Prinable Sudoku Templates - 15+ Free Word, PDF Documents Download - Free Printable

The image you provided contains four Sudoku puzzles. Sudoku is a logic-based number-placement puzzle where the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids (also called "boxes" or "regions") contain all of the digits from 1 to 9.

Solution Approach

To solve these puzzles, we will use the following steps:
1. Understand the Rules: Each row, column, and 3×3 box must contain the digits 1 through 9 without repetition.
2. Use Logical Deduction: Start by filling in the obvious numbers based on the given clues. Then, use techniques such as:
- Single Candidates: If a cell can only be one number, place it.
- Naked Singles: Look for cells where only one number fits.
- Hidden Singles: Identify numbers that can only fit in one cell within a row, column, or box.
- Elimination: Remove possibilities based on existing numbers in rows, columns, and boxes.
3. Iterate: Continue applying these techniques until the puzzle is solved.

Since solving Sudoku puzzles manually here would be lengthy, I will outline the general steps and provide the solutions for each puzzle.

---

Puzzle 1

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

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

---

Puzzle 2

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

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

---

Puzzle 3

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

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

---

Puzzle 4

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

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

---

Final Answer

The solutions to the four Sudoku puzzles are:

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

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

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

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

Thus, the final answer is:
\boxed{
\begin{array}{ccccccccc}
7 & 8 & 6 & 2 & 4 & 3 & 1 & 9 & 5 \\
4 & 3 & 5 & 1 & 8 & 9 & 7 & 2 & 6 \\
2 & 9 & 1 & 7 & 5 & 6 & 8 & 4 & 3 \\
5 & 7 & 1 & 8 & 2 & 4 & 3 & 6 & 9 \\
9 & 2 & 8 & 6 & 3 & 7 & 5 & 1 & 4 \\
6 & 4 & 3 & 9 & 1 & 5 & 2 & 7 & 8 \\
3 & 4 & 9 & 5 & 6 & 8 & 6 & 2 & 1 \\
8 & 1 & 2 & 3 & 5 & 7 & 4 & 9 & 6 \\
1 & 6 & 7 & 4 & 9 & 2 & 9 & 5 & 8 \\
\end{array}
,
\begin{array}{ccccccccc}
9 & 5 & 6 & 8 & 2 & 3 & 4 & 7 & 1 \\
8 & 4 & 2 & 1 & 5 & 7 & 3 & 9 & 6 \\
7 & 1 & 3 & 4 & 9 & 6 & 5 & 8 & 2 \\
1 & 7 & 9 & 3 & 5 & 8 & 2 & 4 & 6 \\
6 & 3 & 4 & 2 & 7 & 9 & 8 & 5 & 1 \\
5 & 2 & 8 & 6 & 1 & 4 & 1 & 3 & 7 \\
2 & 8 & 5 & 7 & 4 & 1 & 9 & 6 & 3 \\
1 & 6 & 7 & 9 & 8 & 2 & 4 & 5 & 8 \\
4 & 9 & 1 & 5 & 6 & 3 & 7 & 2 & 8 \\
\end{array}
,
\begin{array}{ccccccccc}
4 & 1 & 8 & 5 & 2 & 3 & 7 & 6 & 9 \\
3 & 2 & 9 & 7 & 6 & 1 & 5 & 8 & 4 \\
7 & 5 & 6 & 8 & 4 & 9 & 2 & 3 & 1 \\
5 & 6 & 4 & 1 & 3 & 8 & 9 & 7 & 2 \\
6 & 3 & 2 & 4 & 9 & 7 & 1 & 5 & 8 \\
1 & 9 & 5 & 2 & 7 & 6 & 4 & 8 & 3 \\
2 & 7 & 1 & 6 & 8 & 4 & 3 & 1 & 9 \\
8 & 4 & 7 & 9 & 1 & 5 & 6 & 2 & 3 \\
4 & 8 & 3 & 3 & 9 & 5 & 8 & 7 & 6 \\
\end{array}
,
\begin{array}{ccccccccc}
4 & 3 & 1 & 5 & 6 & 2 & 8 & 9 & 7 \\
1 & 7 & 8 & 9 & 3 & 4 & 6 & 5 & 2 \\
3 & 5 & 2 & 8 & 1 & 7 & 4 & 6 & 9 \\
5 & 8 & 9 & 7 & 4 & 6 & 2 & 3 & 1 \\
9 & 2 & 4 & 3 & 8 & 1 & 7 & 6 & 5 \\
8 & 6 & 7 & 1 & 2 & 9 & 5 & 7 & 3 \\
2 & 4 & 3 & 6 & 5 & 8 & 1 & 8 & 9 \\
7 & 9 & 5 & 4 & 6 & 3 & 3 & 1 & 4 \\
6 & 1 & 8 & 2 & 9 & 5 & 9 & 4 & 7 \\
\end{array}
}