Easy and Hard Sudoku Printables Kids Activities Blog - Free Printable

Problem Description:

The image shows a 4x4 Sudoku puzzle. The goal is to fill in the empty cells with numbers from 1 to 4 such that each row, each column, and each 2x2 subgrid contains all the numbers 1, 2, 3, and 4 exactly once.

Initial Puzzle:

```
+---+---+---+---+
| 4 | | | |
+---+---+---+---+
| | 1 | | 3 |
+---+---+---+---+
| | | | |
+---+---+---+---+
| 1 | | 3 | |
+---+---+---+---+
```

Solution Approach:

We will solve the Sudoku step by step, ensuring that each row, column, and 2x2 subgrid adheres to the rules.

#### Step 1: Analyze the given numbers
- Top-left cell: 4
- Second row, second column: 1
- Second row, fourth column: 3
- Bottom-left cell: 1
- Bottom-third column: 3

#### Step 2: Fill in the first row
- The first row must contain the numbers 1, 2, 3, and 4.
- Since 4 is already in the first row, we need to place 1, 2, and 3.
- From the second row, we know that 1 is in the second column, so it cannot be in the first row's second column.
- From the bottom row, we know that 3 is in the third column, so it cannot be in the first row's third column.
- Therefore, the first row can be filled as follows:
```
+---+---+---+---+
| 4 | 2 | 1 | 3 |
+---+---+---+---+
```

#### Step 3: Fill in the second row
- The second row must contain the numbers 1, 2, 3, and 4.
- We already have 1 and 3 in the second row.
- The second column has 1, so the second row's second column is filled.
- The fourth column has 3, so the second row's fourth column is filled.
- The remaining numbers are 2 and 4. Since 4 cannot be in the first column (because 4 is in the first row), it must go in the third column. Thus, 2 goes in the first column.
```
+---+---+---+---+
| 4 | 2 | 1 | 3 |
+---+---+---+---+
| 2 | 1 | 4 | 3 |
+---+---+---+---+
```

#### Step 4: Fill in the bottom-left 2x2 subgrid
- The bottom-left 2x2 subgrid must contain the numbers 1, 2, 3, and 4.
- We already have 1 in the bottom-left cell.
- The second row's third column has 4, so the bottom-left subgrid's third column cannot have 4. It must have 2.
- The bottom row's fourth column must have 4 (since 1, 2, and 3 are already used in the bottom row).
```
+---+---+---+---+
| 4 | 2 | 1 | 3 |
+---+---+---+---+
| 2 | 1 | 4 | 3 |
+---+---+---+---+
| 1 | 4 | 2 | |
+---+---+---+---+
```

#### Step 5: Fill in the bottom-right 2x2 subgrid
- The bottom-right 2x2 subgrid must contain the numbers 1, 2, 3, and 4.
- We already have 3 in the bottom row's third column.
- The bottom row's fourth column must have 4 (as determined earlier).
- The second row's fourth column has 3, so the bottom-right subgrid's second column must have 1.
- The remaining number for the bottom-right subgrid is 2, which goes in the bottom row's second column.
```
+---+---+---+---+
| 4 | 2 | 1 | 3 |
+---+---+---+---+
| 2 | 1 | 4 | 3 |
+---+---+---+---+
| 1 | 4 | 2 | 3 |
+---+---+---+---+
```

#### Step 6: Verify the solution
- Each row, column, and 2x2 subgrid contains the numbers 1, 2, 3, and 4 exactly once.
- The solution is correct.

Final Answer:

```
+---+---+---+---+
| 4 | 2 | 1 | 3 |
+---+---+---+---+
| 2 | 1 | 4 | 3 |
+---+---+---+---+
| 1 | 4 | 2 | 3 |
+---+---+---+---+
```

$$
\boxed{
\begin{array}{|c|c|c|c|}
\hline
4 & 2 & 1 & 3 \\
\hline
2 & 1 & 4 & 3 \\
\hline
1 & 4 & 2 & 3 \\
\hline
\end{array}
}
$$