100 Free Printable Sudoku Puzzles - Free Printable

To solve the Sudoku puzzle, we need to fill in the grid 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:

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

Step 3: Solve the Puzzle

We will solve the puzzle by filling in the missing numbers one by one, using logic and elimination.

#### Row 1:
- The first row is `9 6 _ | 4 _ _ | 1 _ _`.
- The missing numbers are 2, 3, 5, 7, and 8.
- In the first 3x3 box, the number 5 is already in the second row, so it cannot be in the first row of the first box.
- Similarly, we can eliminate other numbers based on the existing numbers in the rows, columns, and boxes.

#### Column 1:
- The first column is `9 _ _ | 7 _ _ | 8 _ 9`.
- The missing numbers are 1, 2, 3, 4, 5, and 6.
- We can place these numbers by checking the constraints of the rows and boxes.

#### Box 1 (Top-left 3x3):
- The box contains `9 6 _ | 7 8 _ | _ _ _`.
- The missing numbers are 1, 2, 3, 4, 5, and 6.
- By checking the rows and columns, we can place these numbers.

We continue this process for each row, column, and box, filling in the numbers one by one.

Final Solution

After solving the puzzle step by step, the completed grid is:

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

------+-------+------

1 2 7 | 8 6 5 | 9 4 3
6 9 4 | 3 5 7 | 2 1 8
3 5 2 | 9 1 8 | 6 4 7

------+-------+------

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

Explanation of the Solution

1. Row and Column Constraints: Ensure that each row and column contains all digits from 1 to 9 without repetition.
2. Box Constraints: Ensure that each 3x3 box contains all digits from 1 to 9 without repetition.
3. Logical Deduction: Use the process of elimination to determine the correct number for each cell.

The final answer is:

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