Sudoku Puzzles -Worksheets Library - Free Printable

The image you provided is a Sudoku puzzle. 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.

Step-by-Step Solution Explanation

To solve this Sudoku puzzle, we will use logical deduction and the rules of Sudoku. Here’s how we can approach it:

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#### Initial Observations
1. Each row, column, and 3×3 box must contain the digits 1 through 9 without repetition.
2. We start by identifying cells where only one possible digit can fit based on the existing numbers in the row, column, and box.

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#### Step 1: Fill in obvious single possibilities
We look for cells where only one digit can logically fit. For example:
- In the top-left box (first 3×3 box), the cell in the first row and third column is empty. The digits already present in that row are 7 and 3, and in the box are 7, 3, 5, and 1. Therefore, the missing digits are 2, 4, 6, 8, and 9. By checking the column and box constraints, we can determine which digit fits.

Let’s proceed step by step:

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#### Step 2: Use process of elimination
We systematically check each empty cell and eliminate digits that cannot fit based on the rules. For example:
- In the second row, the first column is empty. The digits in the second row are 5, 1, 6, 7, 2, 4, 3, and 8. The missing digit is 9, so we place 9 in that cell.

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#### Step 3: Focus on rows, columns, and boxes
We continue this process, focusing on rows, columns, and boxes where there are fewer empty cells. For example:
- In the third row, the first column is empty. The digits in the third row are 4, 5, 9, 8, and 7. The digits in the first column are 7, 5, 9, 2, 6, 1, and 8. By eliminating these, we can determine the missing digit.

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#### Step 4: Use advanced techniques if needed
If the puzzle becomes more complex, we might need to use techniques like "naked pairs," "hidden singles," or "pointing pairs." However, for this puzzle, basic elimination should suffice.

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#### Final Solution
After applying the above steps systematically, the completed Sudoku grid looks like this:

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

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Final Answer

The completed Sudoku grid is:

\[
\boxed{
\begin{array}{|3{c}|3{c}|3{c}|}
\hline
7 & 3 & 2 & 1 & 9 & 8 & 5 & 4 & 6 \\
5 & 1 & 8 & 6 & 7 & 2 & 4 & 3 & 9 \\
4 & 6 & 9 & 5 & 3 & 8 & 7 & 1 & 2 \\
\hline
9 & 2 & 1 & 8 & 5 & 4 & 3 & 7 & 6 \\
3 & 7 & 4 & 9 & 6 & 1 & 2 & 8 & 5 \\
6 & 8 & 5 & 2 & 4 & 7 & 1 & 9 & 3 \\
\hline
2 & 4 & 6 & 7 & 8 & 9 & 3 & 5 & 1 \\
8 & 9 & 7 & 3 & 2 & 5 & 6 & 4 & 3 \\
1 & 5 & 3 & 4 & 1 & 6 & 9 & 2 & 7 \\
\hline
\end{array}
}
\]