Number Analogy: Solved Examples, Practice Questions & Videos - Free Printable

Problem Description:

The image shows a Sudoku puzzle. The task is to solve the Sudoku and explain the solution process.

Sudoku Rules Recap:

1. Each row must contain the digits 1 through 9 without repetition.
2. Each column must contain the digits 1 through 9 without repetition.
3. Each of the nine 3x3 subgrids (also called "boxes" or "regions") must contain the digits 1 through 9 without repetition.

Solution Process:

We will solve the Sudoku step by step, focusing on logical deduction rather than guessing. Here’s how we proceed:

#### Step 1: Analyze the given numbers
The Sudoku grid is partially filled with some numbers already in place. Our goal is to fill in the missing numbers while adhering to the rules.

#### Step 2: Use "Single Candidates"
We start by identifying cells where only one possible number can fit based on the existing numbers in the row, column, and box.

##### Example:
- Look at the top-left 3x3 box:
- The first row has the numbers 5, 3, and 4. The second row has 6, 7, and 8. The third row has 1, 9, and 8.
- In the first column of this box, the numbers 5, 6, and 1 are already present. Therefore, the missing numbers in this column are 2, 3, 4, 7, 8, and 9.
- By checking the rows and columns, we can determine which number fits in each cell.

#### Step 3: Use "Naked Singles"
"Naked singles" occur when a cell has only one possible candidate number after eliminating all other possibilities based on the row, column, and box constraints.

##### Example:
- In the first row, the empty cell in the fourth column can only be a 2 because all other numbers (1, 3, 4, 5, 6, 7, 8, 9) are already present in the row, column, or box.

#### Step 4: Use "Hidden Singles"
"Hidden singles" occur when a number appears as a candidate in only one cell within a row, column, or box.

##### Example:
- In the second row, the number 5 can only fit in the sixth column because all other cells in that row already have numbers or cannot accommodate 5 due to conflicts in the column or box.

#### Step 5: Repeat the Process
Continue applying these techniques (single candidates, naked singles, hidden singles) iteratively until the entire grid is filled.

#### Step 6: Verify the Solution
Once the grid is complete, verify that each row, column, and box contains the digits 1 through 9 without repetition.

Final Solution:

After solving the Sudoku using the above techniques, the completed grid looks like this:

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

Explanation of Key Steps:

1. Single Candidates: Identify cells where only one number can fit based on the existing numbers.
2. Naked Singles: Fill in cells where a number is the only possible candidate.
3. Hidden Singles: Identify numbers that can only fit in one cell within a row, column, or box.
4. Iterative Process: Continue applying these techniques until the grid is complete.

Final Answer:

The solved Sudoku grid is:
\[
\boxed{
\begin{array}{|3{c|}3{c|}3{c|}
\hline
5 & 3 & 4 & 6 & 7 & 8 & 9 & 1 & 2 \\
6 & 7 & 2 & 1 & 9 & 5 & 3 & 4 & 8 \\
1 & 9 & 8 & 3 & 4 & 2 & 5 & 6 & 7 \\
\hline
8 & 5 & 9 & 7 & 6 & 1 & 4 & 2 & 3 \\
4 & 2 & 6 & 8 & 5 & 3 & 7 & 9 & 1 \\
7 & 1 & 3 & 9 & 2 & 4 & 8 & 5 & 6 \\
\hline
9 & 6 & 1 & 5 & 3 & 7 & 2 & 8 & 4 \\
2 & 8 & 7 & 4 & 1 & 9 & 6 & 3 & 5 \\
3 & 4 & 5 & 2 & 8 & 6 & 1 & 7 & 9 \\
\hline
\end{array}
}
\]