FREE EASY SUDUKU PUZZLES PRINTABLE - Free Printable

Problem Description:

The image shows a partially filled Sudoku grid. The task is to solve the Sudoku puzzle by filling in the missing numbers (1 through 9) in each row, column, and 3x3 subgrid, ensuring that no number is repeated in any row, column, or subgrid.

Solution Approach:

Sudoku is a logic-based puzzle where the goal is to fill a 9x9 grid with digits so that each column, each row, and each of the nine 3x3 subgrids contain all of the digits from 1 to 9. To solve this, we will use the following steps:

1. Understand the Rules:
- Each row must contain the digits 1–9 without repetition.
- Each column must contain the digits 1–9 without repetition.
- Each 3x3 subgrid must contain the digits 1–9 without repetition.

2. Use Logical Deduction:
- Start by identifying cells where only one possible number can fit based on the existing numbers in the row, column, and subgrid.
- Use techniques such as "naked singles," "hidden singles," and "candidate elimination" to progressively fill in the grid.

3. Iterate and Solve:
- Continue applying logical deductions until the entire grid is filled.

Step-by-Step Solution:

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

#### Step 1: Fill in obvious single possibilities.
- Row 1, Column 9: The only number missing in Row 1 is 9.
```
| 3 _ _ | 1 _ _ | 6 _ 9
```

- Row 2, Column 6: The only number missing in Row 2 is 2.
```
| 7 5 _ | _ 3 2 | _ 4 8
```

- Row 3, Column 1: The only number missing in Column 1 is 8.
```
| 8 _ 6 | 9 8 4 | 3 _ _
```

#### Step 2: Focus on subgrids and rows/columns.
- Subgrid (1,1): In the top-left subgrid, the only missing number is 4.
```
| 3 _ 4 | 1 _ _ | 6 _ 9
```

- Subgrid (2,1): In the middle-left subgrid, the only missing number in Row 4, Column 3 is 7.
```
| _ _ 7 | _ _ _ | _ 8 _
```

#### Step 3: Continue filling using logical deduction.
- Row 5, Column 5: The only number missing in Row 5 is 5.
```
| 9 1 2 | _ 5 _ | 6 7 4
```

- Row 6, Column 3: The only number missing in Column 3 is 8.
```
| _ 4 8 | _ _ _ | 5 _ _
```

#### Step 4: Progressively fill in the grid.
Continue this process, focusing on rows, columns, and subgrids, and using techniques like "naked singles" and "hidden singles." After several iterations, the complete grid is:

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

Final Answer:

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

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