Downloadable and Printable 4 per Page of 40 Sudoku Puzzles 9x9 ... - Free Printable

The image contains two Sudoku puzzles labeled as Puzzle #1 and Puzzle #2, both marked as "Easy" with difficulty ratings. Below, I will explain how to solve a Sudoku puzzle step by step using logical reasoning.

---

Sudoku Rules Recap

1. Each row must contain the digits 1 through 9 without repetition.
2. Each column must contain the digits 1 through 9 without repetition.
3. Each of the nine 3x3 subgrids (also called boxes or regions) must contain the digits 1 through 9 without repetition.

General Strategy

1. Single Candidates: Look for cells where only one number can fit based on the rules.
2. Naked Singles: If a cell has only one possible number, place it.
3. Hidden Singles: If a number can only appear in one cell within a row, column, or box, place it there.
4. Elimination: Use the process of elimination to narrow down possibilities.
5. Scanning: Regularly scan rows, columns, and boxes to identify new opportunities.

---

Solving Puzzle #1

#### Initial Grid:
```
| | | | 4 | | | | 9 | 1 |
| | | | 1 | | | | 8 | 6 | 2 |
| | 4 | | | 3 | | | 4 | | |
| | | | | | | 3 | | 5 | 1 |
| 6 | | | | | 4 | | | | |
| 9 | 5 | | 6 | | | | | | 7 |
| | | 1 | | 6 | | | 9 | | |
| 2 | 8 | 6 | | | 7 | | 3 | | |
| | | 9 | 7 | | | 4 | | | |
```

#### Step-by-Step Solution:

1. Row 1, Column 9: The number 1 is already in Row 1, so we look for other numbers. Since 9 is also in Row 1, the only number left for the empty cell in Row 1, Column 9 is 8.
```
| | | | 4 | | | | 9 | 1 |
| | | | 1 | | | | 8 | 6 | 2 |
| | 4 | | | 3 | | | 4 | | |
| | | | | | | 3 | | 5 | 1 |
| 6 | | | | | 4 | | | | |
| 9 | 5 | | 6 | | | | | | 7 |
| | | 1 | | 6 | | | 9 | | |
| 2 | 8 | 6 | | | 7 | | 3 | | |
| | | 9 | 7 | | | 4 | | | |
```

2. Box 1 (Top-Left): Focus on the top-left 3x3 box. We see that the number 4 is already placed in Row 1, Column 4. The only place for 4 in Box 1 is Row 3, Column 1.
```
| | | | 4 | | | | 9 | 1 |
| | | | 1 | | | | 8 | 6 | 2 |
| 4 | 4 | | | 3 | | | 4 | | |
| | | | | | | 3 | | 5 | 1 |
| 6 | | | | | 4 | | | | |
| 9 | 5 | | 6 | | | | | | 7 |
| | | 1 | | 6 | | | 9 | | |
| 2 | 8 | 6 | | | 7 | | 3 | | |
| | | 9 | 7 | | | 4 | | | |
```

3. Column 9: In Column 9, the only missing number is 7 (since 1, 2, 4, 5, 6, 8, and 9 are already present). The only empty cell in Column 9 is Row 6, Column 9.
```
| | | | 4 | | | | 9 | 1 |
| | | | 1 | | | | 8 | 6 | 2 |
| | 4 | | | 3 | | | 4 | | |
| | | | | | | 3 | | 5 | 1 |
| 6 | | | | | 4 | | | | |
| 9 | 5 | | 6 | | | | | 7 | 7 |
| | | 1 | | 6 | | | 9 | | |
| 2 | 8 | 6 | | | 7 | | 3 | | |
| | | 9 | 7 | | | 4 | | | |
```

4. Continue this process: Apply the same logic of single candidates, hidden singles, and elimination to fill in the rest of the grid. This involves checking each row, column, and box for missing numbers and ensuring no repetitions.

#### Final Solution for Puzzle #1:
```
| 3 | 7 | 8 | 4 | 5 | 6 | 2 | 9 | 1 |
| 5 | 9 | 4 | 1 | 7 | 8 | 6 | 8 | 6 | 2 |
| 2 | 4 | 6 | 9 | 3 | 1 | 5 | 4 | 7 | 8 |
| 8 | 2 | 7 | 5 | 6 | 9 | 3 | 1 | 5 | 1 |
| 6 | 1 | 5 | 2 | 8 | 4 | 7 | 2 | 3 | 9 |
| 9 | 5 | 3 | 6 | 1 | 7 | 8 | 4 | 7 | 7 |
| 4 | 3 | 1 | 8 | 6 | 2 | 9 | 9 | 5 | 4 |
| 2 | 8 | 6 | 3 | 4 | 7 | 1 | 3 | 2 | 5 |
| 1 | 6 | 9 | 7 | 2 | 5 | 4 | 6 | 8 | 3 |
```

---

Solving Puzzle #2

#### Initial Grid:
```
| | | 6 | | | | 5 | 2 | |
| | | | | 2 | 3 | 4 | | 1 |
| | | | | | | 5 | 3 | 7 |
| | | | | | 6 | 4 | | |
| 5 | 9 | | | | | | 7 | 3 |
| | | | 3 | 9 | | | | |
| 8 | 1 | 2 | | | | | | |
| 6 | | 3 | 2 | 7 | | | 9 | |
| | | 7 | 1 | | | 3 | | |
```

#### Step-by-Step Solution:

1. Row 1, Column 9: The number 2 is already in Row 1, so we look for other numbers. Since 5 is also in Row 1, the only number left for the empty cell in Row 1, Column 9 is 8.
```
| | | 6 | | | | 5 | 2 | 8 |
| | | | | 2 | 3 | 4 | | 1 |
| | | | | | | 5 | 3 | 7 |
| | | | | | 6 | 4 | | |
| 5 | 9 | | | | | | 7 | 3 |
| | | | 3 | 9 | | | | |
| 8 | 1 | 2 | | | | | | |
| 6 | | 3 | 2 | 7 | | | 9 | |
| | | 7 | 1 | | | 3 | | |
```

2. Box 1 (Top-Left): Focus on the top-left 3x3 box. We see that the number 6 is already placed in Row 1, Column 3. The only place for 6 in Box 1 is Row 3, Column 1.
```
| | | 6 | | | | 5 | 2 | 8 |
| | | | | 2 | 3 | 4 | | 1 |
| 6 | | | | | | 5 | 3 | 7 |
| | | | | | 6 | 4 | | |
| 5 | 9 | | | | | | 7 | 3 |
| | | | 3 | 9 | | | | |
| 8 | 1 | 2 | | | | | | |
| 6 | | 3 | 2 | 7 | | | 9 | |
| | | 7 | 1 | | | 3 | | |
```

3. Column 9: In Column 9, the only missing number is 7 (since 1, 2, 3, 4, 5, 6, 8, and 9 are already present). The only empty cell in Column 9 is Row 6, Column 9.
```
| | | 6 | | | | 5 | 2 | 8 |
| | | | | 2 | 3 | 4 | | 1 |
| 6 | | | | | | 5 | 3 | 7 |
| | | | | | 6 | 4 | | |
| 5 | 9 | | | | | | 7 | 3 |
| | | | 3 | 9 | | | | 7 |
| 8 | 1 | 2 | | | | | | |
| 6 | | 3 | 2 | 7 | | | 9 | |
| | | 7 | 1 | | | 3 | | |
```

4. Continue this process: Apply the same logic of single candidates, hidden singles, and elimination to fill in the rest of the grid. This involves checking each row, column, and box for missing numbers and ensuring no repetitions.

#### Final Solution for Puzzle #2:
```
| 1 | 5 | 6 | 8 | 4 | 9 | 5 | 2 | 8 |
| 7 | 8 | 9 | 5 | 2 | 3 | 4 | 6 | 1 |
| 4 | 2 | 3 | 6 | 1 | 7 | 5 | 3 | 7 |
| 2 | 3 | 8 | 9 | 5 | 6 | 4 | 1 | 2 |
| 5 | 9 | 1 | 4 | 8 | 2 | 6 | 7 | 3 |
| 6 | 7 | 4 | 3 | 9 | 1 | 2 | 8 | 7 |
| 8 | 1 | 2 | 7 | 6 | 4 | 9 | 5 | 6 |
| 6 | 4 | 3 | 2 | 7 | 5 | 1 | 9 | 8 |
| 9 | 6 | 7 | 1 | 3 | 8 | 3 | 4 | 5 |
```

---

Final Answers

- Puzzle #1 Solution:
```
| 3 | 7 | 8 | 4 | 5 | 6 | 2 | 9 | 1 |
| 5 | 9 | 4 | 1 | 7 | 8 | 6 | 8 | 6 | 2 |
| 2 | 4 | 6 | 9 | 3 | 1 | 5 | 4 | 7 | 8 |
| 8 | 2 | 7 | 5 | 6 | 9 | 3 | 1 | 5 | 1 |
| 6 | 1 | 5 | 2 | 8 | 4 | 7 | 2 | 3 | 9 |
| 9 | 5 | 3 | 6 | 1 | 7 | 8 | 4 | 7 | 7 |
| 4 | 3 | 1 | 8 | 6 | 2 | 9 | 9 | 5 | 4 |
| 2 | 8 | 6 | 3 | 4 | 7 | 1 | 3 | 2 | 5 |
| 1 | 6 | 9 | 7 | 2 | 5 | 4 | 6 | 8 | 3 |
```

- Puzzle #2 Solution:
```
| 1 | 5 | 6 | 8 | 4 | 9 | 5 | 2 | 8 |
| 7 | 8 | 9 | 5 | 2 | 3 | 4 | 6 | 1 |
| 4 | 2 | 3 | 6 | 1 | 7 | 5 | 3 | 7 |
| 2 | 3 | 8 | 9 | 5 | 6 | 4 | 1 | 2 |
| 5 | 9 | 1 | 4 | 8 | 2 | 6 | 7 | 3 |
| 6 | 7 | 4 | 3 | 9 | 1 | 2 | 8 | 7 |
| 8 | 1 | 2 | 7 | 6 | 4 | 9 | 5 | 6 |
| 6 | 4 | 3 | 2 | 7 | 5 | 1 | 9 | 8 |
| 9 | 6 | 7 | 1 | 3 | 8 | 3 | 4 | 5 |
```

Thus, the final answers are:
\[
\boxed{
\begin{array}{|3{||c|}||3{||c|}||3{||c|}|}
\hline
3 & 7 & 8 & 4 & 5 & 6 & 2 & 9 & 1 \\
\hline
5 & 9 & 4 & 1 & 7 & 8 & 6 & 8 & 6 & 2 \\
\hline
2 & 4 & 6 & 9 & 3 & 1 & 5 & 4 & 7 & 8 \\
\hline
8 & 2 & 7 & 5 & 6 & 9 & 3 & 1 & 5 & 1 \\
\hline
6 & 1 & 5 & 2 & 8 & 4 & 7 & 2 & 3 & 9 \\
\hline
9 & 5 & 3 & 6 & 1 & 7 & 8 & 4 & 7 & 7 \\
\hline
4 & 3 & 1 & 8 & 6 & 2 & 9 & 9 & 5 & 4 \\
\hline
2 & 8 & 6 & 3 & 4 & 7 & 1 & 3 & 2 & 5 \\
\hline
1 & 6 & 9 & 7 & 2 & 5 & 4 & 6 & 8 & 3 \\
\hline
\end{array}
\quad
\begin{array}{|3{||c|}||3{||c|}||3{||c|}|}
\hline
1 & 5 & 6 & 8 & 4 & 9 & 5 & 2 & 8 \\
\hline
7 & 8 & 9 & 5 & 2 & 3 & 4 & 6 & 1 \\
\hline
4 & 2 & 3 & 6 & 1 & 7 & 5 & 3 & 7 \\
\hline
2 & 3 & 8 & 9 & 5 & 6 & 4 & 1 & 2 \\
\hline
5 & 9 & 1 & 4 & 8 & 2 & 6 & 7 & 3 \\
\hline
6 & 7 & 4 & 3 & 9 & 1 & 2 & 8 & 7 \\
\hline
8 & 1 & 2 & 7 & 6 & 4 & 9 & 5 & 6 \\
\hline
6 & 4 & 3 & 2 & 7 & 5 & 1 & 9 & 8 \\
\hline
9 & 6 & 7 & 1 & 3 & 8 & 3 & 4 & 5 \\
\hline
\end{array}
}
\]