Free, Printable Sudoku Puzzles You Can Solve Today - Free Printable

To solve the Sudoku puzzle, we need to fill in the empty cells such that each row, each column, and each of the nine 3x3 subgrids contain all the digits from 1 to 9 exactly once. Let's go through the solution step by step.

Step 1: Understand the Rules

- Each row must contain the digits 1 through 9.
- Each column must contain the digits 1 through 9.
- Each 3x3 subgrid must contain the digits 1 through 9.

Step 2: Analyze the Given Puzzle

The initial grid is as follows:

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

Step 3: Solve the Puzzle

We will solve the puzzle by filling in the missing numbers one by one, using logical deduction.

#### Row 1:
- The first row is `6 _ _ | 6 5 1 | _ 1 _`.
- The missing numbers are 2, 3, 4, 7, 8, and 9.
- In the first 3x3 box, the number 6 is already present, so it cannot be repeated.
- By checking the columns and rows, we can deduce the values:
- The first cell (R1C2) must be 8 (since 8 is missing in the row and column).
- The second cell (R1C3) must be 4 (since 4 is missing in the row and column).
- The fifth cell (R1C6) must be 9 (since 9 is missing in the row and column).
- The seventh cell (R1C7) must be 3 (since 3 is missing in the row and column).
- The eighth cell (R1C8) must be 7 (since 7 is missing in the row and column).
- The ninth cell (R1C9) must be 5 (since 5 is missing in the row and column).

So, the first row becomes: `6 8 4 | 6 5 1 | 3 7 5`.

#### Row 2:
- The second row is `1 7 _ | _ _ _ | 6 _ 2`.
- The missing numbers are 3, 4, 5, 8, and 9.
- By checking the columns and rows, we can deduce the values:
- The third cell (R2C3) must be 9 (since 9 is missing in the row and column).
- The fourth cell (R2C4) must be 8 (since 8 is missing in the row and column).
- The fifth cell (R2C5) must be 4 (since 4 is missing in the row and column).
- The sixth cell (R2C6) must be 5 (since 5 is missing in the row and column).
- The eighth cell (R2C8) must be 3 (since 3 is missing in the row and column).

So, the second row becomes: `1 7 9 | 8 4 5 | 6 3 2`.

#### Row 3:
- The third row is `_ 2 _ | 3 5 _ | _ 9 4`.
- The missing numbers are 1, 6, 7, and 8.
- By checking the columns and rows, we can deduce the values:
- The first cell (R3C1) must be 5 (since 5 is missing in the row and column).
- The third cell (R3C3) must be 8 (since 8 is missing in the row and column).
- The sixth cell (R3C6) must be 7 (since 7 is missing in the row and column).
- The seventh cell (R3C7) must be 1 (since 1 is missing in the row and column).

So, the third row becomes: `5 2 8 | 3 5 7 | 1 9 4`.

#### Row 4:
- The fourth row is `_ _ 3 | _ _ _ | 2 _ _`.
- The missing numbers are 1, 4, 5, 6, 7, and 9.
- By checking the columns and rows, we can deduce the values:
- The first cell (R4C1) must be 7 (since 7 is missing in the row and column).
- The second cell (R4C2) must be 5 (since 5 is missing in the row and column).
- The fourth cell (R4C4) must be 1 (since 1 is missing in the row and column).
- The fifth cell (R4C5) must be 6 (since 6 is missing in the row and column).
- The sixth cell (R4C6) must be 9 (since 9 is missing in the row and column).
- The eighth cell (R4C8) must be 8 (since 8 is missing in the row and column).

So, the fourth row becomes: `7 5 3 | 1 6 9 | 2 8 4`.

#### Row 5:
- The fifth row is `4 8 _ | 9 7 _ | _ 3 6`.
- The missing numbers are 1, 2, 5, and 9.
- By checking the columns and rows, we can deduce the values:
- The third cell (R5C3) must be 2 (since 2 is missing in the row and column).
- The sixth cell (R5C6) must be 5 (since 5 is missing in the row and column).
- The seventh cell (R5C7) must be 9 (since 9 is missing in the row and column).
- The first cell (R5C1) must be 1 (since 1 is missing in the row and column).

So, the fifth row becomes: `4 8 2 | 9 7 5 | 1 3 6`.

#### Row 6:
- The sixth row is `_ _ _ | _ _ _ | _ _ _`.
- The missing numbers are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- By checking the columns and rows, we can deduce the values:
- The first cell (R6C1) must be 3 (since 3 is missing in the row and column).
- The second cell (R6C2) must be 9 (since 9 is missing in the row and column).
- The third cell (R6C3) must be 1 (since 1 is missing in the row and column).
- The fourth cell (R6C4) must be 2 (since 2 is missing in the row and column).
- The fifth cell (R6C5) must be 8 (since 8 is missing in the row and column).
- The sixth cell (R6C6) must be 4 (since 4 is missing in the row and column).
- The seventh cell (R6C7) must be 5 (since 5 is missing in the row and column).
- The eighth cell (R6C8) must be 7 (since 7 is missing in the row and column).
- The ninth cell (R6C9) must be 6 (since 6 is missing in the row and column).

So, the sixth row becomes: `3 9 1 | 2 8 4 | 5 7 6`.

#### Row 7:
- The seventh row is `9 6 _ | 7 9 4 | _ 8 _`.
- The missing numbers are 1, 2, 3, 5, and 8.
- By checking the columns and rows, we can deduce the values:
- The third cell (R7C3) must be 5 (since 5 is missing in the row and column).
- The seventh cell (R7C7) must be 3 (since 3 is missing in the row and column).
- The ninth cell (R7C9) must be 2 (since 2 is missing in the row and column).

So, the seventh row becomes: `9 6 5 | 7 9 4 | 3 8 2`.

#### Row 8:
- The eighth row is `_ _ 5 | _ _ _ | _ _ 7`.
- The missing numbers are 1, 2, 3, 4, 6, 8, and 9.
- By checking the columns and rows, we can deduce the values:
- The first cell (R8C1) must be 2 (since 2 is missing in the row and column).
- The second cell (R8C2) must be 1 (since 1 is missing in the row and column).
- The fourth cell (R8C4) must be 8 (since 8 is missing in the row and column).
- The fifth cell (R8C5) must be 3 (since 3 is missing in the row and column).
- The sixth cell (R8C6) must be 6 (since 6 is missing in the row and column).
- The seventh cell (R8C7) must be 4 (since 4 is missing in the row and column).
- The eighth cell (R8C8) must be 9 (since 9 is missing in the row and column).

So, the eighth row becomes: `2 1 5 | 8 3 6 | 4 9 7`.

#### Row 9:
- The ninth row is `_ _ _ | _ _ _ | _ _ _`.
- The missing numbers are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- By checking the columns and rows, we can deduce the values:
- The first cell (R9C1) must be 8 (since 8 is missing in the row and column).
- The second cell (R9C2) must be 4 (since 4 is missing in the row and column).
- The third cell (R9C3) must be 7 (since 7 is missing in the row and column).
- The fourth cell (R9C4) must be 5 (since 5 is missing in the row and column).
- The fifth cell (R9C5) must be 1 (since 1 is missing in the row and column).
- The sixth cell (R9C6) must be 2 (since 2 is missing in the row and column).
- The seventh cell (R9C7) must be 6 (since 6 is missing in the row and column).
- The eighth cell (R9C8) must be 5 (since 5 is missing in the row and column).
- The ninth cell (R9C9) must be 3 (since 3 is missing in the row and column).

So, the ninth row becomes: `8 4 7 | 5 1 2 | 6 5 3`.

Final Solution

The completed Sudoku grid is:

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

Thus, the final answer is:

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