventh column.
- The number 4 is already in the second column.
- The number 5 is already in the third column.
- The number 8 is already in the ninth column.
- Fill in the remaining numbers:
```
+-------+-------+-------+
| 3 4 6 | 9 2 7 | 1 5 8 |
```

#### Row 7
- The seventh row is `2 4 _ 7 _ _ 9 8 5`.
- Missing numbers: 1, 3, 6.
- Check the 3x3 box and columns:
- The number 1 is already in the first column.
- The number 3 is already in the third column.
- The number 6 is already in the sixth column.
- Fill in the remaining numbers:
```
+-------+-------+-------+
| 2 4 3 | 7 1 6 | 9 8 5 |
```

#### Row 8
- The eighth row is `6 9 7 _ _ _ 8 5 3`.
- Missing numbers: 1, 2, 4.
- Check the 3x3 box and columns:
- The number 1 is already in the first column.
- The number 2 is already in the second column.
- The number 4 is already in the third column.
- Fill in the remaining numbers:
```
+-------+-------+-------+
| 6 9 7 | 3 4 2 | 8 5 1 |
```

#### Row 9
- The ninth row is `1 8 5 2 4 3 9 6 7`.
- All numbers are already filled.

Final Solution

The completed Sudoku grid is:

```
+-------+-------+-------+
| 7 8 9 | 1 3 4 | 2 5 6 |
| 5 1 2 | 6 7 2 | 4 3 8 |
| 6 3 4 | 5 9 8 | 1 7 2 |
+-------+-------+-------+
| 9 2 1 | 8 5 6 | 3 7 4 |
| 5 7 8 | 4 3 1 | 2 6 9 |
| 3 4 6 | 9 2 7 | 1 5 8 |
+-------+-------+-------+
| 2 4 3 | 7 1 6 | 9 8 5 |
| 6 9 7 | 3 4 2 | 8 5 1 |
| 1 8 5 | 2 4 3 | 9 6 7 |
+-------+-------+-------+
```

Final Answer:

\boxed{
\begin{array}{|3{||c|}3{||c|}3{||c|}}
\hline
7 & 8 & 9 & 1 & 3 & 4 & 2 & 5 & 6 \\
\hline
5 & 1 & 2 & 6 & 7 & 2 & 4 & 3 & 8 \\
\hline
6 & 3 & 4 & 5 & 9 & 8 & 1 & 7 & 2 \\
\hline
9 & 2 & 1 & 8 & 5 & 6 & 3 & 7 & 4 \\
\hline
5 & 7 & 8 & 4 & 3 & 1 & 2 & 6 & 9 \\
\hline
3 & 4 & 6 & 9 & 2 & 7 & 1 & 5 & 8 \\
\hline
2 & 4 & 3 & 7 & 1 & 6 & 9 & 8 & 5 \\
\hline
6 & 9 & 7 & 3 & 4 & 2 & 8 & 5 & 1 \\
\hline
1 & 8 & 5 & 2 & 4 & 3 & 9 & 6 & 7 \\
\hline
\end{array}
}