100 Free Printable Sudoku Puzzles - Free Printable
Educational worksheet: 100 Free Printable Sudoku Puzzles. Download and print for classroom or home learning activities.
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Step-by-step solution for: 100 Free Printable Sudoku Puzzles
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Show Answer Key & Explanations
Step-by-step solution for: 100 Free Printable Sudoku Puzzles
It looks like you've uploaded a Sudoku puzzle. Let's solve it step by step and explain the logic.
Here is the given Sudoku grid:
```
+-------+-------+-------+
| 9 6 | 4 | 3 |
| 5 7 8 | 2 | |
| 1 9 | 5 | |
+-------+-------+-------+
| 9 | 1 | 8 |
| 5 | 9 | 6 2 |
| 4 | 9 6 | 1 |
+-------+-------+-------+
| 4 | 3 | 1 |
| 7 | 9 2 6 | 5 |
| 2 | 5 9 8 | |
+-------+-------+-------+
```
We will solve this using standard Sudoku rules: each row, column, and 3x3 box must contain digits 1–9 with no repetition.
Let’s denote empty cells as `0` for clarity and fill in step by step.
---
We'll go through the grid and look for cells where only one number can fit.
#### Box 1 (Top-left 3x3):
```
9 6 ?
5 7 8
1 ? 9
```
Missing numbers in this box: 2, 3, 4
- Row 1: 9,6,? → needs 1,2,3,4,5,7,8 → but box already has 9,6,5,7,8,1,9 → missing 2,3,4
- Column 3: ?,8,9 → so far has 8,9 → possible: 1,2,3,4,5,6,7
- But in cell (1,3): cannot be 6 (same row), 5 (same col), 8,9 (same box) → possible: 1,2,3,4,7
But box needs 2,3,4 — so (1,3) ∈ {2,3,4}
But let's check other constraints.
Wait — actually, let's label rows and columns properly.
Let me write the full grid with positions:
```
Row 1: 9 6 _ | 4 _ _ | _ _ 3
Row 2: 5 7 8 | 2 _ _ | _ _ _
Row 3: 1 _ 9 | _ _ 5 | _ _ _
-----------------------------
Row 4: _ 9 _ | 1 _ _ | _ 8 _
Row 5: 5 _ _ | _ _ 9 | 6 _ 2
Row 6: 4 _ _ | 9 _ 6 | _ _ 1
-----------------------------
Row 7: _ _ 4 | _ _ 3 | _ _ 1
Row 8: _ _ 7 | 9 2 6 | _ _ 5
Row 9: _ 2 _ | 5 9 8 | _ _ _
```
Now let's solve systematically.
---
Row 1: 9,6,?,4,?,?,?,?3
So missing: 1,2,5,7,8
Column 3: ?,8,9,?,9,6,4,7,?
So values in col 3: 8,9,9,6,4,7 → wait, duplicates? No, each column must have unique.
List column 3:
- (1,3): ?
- (2,3): 8
- (3,3): 9
- (4,3): ?
- (5,3): ?
- (6,3): 6
- (7,3): 4
- (8,3): 7
- (9,3): ?
So column 3 has: 8,9,6,4,7 → missing: 1,2,3,5
Box 1 (top-left): contains (1,1)=9, (1,2)=6, (2,1)=5, (2,2)=7, (2,3)=8, (3,1)=1, (3,3)=9
So box 1 has: 9,6,5,7,8,1,9 → duplicates? (3,3)=9 and (1,1)=9 — okay, same box.
Numbers present: 1,5,6,7,8,9 → missing: 2,3,4
So (1,3) must be in {2,3,4} (from box), and also from row and column.
From row 1: missing 1,2,5,7,8 → but 1,5,7,8 not in {2,3,4}, so (1,3) ∈ {2,3,4}
From column 3: missing 1,2,3,5 → so (1,3) ∈ {2,3}
So (1,3) ∈ {2,3}
But box 1 needs 2,3,4 — so if (1,3) is 2 or 3, then 4 must be placed somewhere else in box 1.
Now look at (1,3): can it be 2?
Try to find better candidates.
Look at cell (1,8) — that’s the last cell in row 1.
Row 1: 9,6,?,4,?,?,?,?3 → so missing: 1,2,5,7,8
But we don't know much yet.
Let’s try another approach.
---
So missing: 2,3,4,6,7,8
But let’s look at column 2:
Col 2:
- (1,2): 6
- (2,2): 7
- (3,2): ?
- (4,2): 9
- (5,2): ?
- (6,2): ?
- (7,2): ?
- (8,2): ?
- (9,2): 2
So col 2 has: 6,7,9,2 → missing: 1,3,4,5,8
(3,2) is in row 3 and box 1.
Box 1 has: 9,6,5,7,8,1,9 → missing: 2,3,4
So (3,2) ∈ {2,3,4}
Also, row 3: missing 2,3,4,6,7,8 → so (3,2) ∈ {2,3,4}
And col 2: missing 1,3,4,5,8 → so (3,2) ∈ {3,4}
So (3,2) ∈ {3,4}
Now look at cell (3,5) — middle of row 3.
Row 3: 1,?,9,?,?,5,?,?,?
So missing: 2,3,4,6,7,8
Col 5: ?,?,? (row1-3), ?,?,? (row4-6), ?,2,9
Col 5:
- (1,5): ?
- (2,5): ?
- (3,5): ?
- (4,5): ?
- (5,5): ?
- (6,5): ?
- (7,5): ?
- (8,5): 2
- (9,5): 9
So col 5 missing: 1,3,4,5,6,7,8
Box 2 (middle top): (1,4)=4, (1,5)=?, (1,6)=?, (2,4)=2, (2,5)=?, (2,6)=?, (3,4)=?, (3,5)=?, (3,6)=5
Box 2 has: 4,2,5 → missing: 1,3,6,7,8,9
So (3,5) ∈ {1,3,6,7,8,9} but row 3 missing: 2,3,4,6,7,8 → so (3,5) ∈ {3,6,7,8}
And col 5 missing: 1,3,4,5,6,7,8 → so (3,5) ∈ {3,6,7,8}
So still broad.
Let’s look at box 4 (middle left): rows 4-6, cols 1-3
Box 4:
- (4,1): ?
- (4,2): 9
- (4,3): ?
- (5,1): 5
- (5,2): ?
- (5,3): ?
- (6,1): 4
- (6,2): ?
- (6,3): 6
So numbers present: 9,5,4,6 → missing: 1,2,3,7,8
Also, row 4: ?,9,?,1,?,?,?,8,? → so missing: 2,3,4,5,6,7
But (4,1) ∈ {1,2,3,7,8} from box
But col 1:
- (1,1): 9
- (2,1): 5
- (3,1): 1
- (4,1): ?
- (5,1): 5 → duplicate! Wait — (2,1)=5, (5,1)=5 — same column!
Oh! That’s a problem.
Wait: (2,1)=5, (5,1)=5 — both in col 1 → conflict?
No — (5,1)=5, (2,1)=5 → same column, two 5s? That violates Sudoku.
Wait — did I misread?
Let me recheck the original:
Row 2: 5 7 8 | 2 ... → so (2,1)=5
Row 5: 5 ... | ... 9 | 6 ... 2 → so (5,1)=5
Yes — both (2,1) and (5,1) are 5 → same column → invalid?
But that can’t be — maybe I made a mistake.
Wait — is that possible?
Let me double-check the original image.
You said:
```
9 6 | 4 | 3
5 7 8 | 2 |
1 9 | 5 |
------+-------+------
9 | 1 | 8
5 | 9 | 6 2
4 | 9 6 | 1
------+-------+------
4 | 3 | 1
7 | 9 2 6 | 5
2 | 5 9 8 |
```
So:
- Row 2: 5,7,8,2,... → (2,1)=5
- Row 5: 5, ?, ?, ?, ?, 9, 6, ?, 2 → (5,1)=5
Yes — both (2,1) and (5,1) are 5 → same column → impossible.
But that means the puzzle is invalid?
Wait — unless I misread the layout.
Let me count the cells.
Each row has 9 cells.
Let me write it clearly with positions.
Assume the grid is:
Row 1: 9 6 _ | 4 _ _ | _ _ 3
Row 2: 5 7 8 | 2 _ _ | _ _ _
Row 3: 1 _ 9 | _ _ 5 | _ _ _
Row 4: _ 9 _ | 1 _ _ | _ 8 _
Row 5: 5 _ _ | _ _ 9 | 6 _ 2
Row 6: 4 _ _ | 9 _ 6 | _ _ 1
Row 7: _ _ 4 | _ _ 3 | _ _ 1
Row 8: _ _ 7 | 9 2 6 | _ _ 5
Row 9: _ 2 _ | 5 9 8 | _ _ _
Now check column 1:
- (1,1): 9
- (2,1): 5
- (3,1): 1
- (4,1): ?
- (5,1): 5 ← here!
- (6,1): 4
- (7,1): ?
- (8,1): ?
- (9,1): ?
So (2,1)=5 and (5,1)=5 — both in column 1 → duplicate 5 in column 1 → invalid
But that can't be right — probably I misread the puzzle.
Wait — look at row 5: "5 | 9 | 6 2"
So first three cells: 5, ?, ?, then next three: ?, ?, 9, then last three: 6, ?, 2
So (5,1)=5, yes.
Row 2: 5,7,8 → (2,1)=5
So both (2,1) and (5,1) are 5 → same column → impossible.
Unless the puzzle has a typo.
Alternatively, perhaps the vertical bars are not separating boxes correctly?
Let me see the original formatting:
```
+-------+-------+-------+
| 9 6 | 4 | 3 |
| 5 7 8 | 2 | |
| 1 9 | 5 | |
+-------+-------+-------+
| 9 | 1 | 8 |
| 5 | 9 | 6 2 |
| 4 | 9 6 | 1 |
+-------+-------+-------+
| 4 | 3 | 1 |
| 7 | 9 2 6 | 5 |
| 2 | 5 9 8 | |
+-------+-------+-------+
```
Ah! The issue might be that the spacing is off.
For example, in row 2: "| 5 7 8 | 2 | |" — so (2,1)=5, (2,2)=7, (2,3)=8
In row 5: "| 5 | 9 | 6 2 |" — so (5,1)=5, (5,2)=?, (5,3)=?, (5,4)=?, (5,5)=?, (5,6)=9, (5,7)=6, (5,8)=?, (5,9)=2
So (5,1)=5 — yes.
But (2,1)=5 — yes.
So both (2,1) and (5,1) are 5 — same column → invalid.
But that suggests the puzzle is unsolvable due to a mistake.
Wait — could it be that the second 5 is not in column 1?
Let me count carefully.
Row 5: "5 | 9 | 6 2"
The first group: "5 " — that's three cells: (5,1), (5,2), (5,3)
So (5,1)=5, (5,2)=?, (5,3)=?
Then next group: " 9" — (5,4)=?, (5,5)=?, (5,6)=9
Then "6 2" — (5,7)=6, (5,8)=?, (5,9)=2
So (5,1)=5 — correct.
Row 2: "5 7 8" — so (2,1)=5, (2,2)=7, (2,3)=8
So yes, both (2,1) and (5,1) are 5 → column 1 has two 5s → impossible.
Therefore, either the puzzle is invalid, or there's a typo.
But perhaps the first 5 in row 5 is not in column 1?
Wait — maybe the formatting is off.
Let me try to reconstruct the grid based on the visual structure.
Looking at the original:
```
+-------+-------+-------+
| 9 6 | 4 | 3 |
| 5 7 8 | 2 | |
| 1 9 | 5 | |
+-------+-------+-------+
| 9 | 1 | 8 |
| 5 | 9 | 6 2 |
| 4 | 9 6 | 1 |
+-------+-------+-------+
| 4 | 3 | 1 |
| 7 | 9 2 6 | 5 |
| 2 | 5 9 8 | |
+-------+-------+-------+
```
Let me parse each row:
Row 1: | 9 6 | 4 | 3 |
- First box: 9,6,?
- Second box: 4,?,?
- Third box: ?,?,3
So (1,1)=9, (1,2)=6, (1,3)=?, (1,4)=4, (1,5)=?, (1,6)=?, (1,7)=?, (1,8)=?, (1,9)=3
Row 2: | 5 7 8 | 2 | |
- (2,1)=5, (2,2)=7, (2,3)=8, (2,4)=2, (2,5)=?, (2,6)=?, (2,7)=?, (2,8)=?, (2,9)=?
Row 3: | 1 9 | 5 | |
- (3,1)=1, (3,2)=?, (3,3)=9, (3,4)=?, (3,5)=?, (3,6)=5, (3,7)=?, (3,8)=?, (3,9)=?
Row 4: | 9 | 1 | 8 |
- (4,1)=?, (4,2)=9, (4,3)=?, (4,4)=1, (4,5)=?, (4,6)=?, (4,7)=?, (4,8)=8, (4,9)=?
Row 5: | 5 | 9 | 6 2 |
- (5,1)=5, (5,2)=?, (5,3)=?, (5,4)=?, (5,5)=?, (5,6)=9, (5,7)=6, (5,8)=?, (5,9)=2
Row 6: | 4 | 9 6 | 1 |
- (6,1)=4, (6,2)=?, (6,3)=?, (6,4)=9, (6,5)=?, (6,6)=6, (6,7)=?, (6,8)=?, (6,9)=1
Row 7: | 4 | 3 | 1 |
- (7,1)=?, (7,2)=?, (7,3)=4, (7,4)=?, (7,5)=?, (7,6)=3, (7,7)=?, (7,8)=?, (7,9)=1
Row 8: | 7 | 9 2 6 | 5 |
- (8,1)=?, (8,2)=?, (8,3)=7, (8,4)=9, (8,5)=2, (8,6)=6, (8,7)=?, (8,8)=?, (8,9)=5
Row 9: | 2 | 5 9 8 | |
- (9,1)=?, (9,2)=2, (9,3)=?, (9,4)=5, (9,5)=9, (9,6)=8, (9,7)=?, (9,8)=?, (9,9)=?
Now check column 1:
- (1,1)=9
- (2,1)=5
- (3,1)=1
- (4,1)=?
- (5,1)=5 ← again 5
- (6,1)=4
- (7,1)=?
- (8,1)=?
- (9,1)=?
So (2,1)=5 and (5,1)=5 → both in column 1 → duplicate → invalid puzzle
Unless there's a typo.
Perhaps in row 5, the "5" is not in column 1?
But the format shows "| 5 | ..." — the first part is "5 " — which should be three cells: (5,1), (5,2), (5,3)
So (5,1)=5.
But (2,1)=5 — conflict.
So the puzzle as given has a mistake.
But maybe the user meant something else.
Wait — could it be that the second "5" in row 5 is not in column 1?
Let me read the line again: "| 5 | 9 | 6 2 |"
The first group is "5 " — five characters: '5', space, space, space, space — so likely (5,1)=5, (5,2)=?, (5,3)=?
Yes.
But perhaps the intended puzzle has a different number.
Maybe it's not 5, but another digit.
Or perhaps it's a different row.
Another possibility: maybe the first 5 in row 5 is not in column 1, but in column 2?
But the format suggests otherwise.
Alternatively, perhaps the user made a mistake in typing.
Given that, let's assume it's a typo, and (5,1) is not 5.
But it's written as "5 " — so likely it is 5.
Perhaps the second 5 is in a different position.
Wait — look at row 8: "| 7 | 9 2 6 | 5 |" — (8,3)=7
Row 9: "| 2 | 5 9 8 | |" — (9,2)=2
No other 5s in column 1 except (2,1) and (5,1).
So unless the puzzle is wrong, it's unsolvable.
But let's assume it's a typo, and (5,1) is not 5.
But that would be guessing.
Alternatively, perhaps the "5" in row 5 is not in column 1.
But the way it's written: "| 5 | ..." — the first cell is 5.
Unless the formatting is off.
Another idea: perhaps the "5" in row 5 is actually in column 2, and the first cell is blank.
But it's written as "5 " — which is one digit followed by spaces — so likely (5,1)=5.
Given the conflict, I suspect there's a typo in the puzzle.
Perhaps (2,1) is not 5.
But it's written as "5 7 8" — so (2,1)=5.
Alternatively, maybe (5,1) is not 5 — but the text says "5 " — so it is.
Unless the puzzle has a different interpretation.
Wait — perhaps the vertical bar after the first group is misplaced.
But the structure is consistent.
Another possibility: maybe the number in (5,1) is not 5, but the text has a typo.
For example, if (5,1) were 6 or something.
But without clarification, I can't proceed.
However, let's assume that (5,1) is not 5, but instead the puzzle has a different number.
But that's not fair.
Perhaps I miscalculated.
Let me list all values in column 1:
- (1,1): 9
- (2,1): 5
- (3,1): 1
- (4,1): ?
- (5,1): 5 — duplicate
- (6,1): 4
- (7,1): ?
- (8,1): ?
- (9,1): ?
So indeed, two 5s in column 1.
Therefore, the puzzle as given is invalid.
But since you asked to solve it, perhaps there's a mistake in my parsing.
Let me try to see if the "5" in row 5 is not in column 1.
Look at the line: "| 5 | 9 | 6 2 |"
The first box is "5 " — three cells: first is 5, second and third are blank.
So (5,1)=5.
Similarly, row 2: "5 7 8" — (2,1)=5.
So both are 5.
Thus, the puzzle has an error.
Perhaps the user meant (5,1) to be a different number, like 6 or 7.
But without knowing, I can't solve it.
Alternatively, maybe the first 5 in row 5 is not in column 1, but in column 2.
But the formatting doesn't suggest that.
Another possibility: perhaps the puzzle is not 9x9, but it is.
Given the information, I conclude that the puzzle has a duplicate 5 in column 1, making it unsolvable.
Please verify the puzzle and ensure that (5,1) is not 5, or (2,1) is not 5.
If you can confirm the correct values, I can help solve it.
Otherwise, the puzzle is invalid.
Final Answer: The puzzle contains a duplicate 5 in column 1 (at positions (2,1) and (5,1)), which violates Sudoku rules. Therefore, it is unsolvable as given. Please check the input for errors.
Here is the given Sudoku grid:
```
+-------+-------+-------+
| 9 6 | 4 | 3 |
| 5 7 8 | 2 | |
| 1 9 | 5 | |
+-------+-------+-------+
| 9 | 1 | 8 |
| 5 | 9 | 6 2 |
| 4 | 9 6 | 1 |
+-------+-------+-------+
| 4 | 3 | 1 |
| 7 | 9 2 6 | 5 |
| 2 | 5 9 8 | |
+-------+-------+-------+
```
We will solve this using standard Sudoku rules: each row, column, and 3x3 box must contain digits 1–9 with no repetition.
Let’s denote empty cells as `0` for clarity and fill in step by step.
---
Step 1: Fill in obvious numbers
We'll go through the grid and look for cells where only one number can fit.
#### Box 1 (Top-left 3x3):
```
9 6 ?
5 7 8
1 ? 9
```
Missing numbers in this box: 2, 3, 4
- Row 1: 9,6,? → needs 1,2,3,4,5,7,8 → but box already has 9,6,5,7,8,1,9 → missing 2,3,4
- Column 3: ?,8,9 → so far has 8,9 → possible: 1,2,3,4,5,6,7
- But in cell (1,3): cannot be 6 (same row), 5 (same col), 8,9 (same box) → possible: 1,2,3,4,7
But box needs 2,3,4 — so (1,3) ∈ {2,3,4}
But let's check other constraints.
Wait — actually, let's label rows and columns properly.
Let me write the full grid with positions:
```
Row 1: 9 6 _ | 4 _ _ | _ _ 3
Row 2: 5 7 8 | 2 _ _ | _ _ _
Row 3: 1 _ 9 | _ _ 5 | _ _ _
-----------------------------
Row 4: _ 9 _ | 1 _ _ | _ 8 _
Row 5: 5 _ _ | _ _ 9 | 6 _ 2
Row 6: 4 _ _ | 9 _ 6 | _ _ 1
-----------------------------
Row 7: _ _ 4 | _ _ 3 | _ _ 1
Row 8: _ _ 7 | 9 2 6 | _ _ 5
Row 9: _ 2 _ | 5 9 8 | _ _ _
```
Now let's solve systematically.
---
Step 1: Look at Cell (1,3)
Row 1: 9,6,?,4,?,?,?,?3
So missing: 1,2,5,7,8
Column 3: ?,8,9,?,9,6,4,7,?
So values in col 3: 8,9,9,6,4,7 → wait, duplicates? No, each column must have unique.
List column 3:
- (1,3): ?
- (2,3): 8
- (3,3): 9
- (4,3): ?
- (5,3): ?
- (6,3): 6
- (7,3): 4
- (8,3): 7
- (9,3): ?
So column 3 has: 8,9,6,4,7 → missing: 1,2,3,5
Box 1 (top-left): contains (1,1)=9, (1,2)=6, (2,1)=5, (2,2)=7, (2,3)=8, (3,1)=1, (3,3)=9
So box 1 has: 9,6,5,7,8,1,9 → duplicates? (3,3)=9 and (1,1)=9 — okay, same box.
Numbers present: 1,5,6,7,8,9 → missing: 2,3,4
So (1,3) must be in {2,3,4} (from box), and also from row and column.
From row 1: missing 1,2,5,7,8 → but 1,5,7,8 not in {2,3,4}, so (1,3) ∈ {2,3,4}
From column 3: missing 1,2,3,5 → so (1,3) ∈ {2,3}
So (1,3) ∈ {2,3}
But box 1 needs 2,3,4 — so if (1,3) is 2 or 3, then 4 must be placed somewhere else in box 1.
Now look at (1,3): can it be 2?
Try to find better candidates.
Look at cell (1,8) — that’s the last cell in row 1.
Row 1: 9,6,?,4,?,?,?,?3 → so missing: 1,2,5,7,8
But we don't know much yet.
Let’s try another approach.
---
Look at Row 3: 1 _ 9 | _ _ 5 | _ _ _
So missing: 2,3,4,6,7,8
But let’s look at column 2:
Col 2:
- (1,2): 6
- (2,2): 7
- (3,2): ?
- (4,2): 9
- (5,2): ?
- (6,2): ?
- (7,2): ?
- (8,2): ?
- (9,2): 2
So col 2 has: 6,7,9,2 → missing: 1,3,4,5,8
(3,2) is in row 3 and box 1.
Box 1 has: 9,6,5,7,8,1,9 → missing: 2,3,4
So (3,2) ∈ {2,3,4}
Also, row 3: missing 2,3,4,6,7,8 → so (3,2) ∈ {2,3,4}
And col 2: missing 1,3,4,5,8 → so (3,2) ∈ {3,4}
So (3,2) ∈ {3,4}
Now look at cell (3,5) — middle of row 3.
Row 3: 1,?,9,?,?,5,?,?,?
So missing: 2,3,4,6,7,8
Col 5: ?,?,? (row1-3), ?,?,? (row4-6), ?,2,9
Col 5:
- (1,5): ?
- (2,5): ?
- (3,5): ?
- (4,5): ?
- (5,5): ?
- (6,5): ?
- (7,5): ?
- (8,5): 2
- (9,5): 9
So col 5 missing: 1,3,4,5,6,7,8
Box 2 (middle top): (1,4)=4, (1,5)=?, (1,6)=?, (2,4)=2, (2,5)=?, (2,6)=?, (3,4)=?, (3,5)=?, (3,6)=5
Box 2 has: 4,2,5 → missing: 1,3,6,7,8,9
So (3,5) ∈ {1,3,6,7,8,9} but row 3 missing: 2,3,4,6,7,8 → so (3,5) ∈ {3,6,7,8}
And col 5 missing: 1,3,4,5,6,7,8 → so (3,5) ∈ {3,6,7,8}
So still broad.
Let’s look at box 4 (middle left): rows 4-6, cols 1-3
Box 4:
- (4,1): ?
- (4,2): 9
- (4,3): ?
- (5,1): 5
- (5,2): ?
- (5,3): ?
- (6,1): 4
- (6,2): ?
- (6,3): 6
So numbers present: 9,5,4,6 → missing: 1,2,3,7,8
Also, row 4: ?,9,?,1,?,?,?,8,? → so missing: 2,3,4,5,6,7
But (4,1) ∈ {1,2,3,7,8} from box
But col 1:
- (1,1): 9
- (2,1): 5
- (3,1): 1
- (4,1): ?
- (5,1): 5 → duplicate! Wait — (2,1)=5, (5,1)=5 — same column!
Oh! That’s a problem.
Wait: (2,1)=5, (5,1)=5 — both in col 1 → conflict?
No — (5,1)=5, (2,1)=5 → same column, two 5s? That violates Sudoku.
Wait — did I misread?
Let me recheck the original:
Row 2: 5 7 8 | 2 ... → so (2,1)=5
Row 5: 5 ... | ... 9 | 6 ... 2 → so (5,1)=5
Yes — both (2,1) and (5,1) are 5 → same column → invalid?
But that can’t be — maybe I made a mistake.
Wait — is that possible?
Let me double-check the original image.
You said:
```
9 6 | 4 | 3
5 7 8 | 2 |
1 9 | 5 |
------+-------+------
9 | 1 | 8
5 | 9 | 6 2
4 | 9 6 | 1
------+-------+------
4 | 3 | 1
7 | 9 2 6 | 5
2 | 5 9 8 |
```
So:
- Row 2: 5,7,8,2,... → (2,1)=5
- Row 5: 5, ?, ?, ?, ?, 9, 6, ?, 2 → (5,1)=5
Yes — both (2,1) and (5,1) are 5 → same column → impossible.
But that means the puzzle is invalid?
Wait — unless I misread the layout.
Let me count the cells.
Each row has 9 cells.
Let me write it clearly with positions.
Assume the grid is:
Row 1: 9 6 _ | 4 _ _ | _ _ 3
Row 2: 5 7 8 | 2 _ _ | _ _ _
Row 3: 1 _ 9 | _ _ 5 | _ _ _
Row 4: _ 9 _ | 1 _ _ | _ 8 _
Row 5: 5 _ _ | _ _ 9 | 6 _ 2
Row 6: 4 _ _ | 9 _ 6 | _ _ 1
Row 7: _ _ 4 | _ _ 3 | _ _ 1
Row 8: _ _ 7 | 9 2 6 | _ _ 5
Row 9: _ 2 _ | 5 9 8 | _ _ _
Now check column 1:
- (1,1): 9
- (2,1): 5
- (3,1): 1
- (4,1): ?
- (5,1): 5 ← here!
- (6,1): 4
- (7,1): ?
- (8,1): ?
- (9,1): ?
So (2,1)=5 and (5,1)=5 — both in column 1 → duplicate 5 in column 1 → invalid
But that can't be right — probably I misread the puzzle.
Wait — look at row 5: "5 | 9 | 6 2"
So first three cells: 5, ?, ?, then next three: ?, ?, 9, then last three: 6, ?, 2
So (5,1)=5, yes.
Row 2: 5,7,8 → (2,1)=5
So both (2,1) and (5,1) are 5 → same column → impossible.
Unless the puzzle has a typo.
Alternatively, perhaps the vertical bars are not separating boxes correctly?
Let me see the original formatting:
```
+-------+-------+-------+
| 9 6 | 4 | 3 |
| 5 7 8 | 2 | |
| 1 9 | 5 | |
+-------+-------+-------+
| 9 | 1 | 8 |
| 5 | 9 | 6 2 |
| 4 | 9 6 | 1 |
+-------+-------+-------+
| 4 | 3 | 1 |
| 7 | 9 2 6 | 5 |
| 2 | 5 9 8 | |
+-------+-------+-------+
```
Ah! The issue might be that the spacing is off.
For example, in row 2: "| 5 7 8 | 2 | |" — so (2,1)=5, (2,2)=7, (2,3)=8
In row 5: "| 5 | 9 | 6 2 |" — so (5,1)=5, (5,2)=?, (5,3)=?, (5,4)=?, (5,5)=?, (5,6)=9, (5,7)=6, (5,8)=?, (5,9)=2
So (5,1)=5 — yes.
But (2,1)=5 — yes.
So both (2,1) and (5,1) are 5 — same column → invalid.
But that suggests the puzzle is unsolvable due to a mistake.
Wait — could it be that the second 5 is not in column 1?
Let me count carefully.
Row 5: "5 | 9 | 6 2"
The first group: "5 " — that's three cells: (5,1), (5,2), (5,3)
So (5,1)=5, (5,2)=?, (5,3)=?
Then next group: " 9" — (5,4)=?, (5,5)=?, (5,6)=9
Then "6 2" — (5,7)=6, (5,8)=?, (5,9)=2
So (5,1)=5 — correct.
Row 2: "5 7 8" — so (2,1)=5, (2,2)=7, (2,3)=8
So yes, both (2,1) and (5,1) are 5 → column 1 has two 5s → impossible.
Therefore, either the puzzle is invalid, or there's a typo.
But perhaps the first 5 in row 5 is not in column 1?
Wait — maybe the formatting is off.
Let me try to reconstruct the grid based on the visual structure.
Looking at the original:
```
+-------+-------+-------+
| 9 6 | 4 | 3 |
| 5 7 8 | 2 | |
| 1 9 | 5 | |
+-------+-------+-------+
| 9 | 1 | 8 |
| 5 | 9 | 6 2 |
| 4 | 9 6 | 1 |
+-------+-------+-------+
| 4 | 3 | 1 |
| 7 | 9 2 6 | 5 |
| 2 | 5 9 8 | |
+-------+-------+-------+
```
Let me parse each row:
Row 1: | 9 6 | 4 | 3 |
- First box: 9,6,?
- Second box: 4,?,?
- Third box: ?,?,3
So (1,1)=9, (1,2)=6, (1,3)=?, (1,4)=4, (1,5)=?, (1,6)=?, (1,7)=?, (1,8)=?, (1,9)=3
Row 2: | 5 7 8 | 2 | |
- (2,1)=5, (2,2)=7, (2,3)=8, (2,4)=2, (2,5)=?, (2,6)=?, (2,7)=?, (2,8)=?, (2,9)=?
Row 3: | 1 9 | 5 | |
- (3,1)=1, (3,2)=?, (3,3)=9, (3,4)=?, (3,5)=?, (3,6)=5, (3,7)=?, (3,8)=?, (3,9)=?
Row 4: | 9 | 1 | 8 |
- (4,1)=?, (4,2)=9, (4,3)=?, (4,4)=1, (4,5)=?, (4,6)=?, (4,7)=?, (4,8)=8, (4,9)=?
Row 5: | 5 | 9 | 6 2 |
- (5,1)=5, (5,2)=?, (5,3)=?, (5,4)=?, (5,5)=?, (5,6)=9, (5,7)=6, (5,8)=?, (5,9)=2
Row 6: | 4 | 9 6 | 1 |
- (6,1)=4, (6,2)=?, (6,3)=?, (6,4)=9, (6,5)=?, (6,6)=6, (6,7)=?, (6,8)=?, (6,9)=1
Row 7: | 4 | 3 | 1 |
- (7,1)=?, (7,2)=?, (7,3)=4, (7,4)=?, (7,5)=?, (7,6)=3, (7,7)=?, (7,8)=?, (7,9)=1
Row 8: | 7 | 9 2 6 | 5 |
- (8,1)=?, (8,2)=?, (8,3)=7, (8,4)=9, (8,5)=2, (8,6)=6, (8,7)=?, (8,8)=?, (8,9)=5
Row 9: | 2 | 5 9 8 | |
- (9,1)=?, (9,2)=2, (9,3)=?, (9,4)=5, (9,5)=9, (9,6)=8, (9,7)=?, (9,8)=?, (9,9)=?
Now check column 1:
- (1,1)=9
- (2,1)=5
- (3,1)=1
- (4,1)=?
- (5,1)=5 ← again 5
- (6,1)=4
- (7,1)=?
- (8,1)=?
- (9,1)=?
So (2,1)=5 and (5,1)=5 → both in column 1 → duplicate → invalid puzzle
Unless there's a typo.
Perhaps in row 5, the "5" is not in column 1?
But the format shows "| 5 | ..." — the first part is "5 " — which should be three cells: (5,1), (5,2), (5,3)
So (5,1)=5.
But (2,1)=5 — conflict.
So the puzzle as given has a mistake.
But maybe the user meant something else.
Wait — could it be that the second "5" in row 5 is not in column 1?
Let me read the line again: "| 5 | 9 | 6 2 |"
The first group is "5 " — five characters: '5', space, space, space, space — so likely (5,1)=5, (5,2)=?, (5,3)=?
Yes.
But perhaps the intended puzzle has a different number.
Maybe it's not 5, but another digit.
Or perhaps it's a different row.
Another possibility: maybe the first 5 in row 5 is not in column 1, but in column 2?
But the format suggests otherwise.
Alternatively, perhaps the user made a mistake in typing.
Given that, let's assume it's a typo, and (5,1) is not 5.
But it's written as "5 " — so likely it is 5.
Perhaps the second 5 is in a different position.
Wait — look at row 8: "| 7 | 9 2 6 | 5 |" — (8,3)=7
Row 9: "| 2 | 5 9 8 | |" — (9,2)=2
No other 5s in column 1 except (2,1) and (5,1).
So unless the puzzle is wrong, it's unsolvable.
But let's assume it's a typo, and (5,1) is not 5.
But that would be guessing.
Alternatively, perhaps the "5" in row 5 is not in column 1.
But the way it's written: "| 5 | ..." — the first cell is 5.
Unless the formatting is off.
Another idea: perhaps the "5" in row 5 is actually in column 2, and the first cell is blank.
But it's written as "5 " — which is one digit followed by spaces — so likely (5,1)=5.
Given the conflict, I suspect there's a typo in the puzzle.
Perhaps (2,1) is not 5.
But it's written as "5 7 8" — so (2,1)=5.
Alternatively, maybe (5,1) is not 5 — but the text says "5 " — so it is.
Unless the puzzle has a different interpretation.
Wait — perhaps the vertical bar after the first group is misplaced.
But the structure is consistent.
Another possibility: maybe the number in (5,1) is not 5, but the text has a typo.
For example, if (5,1) were 6 or something.
But without clarification, I can't proceed.
However, let's assume that (5,1) is not 5, but instead the puzzle has a different number.
But that's not fair.
Perhaps I miscalculated.
Let me list all values in column 1:
- (1,1): 9
- (2,1): 5
- (3,1): 1
- (4,1): ?
- (5,1): 5 — duplicate
- (6,1): 4
- (7,1): ?
- (8,1): ?
- (9,1): ?
So indeed, two 5s in column 1.
Therefore, the puzzle as given is invalid.
But since you asked to solve it, perhaps there's a mistake in my parsing.
Let me try to see if the "5" in row 5 is not in column 1.
Look at the line: "| 5 | 9 | 6 2 |"
The first box is "5 " — three cells: first is 5, second and third are blank.
So (5,1)=5.
Similarly, row 2: "5 7 8" — (2,1)=5.
So both are 5.
Thus, the puzzle has an error.
Perhaps the user meant (5,1) to be a different number, like 6 or 7.
But without knowing, I can't solve it.
Alternatively, maybe the first 5 in row 5 is not in column 1, but in column 2.
But the formatting doesn't suggest that.
Another possibility: perhaps the puzzle is not 9x9, but it is.
Given the information, I conclude that the puzzle has a duplicate 5 in column 1, making it unsolvable.
Please verify the puzzle and ensure that (5,1) is not 5, or (2,1) is not 5.
If you can confirm the correct values, I can help solve it.
Otherwise, the puzzle is invalid.
Final Answer: The puzzle contains a duplicate 5 in column 1 (at positions (2,1) and (5,1)), which violates Sudoku rules. Therefore, it is unsolvable as given. Please check the input for errors.
Parent Tip: Review the logic above to help your child master the concept of printable sudoku hard 4 per page.