Sudoku Expert Level Book 1: 150 Extreme Hardest Sudoku Puzzles for Expert Advanced Level Puzzlers With Solutions - Free Printable

The image shows a Sudoku puzzle grid with some numbers already filled in. The task is to solve the Sudoku puzzle by filling in the remaining cells such that each row, column, and 3x3 subgrid contains all the digits from 1 to 9 without repetition.

Sudoku Rules Recap:

1. Each row must contain the digits 1 through 9.
2. Each column must contain the digits 1 through 9.
3. Each 3x3 subgrid (also called a "box" or "region") must contain the digits 1 through 9.

Given Puzzle Grid:

Here is the initial state of the Sudoku grid as shown in the image:

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

Step-by-Step Solution:

#### Step 1: Analyze the given clues
We start by identifying which rows, columns, and boxes have the most information. This helps us make progress quickly.

#### Step 2: Use basic elimination techniques
We will use the following strategies:
1. Single Candidates: If a cell can only contain one possible number based on the rules, fill it in.
2. Naked Singles: Look for cells where only one number is possible in a row, column, or box.
3. Hidden Singles: Identify numbers that can only fit in one cell within a row, column, or box.

#### Step 3: Solve the puzzle iteratively
We will solve the puzzle step by step, filling in cells as we go.

---

Detailed Solution Process:

#### Row 1:
- Focus on the top-left 3x3 box. The number `6` is already placed in the third column.
- In Row 1, Column 1, the possible candidates are `1, 2, 4, 5, 7, 8, 9`. By checking the constraints of the box and column, we can narrow it down.

#### Column 9:
- The number `3` is already in Row 1, Column 9.
- In Row 9, Column 9, the number `5` is already placed. We need to ensure no conflicts arise when filling other cells.

#### Box 3 (Top-Right):
- The number `6` is already in Row 1, Column 9.
- The number `2` is in Row 2, Column 8.
- Use these clues to fill in the rest of the box.

#### Continue Filling:
By systematically applying the above strategies, we can fill in the entire grid. Here is the completed solution:

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

Final Answer:

The completed Sudoku grid is:

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

Thus, the final answer is:

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