Easy Sudoku puzzle for printable solving.

Let's solve this Sudoku puzzle step by step.

---

🔍 Understanding the Puzzle

This is a standard 9×9 Sudoku grid, with some numbers already filled in. The goal is to fill in the empty cells so that:

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

We'll label the rows from top to bottom as R1 to R9 and columns from left to right as C1 to C9.

---

🧩 Step-by-step Solution

We’ll go through logical deductions using single candidates, naked singles, and elimination techniques.

Here’s the initial grid:

```
R1: 3 _ 1 | 2 6 5 | _ _ _
R2: 8 _ 5 | _ _ _ | _ 7 _
R3: _ 9 7 | 2 1 3 | _ 8 _
------+-------+------
R4: 9 6 _ | 4 _ 8 | _ _ 4
R5: _ 2 3 | _ 9 _ | _ 8 _
R6: 2 _ _ | 8 5 _ | _ _ _
------+-------+------
R7: _ _ 7 | 1 _ _ | 4 6 _
R8: 1 _ 6 | _ 7 8 | _ _ 3
R9: _ _ _ | _ _ _ | _ _ _
```

We'll now proceed.

---

✔ Step 1: Look for easy placements

#### Box 1 (Top-left):
Cells:
```
3 _ 1
8 _ 5
_ 9 7
```

Missing numbers: 2, 4, 6

Check each cell:

- R1C2: Can't be 3,1,8,5,9,7 → possible: 2,4,6
- R2C2: Can't be 3,1,8,5,9,7 → same: 2,4,6
- R3C1: Can't be 3,1,8,5,9,7 → 2,4,6

Now look at Column 2: values are:
- R1C2: ?
- R2C2: ?
- R3C2: 9
- R4C2: 6
- R5C2: 2
- R6C2: ?
- R7C2: ?
- R8C2: ?
- R9C2: ?

So column 2 has: 9,6,2 → missing: 1,3,4,5,7,8

But in box 1, only 2,4,6 are missing. So R1C2, R2C2, R3C1 must be 2,4,6 in some order.

Wait — but R5C2 = 2, so 2 is already in column 2 → R1C2 and R2C2 cannot be 2.

So R1C2 and R2C2 ∈ {4,6}, and R3C1 ∈ {2,4,6}

But R3C1 can't be 4 or 6 if they're used in row or column?

Let’s check R3: `_, 9, 7, 2, 1, 3, _, 8, _` → missing: 4,5,6

So R3C1 ∈ {4,5,6}, but from box 1, it must be 2,4,6 → intersection: 4,6

But earlier we said R1C2 and R2C2 can’t be 2 → so they must be 4 and 6.

So R1C2 and R2C2 ∈ {4,6}

Now let’s look at R1: `3, _, 1, 2, 6, 5, _, _, _` → missing: 4,7,8,9

So R1C2 ∈ {4,7,8,9} → but from above, only 4 or 6 possible → so R1C2 = 4

Then R2C2 must be 6 (only remaining in {4,6})

And R3C1 must be 2 (since 4 and 6 taken)

✔ So far:
- R1C2 = 4
- R2C2 = 6
- R3C1 = 2

Update grid:

```
R1: 3 4 1 | 2 6 5 | _ _ _
R2: 8 6 5 | _ _ _ | _ 7 _
R3: 2 9 7 | 2 1 3 | _ 8 _ ← Wait! R3C4 = 2, but R3C1 = 2 → conflict!
```

Oh no! R3C1 = 2 and R3C4 = 2 → same row → not allowed!

Contradiction!

So our assumption must be wrong.

Where did we go wrong?

Ah! We assumed R1C2 = 4 because R5C2 = 2 → so R1C2 ≠ 2 → so R1C2 ∈ {4,6}

But then R2C2 must be the other of {4,6}

But R3C1 ∈ {2,4,6} from box 1

But R3C1 cannot be 2 because R3C4 = 2 → same row → invalid

So R3C1 ∈ {4,6}

But R1C2 and R2C2 also ∈ {4,6}

So all three cells: R1C2, R2C2, R3C1 must be 4 and 6 → only two numbers for three cells → impossible unless one repeats → but can't.

Wait — box 1 missing numbers: 2,4,6

But R3C1 can’t be 2 → so R3C1 ∈ {4,6}

R1C2 ∈ {4,6} (since 2 excluded due to column)

R2C2 ∈ {4,6} (same reason)

So three cells need to take 2,4,6 → but 2 can't go anywhere in box 1?

Is there a place for 2?

Let’s list all empty cells in box 1:

- R1C2
- R2C2
- R3C1

Can any of them be 2?

- R1C2: column 2 has R5C2=2 → so no, 2 already in column → R1C2 ≠ 2
- R2C2: same column → R2C2 ≠ 2
- R3C1: row 3 has R3C4=2 → so R3C1 ≠ 2

So no cell in box 1 can have 2 → but 2 is missing in box 1 → contradiction!

Wait — this means the puzzle is invalid? But that can't be.

Let me double-check.

Box 1:
```
R1: 3 _ 1
R2: 8 _ 5
R3: _ 9 7
```

Numbers present: 3,1,8,5,9,7 → missing: 2,4,6

Now check possibilities:

- R1C2: row 1 has 3,1,2,6,5 → missing: 4,7,8,9 → so R1C2 ∈ {4,7,8,9}
- Column 2: R1C2, R2C2, R3C2=9, R4C2=6, R5C2=2, R6C2=?, R7C2=?, R8C2=?, R9C2=?
→ So column 2 has: 9,6,2 → missing: 1,3,4,5,7,8
→ So R1C2 ∈ {4,7,8} (from row) ∩ {1,3,4,5,7,8} = {4,7,8}
- Also, box 1 requires 2,4,6 → so R1C2 must be 4 (only common possibility)

So R1C2 = 4

Then R2C2: row 2: 8,?,5,... → missing: 1,2,3,4,6,9
Column 2: has 4 (now), 9,6,2 → so missing: 1,3,5,7,8
→ R2C2 ∈ {1,3,5,7,8} ∩ {1,2,3,4,6,9} = {1,3}

But box 1 needs 2,4,6 → R2C2 must be 2,4,6 → but 2 and 4 are in column 2 already → R2C2 cannot be 2 or 4 → so R2C2 ∈ {6} (only possibility)

So R2C2 = 6

Then R3C1: row 3: ?,9,7,2,1,3,?,8,? → missing: 4,5,6
Column 1: R1C1=3, R2C1=8, R3C1=?, R4C1=9, R5C1=?, R6C1=2, R7C1=?, R8C1=1, R9C1=?
→ So column 1 has: 3,8,9,2,1 → missing: 4,5,6,7
→ R3C1 ∈ {4,5,6} ∩ {4,5,6} = {4,5,6}

Box 1 needs 2,4,6 → but 2 can't go in R3C1 (row 3 has R3C4=2) → so R3C1 ∈ {4,6}

Now, R1C2=4, R2C2=6 → so in box 1, 4 and 6 are used → so R3C1 must be 2 → but 2 is not available in row or column → contradiction again!

Wait — box 1 needs 2,4,6

- R1C2 = 4
- R2C2 = 6
- So only R3C1 can be 2

But R3C1 cannot be 2 because:
- Row 3 already has R3C4 = 2 → duplicate

So no cell in box 1 can hold 2 → impossible!

This suggests either the puzzle is unsolvable or I made an error.

Let me recheck the original image.

Original grid:

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

Look at R3C4 = 2 → yes

R3C1 → currently blank

But in box 1, we have:
- R1C1=3, R1C2=?, R1C3=1
- R2C1=8, R2C2=?, R2C3=5
- R3C1=?, R3C2=9, R3C3=7

So numbers in box 1: 3,1,8,5,9,7 → missing: 2,4,6

Now, where can 2 go?

- R1C2: column 2 has R5C2=2 → so can't be 2
- R2C2: same column → can't be 2
- R3C1: row 3 has R3C4=2 → can't be 2

So no cell in box 1 can have 2 → contradiction

Therefore, the puzzle is invalid?

But that can't be — maybe I misread the puzzle.

Wait — let's check R3C4 → is it 2?

Yes: R3: `_ 9 7 | 2 1 3 | _ 8 _` → so R3C4 = 2

And R5C2 = 2 → yes

So both are in different rows and columns, but the issue is that 2 appears in both row 3 and column 2, which is fine, but in box 1, we need a 2, but no cell can accept it.

So this puzzle has no solution?

But that seems unlikely.

Wait — perhaps I misread the grid.

Let me recheck the original image.

You said: "I uploaded an image with a task"

But since I can't see images, I rely on your text.

You wrote:

```
3 1 2 6 5
8 5 7
9 6 4 2 1 3
9 8 4
2 3 8 5
2 7 1 4 6
1 6 7 8 3
```

Wait — you may have formatted it incorrectly.

Let me reconstruct the grid properly.

From your text:

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

Yes, that matches.

Now, let's look at R3C4 = 2 — correct

But wait — is R3C4 in box 1? No!

Box 1 is top-left: R1-3, C1-3

R3C4 is in box 2 (middle-top)

So 2 in R3C4 is not in box 1 — so no problem!

My mistake!

Box 1 is only C1-3, R1-3

R3C4 is in C4, so outside box 1.

So R3C1 can be 2 — no conflict with R3C4, because they are in different columns.

R3C1 and R3C4 are in the same row, but different columns — so they can't both be 2.

But R3C4 = 2 → so R3C1 ≠ 2 → yes, that's still true.

But R3C1 is in row 3, which has R3C4 = 2 → so R3C1 ≠ 2

So R3C1 ∈ {4,6} (from box 1)

Similarly, R1C2: column 2 has R5C2 = 2 → so R1C2 ≠ 2

R2C2: same column → ≠ 2

So in box 1, the three empty cells: R1C2, R2C2, R3C1

All must be 2,4,6

But 2 cannot go in any of them:

- R1C2: column 2 has 2 → no
- R2C2: column 2 has 2 → no
- R3C1: row 3 has 2 → no

So 2 cannot be placed in box 1 → contradiction

But box 1 has no 2 → so must have one

So the only way is if 2 is already in box 1?

Let’s list all numbers in box 1:

- R1: 3, ?, 1
- R2: 8, ?, 5
- R3: ?, 9, 7

So values: 3,1,8,5,9,7 → missing: 2,4,6

No 2 present.

But no cell can accept 2:

- R1C2: column 2 has R5C2 = 2 → so can't have 2
- R2C2: same column → can't have 2
- R3C1: row 3 has R3C4 = 2 → can't have 2

So indeed, no cell in box 1 can contain 2 → impossible

Therefore, the puzzle is invalid — no solution exists.

But that can't be right. Let's double-check the given numbers.

Perhaps I misread the grid.

Let me write it clearly with positions:

```
Row 1: 3 _ 1 | 2 6 5 | _ _ _
Row 2: 8 _ 5 | _ _ _ | _ 7 _
Row 3: _ 9 7 | 2 1 3 | _ 8 _
Row 4: 9 6 _ | 4 _ 8 | _ _ 4
Row 5: _ 2 3 | _ 9 _ | _ 8 _
Row 6: 2 _ _ | 8 5 _ | _ _ _
Row 7: _ _ 7 | 1 _ _ | 4 6 _
Row 8: 1 _ 6 | _ 7 8 | _ _ 3
Row 9: _ _ _ | _ _ _ | _ _ _
```

Now, is there a 2 in column 2?

- R1C2: ?
- R2C2: ?
- R3C2: 9
- R4C2: 6
- R5C2: 2 → yes
- R6C2: ?
- R7C2: ?
- R8C2: ?
- R9C2: ?

So column 2 has a 2 at R5C2 → so no other cell in column 2 can have 2.

So R1C2 ≠ 2, R2C2 ≠ 2

Row 3 has R3C4 = 2 → so R3C1 ≠ 2

So no cell in box 1 can have 2 → but box 1 is missing 2 → contradiction

Therefore, the puzzle is unsolvable as given.

But wait — could the number in R5C2 be something else?

R5C2 is in row 5: `_ 2 3 | _ 9 _ | _ 8 _` → so it is 2

Yes.

Unless there's a typo in the puzzle.

Perhaps the number in R3C4 is not 2?

R3: `_ 9 7 | 2 1 3 | _ 8 _` → yes, R3C4 = 2

So it seems the puzzle has a conflict.

Alternatively, maybe I should try to solve it anyway and see.

But logically, it's impossible.

Unless...

Wait — is it possible that R3C4 is not in the same row as R3C1? No, it is.

So row 3 has R3C4 = 2, so R3C1 cannot be 2.

So no cell in box 1 can have 2.

But box 1 has no 2, and no place to put it.

So the puzzle is invalid.

But let's check online or see if it's a known puzzle.

Alternatively, maybe the number in R5C2 is not 2.

But in your text: "2 3" in R5, second cell is 2.

Yes.

Perhaps the number in R3C4 is not 2.

But it is written as "2 1 3" in the middle section.

Yes.

So unless there's a typo in the puzzle, it's unsolvable.

But since you said "solve the problem", likely there's a typo.

Let me assume that R5C2 is not 2, but something else.

But in your input, it's clearly "2".

Wait — perhaps the number in R3C4 is not 2.

Let me re-read your input:

> 9 6 4 2 1 3

That's R4: 9 6 _ | 4 _ 8 | _ _ 4

R3: _ 9 7 | 2 1 3 | _ 8 _

Yes, R3C4 = 2

So it's correct.

Therefore, the puzzle has a contradiction.

But let's try to continue anyway.

Maybe I can try to fill in other parts.

Let’s look at box 4 (middle-left): R4-6, C1-3

```
9 6 _
_ 2 3
2 _ _
```

So numbers: 9,6,2,3,2 → wait, two 2s? R5C1 and R6C1 both have 2?

R5C1 = ? , R6C1 = 2

R4C1 = 9, R4C2 = 6, R4C3 = ?

R5C1 = ?, R5C2 = 2, R5C3 = 3

R6C1 = 2, R6C2 = ?, R6C3 = ?

So R6C1 = 2

But R5C2 = 2 — different cells, ok.

In box 4, we have:
- R4: 9,6,?
- R5: ?,2,3
- R6: 2,?,?

Numbers present: 9,6,2,3,2 → duplicate 2? No, R6C1 = 2, R5C2 = 2 — different cells, but in the same box? Yes, both in box 4.

R5C2 is in C2, which is in box 4? Box 4 is C1-3, R4-6 → yes.

So R5C2 = 2, R6C1 = 2 → both in box 4 → same box → duplicate 2 → invalid!

Oh! Here's the real problem!

R5C2 = 2, and R6C1 = 2, and both are in box 4 (middle-left) → so two 2s in the same box → invalid!

So the puzzle has a duplicate 2 in box 4.

But is that true?

R5C2 = 2 → yes

R6C1 = 2 → yes

Are they in the same box?

Box 4: R4-6, C1-3

- R5C2: row 5, col 2 → yes
- R6C1: row 6, col 1 → yes

So both in box 4 → so two 2s in the same box → violates Sudoku rules.

Therefore, the puzzle is invalid — it has a duplicate number in a box.

So it cannot be solved.

But perhaps you meant something else.

Maybe the number in R6C1 is not 2?

But in your text: "2 _ _ | 8 5 _ | _ _ _" → so R6C1 = 2

Yes.

Or perhaps R5C2 is not 2.

But " _ 2 3 " in row 5 → so R5C2 = 2

So both are 2, in the same box.

So the puzzle is unsolvable due to a duplicate.

Therefore, there is no valid solution.

But since you asked to solve it, likely there's a typo.

Common typo: perhaps R6C1 is not 2, but another number.

Or R5C2 is not 2.

But based on what you provided, it's invalid.

✔ Final Answer:

The Sudoku puzzle as given contains a duplicate number '2' in box 4 (cells R5C2 and R6C1), which violates Sudoku rules. Additionally, the number '2' cannot be placed in box 1 due to constraints from row and column conflicts. Therefore, the puzzle has no valid solution.

Please verify the puzzle for typos, especially in row 5 and row 6.

If you can provide a corrected version, I'd be happy to solve it!