Printables - Sudoku Game 05 | HP® Official Site - Free Printable

Problem: Solve the Sudoku Puzzle

The provided image contains a 9x9 Sudoku grid with some numbers already filled in. The goal is to fill in the remaining cells such that each row, each column, and each of the nine 3x3 subgrids contain all of the digits from 1 to 9 exactly once.

#### Step-by-Step Solution:

1. Understand the Rules:
- Each row must contain the digits 1 through 9 without repetition.
- Each column must contain the digits 1 through 9 without repetition.
- Each 3x3 subgrid (also called a "box") must contain the digits 1 through 9 without repetition.

2. Analyze the Given Grid:
The initial grid is as follows:
```
| 9 1 2 | 6 | 8 3 |
| 2 | | 9 4 7|
| 5 | 3 | 8 |
|-------|-------|--------|
| 6 | 4 1 | |
| 1 | 8 | 9 5 |
| 6 9 | 2 | |
|-------|-------|--------|
| 2 3 | 4 | 1 6 |
| | | |
| | | |
```

3. Solve the Puzzle Step-by-Step:
We will solve the puzzle by filling in the missing numbers one cell at a time, ensuring that the rules are followed.

#### Row 1:
- The first row is `9 1 2 | _ _ _ | 8 3 _`.
- Missing digits: 4, 5, 6, 7.
- The third box (rightmost) already has 8 and 3, so the missing digits for this box are 4, 5, 6, 7.
- Fill in the missing digits based on the constraints of the row and box:
```
| 9 1 2 | 5 7 4 | 8 3 6 |
```

#### Row 2:
- The second row is `_ _ 2 | _ _ _ | _ 9 4 7`.
- Missing digits: 1, 3, 5, 6, 8.
- Use the constraints of the row, column, and box to fill in the missing digits:
```
| 3 8 2 | 1 5 6 | 7 9 4 |
```

#### Row 3:
- The third row is `5 _ _ | _ 3 _ | _ 8 _`.
- Missing digits: 1, 2, 4, 6, 7, 9.
- Use the constraints of the row, column, and box to fill in the missing digits:
```
| 5 7 4 | 2 3 9 | 6 8 1 |
```

#### Row 4:
- The fourth row is `6 _ _ | 4 1 _ | _ _ _`.
- Missing digits: 2, 3, 5, 7, 8, 9.
- Use the constraints of the row, column, and box to fill in the missing digits:
```
| 6 9 8 | 4 1 5 | 3 7 2 |
```

#### Row 5:
- The fifth row is `1 _ _ | 8 _ _ | _ 9 5`.
- Missing digits: 2, 3, 4, 6, 7.
- Use the constraints of the row, column, and box to fill in the missing digits:
```
| 1 4 5 | 8 7 3 | 2 9 6 |
```

#### Row 6:
- The sixth row is `_ 6 9 | _ 2 _ | _ _ _`.
- Missing digits: 1, 3, 4, 5, 7, 8.
- Use the constraints of the row, column, and box to fill in the missing digits:
```
| 7 6 9 | 5 2 1 | 4 3 8 |
```

#### Row 7:
- The seventh row is `_ _ 2 | _ 3 _ | 4 1 6`.
- Missing digits: 5, 7, 8, 9.
- Use the constraints of the row, column, and box to fill in the missing digits:
```
| 8 5 2 | 9 3 7 | 4 1 6 |
```

#### Row 8:
- The eighth row is `_ _ _ | _ _ _ | _ _ _`.
- Missing digits: 1, 2, 3, 4, 5, 6, 7, 8, 9.
- Use the constraints of the row, column, and box to fill in the missing digits:
```
| 4 3 1 | 6 8 2 | 5 7 9 |
```

#### Row 9:
- The ninth row is `_ _ _ | _ _ _ | _ _ _`.
- Missing digits: 1, 2, 3, 4, 5, 6, 7, 8, 9.
- Use the constraints of the row, column, and box to fill in the missing digits:
```
| 2 7 6 | 3 5 4 | 9 8 1 |
```

4. Final Solved Grid:
The completed Sudoku grid is:
```
| 9 1 2 | 5 7 4 | 8 3 6 |
| 3 8 2 | 1 5 6 | 7 9 4 |
| 5 7 4 | 2 3 9 | 6 8 1 |
|-------|-------|--------|
| 6 9 8 | 4 1 5 | 3 7 2 |
| 1 4 5 | 8 7 3 | 2 9 6 |
| 7 6 9 | 5 2 1 | 4 3 8 |
|-------|-------|--------|
| 8 5 2 | 9 3 7 | 4 1 6 |
| 4 3 1 | 6 8 2 | 5 7 9 |
| 2 7 6 | 3 5 4 | 9 8 1 |
```

Final Answer:

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