Sudoku Puzzle | Education World - Free Printable

Let's solve Puzzle #1, which is a 9×9 Sudoku puzzle. The goal of Sudoku is to fill the grid so that:

- Each row contains digits 1 through 9 with no repetition.
- Each column contains digits 1 through 9 with no repetition.
- Each of the nine 3×3 subgrids (also called "boxes") contains digits 1 through 9 with no repetition.

---

Step 1: Understand the Given Grid

Here is the initial puzzle:

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

We need to check if this is already a valid completed Sudoku, or if there are missing numbers.

But wait — looking closely, every cell appears to be filled. Let’s verify whether this is a valid Sudoku solution.

---

Step 2: Validate Rows

Check each row for digits 1–9, no duplicates.

- Row 1: 2,3,4,9,5,6,8,1,7 → all unique ✔
- Row 2: 9,5,7,8,1,4,2,6,3 → all unique ✔
- Row 3: 1,8,6,3,7,2,4,5,9 → all unique ✔
- Row 4: 5,4,9,6,8,1,7,3,2 → all unique ✔
- Row 5: 6,1,8,7,2,3,5,9,4 → all unique ✔
- Row 6: 7,2,3,4,9,5,6,8,1 → all unique ✔
- Row 7: 3,9,2,5,6,7,1,4,8 → all unique ✔
- Row 8: 4,7,5,1,3,8,9,2,6 → all unique ✔
- Row 9: 8,6,1,2,4,9,3,7,5 → all unique ✔

✔ All rows are valid.

---

Step 3: Validate Columns

Check each column:

- Col 1: 2,9,1,5,6,7,3,4,8 → 2,9,1,5,6,7,3,4,8 → all unique ✔
- Col 2: 3,5,8,4,1,2,9,7,6 → 3,5,8,4,1,2,9,7,6 → all unique ✔
- Col 3: 4,7,6,9,8,3,2,5,1 → 4,7,6,9,8,3,2,5,1 → all unique ✔
- Col 4: 9,8,3,6,7,4,5,1,2 → 9,8,3,6,7,4,5,1,2 → all unique ✔
- Col 5: 5,1,7,8,2,9,6,3,4 → 5,1,7,8,2,9,6,3,4 → all unique ✔
- Col 6: 6,4,2,1,3,5,7,8,9 → 6,4,2,1,3,5,7,8,9 → all unique ✔
- Col 7: 8,2,4,7,5,6,1,9,3 → 8,2,4,7,5,6,1,9,3 → all unique ✔
- Col 8: 1,6,5,3,9,8,4,2,7 → 1,6,5,3,9,8,4,2,7 → all unique ✔
- Col 9: 7,3,9,2,4,1,8,6,5 → 7,3,9,2,4,1,8,6,5 → all unique ✔

✔ All columns are valid.

---

Step 4: Validate 3×3 Boxes

Now check each 3×3 box:

#### Box 1 (Top-left): Rows 1–3, Cols 1–3
```
2 3 4
9 5 7
1 8 6
```
Digits: 2,3,4,9,5,7,1,8,6 → all unique ✔

#### Box 2 (Top-middle): Rows 1–3, Cols 4–6
```
9 5 6
8 1 4
3 7 2
```
Digits: 9,5,6,8,1,4,3,7,2 → all unique ✔

#### Box 3 (Top-right): Rows 1–3, Cols 7–9
```
8 1 7
2 6 3
4 5 9
```
Digits: 8,1,7,2,6,3,4,5,9 → all unique ✔

#### Box 4 (Middle-left): Rows 4–6, Cols 1–3
```
5 4 9
6 1 8
7 2 3
```
Digits: 5,4,9,6,1,8,7,2,3 → all unique ✔

#### Box 5 (Center): Rows 4–6, Cols 4–6
```
6 8 1
7 2 3
4 9 5
```
Digits: 6,8,1,7,2,3,4,9,5 → all unique ✔

#### Box 6 (Middle-right): Rows 4–6, Cols 7–9
```
7 3 2
5 9 4
6 8 1
```
Digits: 7,3,2,5,9,4,6,8,1 → all unique ✔

#### Box 7 (Bottom-left): Rows 7–9, Cols 1–3
```
3 9 2
4 7 5
8 6 1
```
Digits: 3,9,2,4,7,5,8,6,1 → all unique ✔

#### Box 8 (Bottom-middle): Rows 7–9, Cols 4–6
```
5 6 7
1 3 8
2 4 9
```
Digits: 5,6,7,1,3,8,2,4,9 → all unique ✔

#### Box 9 (Bottom-right): Rows 7–9, Cols 7–9
```
1 4 8
9 2 6
3 7 5
```
Digits: 1,4,8,9,2,6,3,7,5 → all unique ✔

✔ All boxes are valid.

---

✔ Conclusion

The given puzzle is already a complete and valid Sudoku solution. There are no empty cells, and all rules are satisfied.

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Final Answer:

✔ The Sudoku puzzle is correctly solved. No changes needed.

It is a valid Sudoku solution.