5x5 Jigsaw Sudoku Puzzle #1 - Free Printable

Problem Description:

The task is to solve a 5x5 Jigsaw Sudoku puzzle. In this type of Sudoku, the grid is divided into irregularly shaped regions (blocks), and the goal is to fill in the grid such that:
1. Each row contains the numbers 1 through 5 exactly once.
2. Each column contains the numbers 1 through 5 exactly once.
3. Each block (irregular region) contains the numbers 1 through 5 exactly once.

The given puzzle has some pre-filled numbers, and we need to determine the remaining numbers.

Puzzle Grid:

Here is the initial state of the grid with the pre-filled numbers:

```
+---+---+---+---+---+
| | 5 | | | |
+---+---+---+---+---+
| | | | 3 | |
+---+---+---+---+---+
| 5 | | 4 | | 1 |
+---+---+---+---+---+
| | | | | 5 |
+---+---+---+---+---+
| | | | | |
+---+---+---+---+---+
```

Step-by-Step Solution:

#### Step 1: Understand the Blocks
The grid is divided into 5 irregular blocks. Let's identify them:
1. Top-left block: Cells `(1,1)`, `(2,1)`, `(2,2)`
2. Top-middle block: Cells `(1,2)`, `(1,3)`, `(2,3)`
3. Top-right block: Cells `(1,4)`, `(1,5)`, `(2,5)`
4. Middle-left block: Cells `(3,1)`, `(4,1)`, `(5,1)`
5. Middle-middle block: Cells `(3,2)`, `(3,3)`, `(4,2)`, `(4,3)`
6. Middle-right block: Cells `(3,4)`, `(3,5)`, `(4,4)`, `(4,5)`
7. Bottom-left block: Cells `(5,2)`, `(5,3)`
8. Bottom-middle block: Cells `(5,4)`, `(5,5)`

#### Step 2: Fill in the Grid
We will use logical deduction to fill in the missing numbers, ensuring that each row, column, and block contains the numbers 1 through 5 exactly once.

##### Row 1:
- The number 5 is already in column 2.
- The top-middle block must contain the numbers 1, 2, 3, 4, and 5.
- Since 5 is already in column 2, the other cells in this block must be filled with 1, 2, 3, and 4.
- The top-right block must also contain the numbers 1, 2, 3, 4, and 5.
- Since 3 is already in row 2, column 4, the top-right block must have 1, 2, 4, and 5 in the remaining cells.

##### Row 2:
- The number 3 is already in column 4.
- The top-right block must contain 1, 2, 4, and 5.
- Since 5 is already in the top-middle block, it cannot be in the top-right block.
- Therefore, the top-right block must have 1, 2, 4, and 5 in the remaining cells.

##### Row 3:
- The numbers 5, 4, and 1 are already in this row.
- The middle-middle block must contain the numbers 1, 2, 3, 4, and 5.
- Since 4 is already in column 3, the middle-middle block must have 1, 2, 3, and 5 in the remaining cells.

##### Row 4:
- The number 5 is already in column 5.
- The middle-right block must contain the numbers 1, 2, 3, 4, and 5.
- Since 5 is already in column 5, the middle-right block must have 1, 2, 3, and 4 in the remaining cells.

##### Row 5:
- This row is currently empty.
- The bottom-left block must contain the numbers 1, 2, 3, 4, and 5.
- The bottom-middle block must also contain the numbers 1, 2, 3, 4, and 5.

#### Step 3: Logical Deduction
Using the above constraints, we can start filling in the grid step by step. Here is the completed grid:

```
+---+---+---+---+---+
| 2 | 5 | 1 | 4 | 3 |
+---+---+---+---+---+
| 4 | 1 | 2 | 3 | 5 |
+---+---+---+---+---+
| 5 | 3 | 4 | 2 | 1 |
+---+---+---+---+---+
| 3 | 2 | 5 | 1 | 4 |
+---+---+---+---+---+
| 1 | 4 | 3 | 5 | 2 |
+---+---+---+---+---+
```

Final Answer:

The completed 5x5 Jigsaw Sudoku grid is:

\[
\boxed{
\begin{array}{|c|c|c|c|c|}
\hline
2 & 5 & 1 & 4 & 3 \\
\hline
4 & 1 & 2 & 3 & 5 \\
\hline
5 & 3 & 4 & 2 & 1 \\
\hline
3 & 2 & 5 & 1 & 4 \\
\hline
1 & 4 & 3 & 5 & 2 \\
\hline
\end{array}
}
\]