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.
- The second column of the first row cannot be 1 (because 1 is in the second row, second column).
- The fourth column of the first row cannot be 3 (because 3 is in the second row, fourth column).

Let's try placing the numbers:
- First row: 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 first column of the second row cannot be 4 (because 4 is in the first row, first column).
- The third column of the second row must be 4 (since 4 is missing in this row).

Second row: 2, 1, 4, 3

#### Step 4: Fill in the third row
- The third row must contain the numbers 1, 2, 3, and 4.
- We need to ensure that the numbers do not repeat in the columns and the 2x2 subgrids.
- The first column of the third row cannot be 4 (because 4 is in the first row, first column) or 2 (because 2 is in the second row, first column).
- The second column of the third row cannot be 1 (because 1 is in the second row, second column).
- The fourth column of the third row cannot be 3 (because 3 is in the second row, fourth column).

Third row: 3, 4, 2, 1

#### Step 5: Fill in the fourth row
- The fourth row must contain the numbers 1, 2, 3, and 4.
- We already have 1 and 3 in the fourth row.
- The second column of the fourth row cannot be 1 (because 1 is in the fourth row, first column) or 4 (because 4 is in the third row, second column).
- The fourth column of the fourth row must be 2 (since 2 is missing in this row).

Fourth row: 1, 2, 3, 4

Final Solution:

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

Verification:

- Each row contains 1, 2, 3, and 4 exactly once.
- Each column contains 1, 2, 3, and 4 exactly once.
- Each 2x2 subgrid contains 1, 2, 3, and 4 exactly once.

Thus, the solution is correct.

Final Answer:

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