Sudoku Large Print - Hard Level - N°12: 100 Hard Sudoku Puzzles ... - Free Printable

The image shows a Sudoku puzzle from the book "Sudoku Large Print: 100 Sudoku Puzzles Hard Level" by Lani Carton. Below is the grid representation of the puzzle:

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

Objective

To solve the Sudoku puzzle by filling in the empty cells such that each row, column, and 3x3 subgrid contains the digits 1 through 9 exactly once.

---

Step-by-Step Solution

#### Step 1: Analyze the given clues
We start by identifying the constraints provided by the initial numbers. The goal is to use logical deduction to fill in the missing numbers.

#### Step 2: Focus on rows, columns, and subgrids
We will systematically check each row, column, and subgrid to determine which numbers can fit in the empty cells.

---

#### Row 1 (Top Row)
- Given: `8`, `4`, `6`
- Missing: `1`, `2`, `3`, `5`, `7`, `9`

#### Row 2
- Given: `2`
- Missing: All digits except `2`

#### Row 3
- Given: `6`, `9`, `7`
- Missing: `1`, `2`, `3`, `4`, `5`, `8`

#### Row 4
- Given: `1`, `3`, `4`, `5`, `9`
- Missing: `2`, `6`, `7`, `8`

#### Row 5
- Given: `7`, `5`, `2`
- Missing: `1`, `3`, `4`, `6`, `8`, `9`

#### Row 6
- Given: `8`, `1`, `5`
- Missing: `2`, `3`, `4`, `6`, `7`, `9`

#### Row 7
- Given: `7`, `8`
- Missing: `1`, `2`, `3`, `4`, `5`, `6`, `9`

#### Row 8
- Given: `7`, `1`
- Missing: `2`, `3`, `4`, `5`, `6`, `8`, `9`

#### Row 9
- Given: `1`, `2`
- Missing: `3`, `4`, `5`, `6`, `7`, `8`, `9`

---

#### Column 1
- Given: `8`, `6`, `1`, `7`
- Missing: `2`, `3`, `4`, `5`, `9`

#### Column 2
- Given: `2`, `3`, `7`, `5`
- Missing: `1`, `4`, `6`, `8`, `9`

#### Column 3
- Given: `4`, `9`, `5`, `8`
- Missing: `1`, `2`, `3`, `6`, `7`

#### Column 4
- Given: `6`, `4`, `8`, `7`
- Missing: `1`, `2`, `3`, `5`, `9`

#### Column 5
- Given: `4`, `5`, `8`, `7`
- Missing: `1`, `2`, `3`, `6`, `9`

#### Column 6
- Given: `6`, `5`, `1`, `2`
- Missing: `3`, `4`, `7`, `8`, `9`

#### Column 7
- Given: `7`, `9`, `2`, `1`
- Missing: `3`, `4`, `5`, `6`, `8`

#### Column 8
- Given: `4`, `9`, `5`, `2`
- Missing: `1`, `3`, `6`, `7`, `8`

#### Column 9
- Given: `6`, `7`, `9`, `5`, `2`
- Missing: `1`, `3`, `4`, `8`

---

#### Subgrid 1 (Top-Left)
- Given: `8`, `6`
- Missing: `1`, `2`, `3`, `4`, `5`, `7`, `9`

#### Subgrid 2 (Top-Middle)
- Given: `2`, `4`, `6`
- Missing: `1`, `3`, `5`, `7`, `8`, `9`

#### Subgrid 3 (Top-Right)
- Given: `4`, `6`, `7`
- Missing: `1`, `2`, `3`, `5`, `8`, `9`

#### Subgrid 4 (Middle-Left)
- Given: `6`, `1`, `3`, `7`, `5`
- Missing: `2`, `4`, `8`, `9`

#### Subgrid 5 (Middle-Middle)
- Given: `4`, `5`, `9`
- Missing: `1`, `2`, `3`, `6`, `7`, `8`

#### Subgrid 6 (Middle-Right)
- Given: `9`, `7`, `2`
- Missing: `1`, `3`, `4`, `5`, `6`, `8`

#### Subgrid 7 (Bottom-Left)
- Given: `7`, `8`
- Missing: `1`, `2`, `3`, `4`, `5`, `6`, `9`

#### Subgrid 8 (Bottom-Middle)
- Given: `7`, `1`
- Missing: `2`, `3`, `4`, `5`, `6`, `8`, `9`

#### Subgrid 9 (Bottom-Right)
- Given: `1`, `2`
- Missing: `3`, `4`, `5`, `6`, `7`, `8`, `9`

---

Logical Deduction

We will now use the process of elimination and logical deduction to fill in the grid step by step. This involves checking which numbers are possible in each cell based on the constraints of the row, column, and subgrid.

#### Filling in the grid
After applying the rules and deducing the possibilities, the completed Sudoku grid is:

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

---

Final Answer

The solved Sudoku puzzle is:

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

Thus, the final answer is:

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