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It looks like you've uploaded four 4×4 grid puzzles, each labeled Puzzle 1 through Puzzle 4. These appear to be Sudoku-like logic puzzles, where the goal is typically to fill in the empty cells so that each row, each column, and each of the four 2×2 subgrids (also called "regions" or "boxes") contains the numbers 1 to 4 exactly once.
Let’s solve each puzzle step by step.
---
- Each row must contain numbers 1–4, no repeats.
- Each column must contain numbers 1–4, no repeats.
- Each 2×2 box (there are four of them) must contain numbers 1–4, no repeats.
We’ll go one by one.
---
## ✔ Puzzle 1
```
+-----+-----+
| 2 3 | 4 |
| 4 | 2 |
+-----+-----+
| 3 4 | 2 |
| 2 | 3 4 |
+-----+-----+
```
Let’s label rows R1 to R4 and columns C1 to C4.
We’ll start filling in what we can.
#### Box 1 (Top-left): R1C1, R1C2, R2C1, R2C2
Current:
- R1C1 = 2
- R1C2 = 3
- R2C1 = 4
- R2C2 = ?
So missing: 1
→ So R2C2 = 1
Update:
```
+-----+-----+
| 2 3 | 4 |
| 4 1 | 2 |
+-----+-----+
| 3 4 | 2 |
| 2 | 3 4 |
+-----+-----+
```
#### Box 2 (Top-right): R1C3, R1C4, R2C3, R2C4
Current:
- R1C3 = 4
- R1C4 = ?
- R2C3 = 2
- R2C4 = ?
Missing: 1, 3
Now look at Row 1: has 2,3,4 → missing 1 → so R1C4 = 1
Then R2C4 must be 3 (since 1 and 3 left, but 1 used in row)
So:
- R1C4 = 1
- R2C4 = 3
Update:
```
+-----+-----+
| 2 3 | 4 1 |
| 4 1 | 2 3 |
+-----+-----+
| 3 4 | 2 |
| 2 | 3 4 |
+-----+-----+
```
#### Box 3 (Bottom-left): R3C1, R3C2, R4C1, R4C2
Current:
- R3C1 = 3
- R3C2 = 4
- R4C1 = ?
- R4C2 = 2
Missing: 1, 4? Wait — numbers needed: 1, 2, 3, 4 → already have 3,4,2 → missing 1
So only missing number is 1 → R4C1 = 1
But R4C1 is also part of Column 1: current values:
- R1C1 = 2
- R2C1 = 4
- R3C1 = 3
- R4C1 = ?
So missing: 1 → yes, confirms R4C1 = 1
So R4C1 = 1
Now R4C2 = 2 → okay.
Now update:
```
+-----+-----+
| 2 3 | 4 1 |
| 4 1 | 2 3 |
+-----+-----+
| 3 4 | 2 |
| 1 2 | 3 4 |
+-----+-----+
```
Now Box 4 (Bottom-right): R3C3, R3C4, R4C3, R4C4
Current:
- R3C3 = ?
- R3C4 = 2
- R4C3 = 3
- R4C4 = 4
So missing: 1, 4? Wait: numbers: 1,2,3,4 → present: 2,3,4 → missing: 1 → so R3C3 = 1
Now check Row 3: R3 = [3,4,?,2] → missing 1 → so R3C3 = 1 → matches.
So R3C3 = 1
Now only missing is R3C4 → wait, R3C4 is already 2.
Wait — R3C3 is now 1, R3C4 is 2 → row 3: 3,4,1,2 → complete.
Now Column 3:
- R1C3 = 4
- R2C3 = 2
- R3C3 = 1
- R4C3 = 3 → all good.
Column 4:
- R1C4 = 1
- R2C4 = 3
- R3C4 = 2
- R4C4 = 4 → complete.
Now check Box 3 (bottom-left): R3C1=3, R3C2=4, R4C1=1, R4C2=2 → has 1,2,3,4 → good.
All boxes and rows/columns seem satisfied.
✔ Puzzle 1 Solved
Final grid:
```
+-----+-----+
| 2 3 | 4 1 |
| 4 1 | 2 3 |
+-----+-----+
| 3 4 | 1 2 |
| 1 2 | 3 4 |
+-----+-----+
```
---
## ✔ Puzzle 2
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
Let’s analyze.
Start with Box 1 (top-left): R1C1=?, R1C2=3, R2C1=1, R2C2=4
So values: ?,3,1,4 → missing 2 → so R1C1 = 2
Now Row 1: R1 = [2,3,?,1] → missing 4 → so R1C3 = 4
Now Box 2 (top-right): R1C3=4, R1C4=1, R2C3=3, R2C4=?
So values: 4,1,3,? → missing 2 → R2C4 = 2
Now Row 2: R2 = [1,4,3,2] → complete.
Now Column 4: R1C4=1, R2C4=2, R3C4=?, R4C4=4 → missing 3 → R3C4 = 3
Now Row 3: R3 = [1,4,3,3] → wait! Two 3s → conflict?
Wait: R3C1=1, R3C2=4, R3C3=3, R3C4=3 → two 3s → invalid!
But we just set R3C4=3, but R3C3=3 already.
So contradiction.
Wait — let's double-check.
Wait, original Puzzle 2:
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
So:
- R3C1 = 1
- R3C2 = 4
- R3C3 = 3
- R3C4 = ?
So R3 = [1,4,3,?] → missing 2 → so R3C4 = 2
Ah! I made a mistake earlier.
Column 4:
- R1C4 = 1
- R2C4 = ?
- R3C4 = 2
- R4C4 = 4
So missing: 3 → so R2C4 = 3
But earlier we had R2C4 = ? from Box 2.
Let’s restart carefully.
Box 1 (top-left): R1C1=?, R1C2=3, R2C1=1, R2C2=4 → missing 2 → R1C1 = 2
Row 1: R1 = [2,3,?,1] → missing 4 → R1C3 = 4
Box 2 (top-right): R1C3=4, R1C4=1, R2C3=3, R2C4=? → values: 4,1,3,? → missing 2 → R2C4 = 2
But now Row 2: R2 = [1,4,3,2] → valid.
Column 4: R1C4=1, R2C4=2, R3C4=?, R4C4=4 → missing 3 → R3C4 = 3
But Row 3: R3 = [1,4,3,3] → two 3s → invalid!
Contradiction.
Wait — R3C3 is given as 3, R3C4 = 3 → duplicate → impossible.
But R3C3 = 3 is given, R3C4 = ? → if R3C4 = 3, then duplicate.
But Column 4 needs 3 → so R3C4 must be 3 → contradiction.
So this puzzle seems unsolvable?
Wait — maybe I misread.
Let me recheck the original:
Puzzle 2:
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
So:
- R3C3 = 3
- R3C4 = ?
And Column 4: R1C4=1, R2C4=?, R3C4=?, R4C4=4
We need to place 2 and 3 in R2C4 and R3C4.
But Row 3: R3 = [1,4,3,?] → missing 2 → so R3C4 = 2
Then Column 4: R1C4=1, R2C4=?, R3C4=2, R4C4=4 → missing 3 → so R2C4 = 3
Now Row 2: R2 = [1,4,3,3] → wait! R2C3=3, R2C4=3 → duplicate!
Oh! R2C3 = 3 is given, so R2C4 cannot be 3.
Conflict.
So R2C4 cannot be 3, but must be 3 from column → contradiction.
Thus, no solution exists for Puzzle 2?
Wait — is there a typo?
Let’s list all constraints.
R2C3 = 3 (given), R2C4 = ? → so R2C4 ≠ 3
Column 4: R1C4=1, R2C4=?, R3C4=?, R4C4=4
Values needed: 2 and 3
But R2C4 ≠ 3 → so R2C4 = 2 → then R3C4 = 3
But Row 3: R3 = [1,4,3,3] → R3C3=3, R3C4=3 → duplicate → invalid.
No way out.
So Puzzle 2 has no valid solution.
But maybe I missed something.
Wait — is it possible that R3C3 is not 3?
Look again:
Puzzle 2:
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
Yes, R3C3 = 3 is given.
So unless the puzzle is invalid, it's unsolvable.
Alternatively, perhaps the regions are different?
Wait — maybe these aren't standard Sudoku? But they are 4x4 with 2x2 boxes.
Alternatively, maybe the rules are different?
But based on standard logic, Puzzle 2 is unsolvable due to contradiction.
Let’s move on and come back.
---
## ✔ Puzzle 3
```
+-----+-----+
| 1 | 3 4 |
| 4 | 1 |
+-----+-----+
| 3 2 | 1 |
| 1 | 2 3 |
+-----+-----+
```
Let’s solve.
Numbers: ?,1,4,? → missing 2,3
So R1C1 and R2C2 must be 2 and 3 in some order.
Now Row 1: R1 = [?,1,3,4] → missing 2 → so R1C1 = 2
Then R2C2 = 3 (from box 1)
Now R1 = [2,1,3,4] → complete.
R2 = [4,3,1,?] → missing 2 → R2C4 = 2
Now Box 2 (top-right): R1C3=3, R1C4=4, R2C3=1, R2C4=2 → all filled → good.
Now Column 4: R1C4=4, R2C4=2, R3C4=1, R4C4=3 → all good.
Now Row 3: R3 = [3,2,?,1] → missing 4 → R3C3 = 4
Now Box 3 (bottom-left): R3C1=3, R3C2=2, R4C1=1, R4C2=?
Numbers: 3,2,1,? → missing 4 → R4C2 = 4
Now Row 4: R4 = [1,4,2,3] → complete.
Now Box 4 (bottom-right): R3C3=4, R3C4=1, R4C3=2, R4C4=3 → all good.
Now check columns:
- C1: 2,4,3,1 → all good
- C2: 1,3,2,4 → good
- C3: 3,1,4,2 → good
- C4: 4,2,1,3 → good
All boxes:
- Box 1: 2,1,4,3 → good
- Box 2: 3,4,1,2 → good
- Box 3: 3,2,1,4 → good
- Box 4: 4,1,2,3 → good
✔ Puzzle 3 Solved
Final grid:
```
+-----+-----+
| 2 1 | 3 4 |
| 4 3 | 1 2 |
+-----+-----+
| 3 2 | 4 1 |
| 1 4 | 2 3 |
+-----+-----+
```
---
## ✔ Puzzle 4
```
+-----+-----+
| | 3 4 |
| 3 | 1 2 |
+-----+-----+
| 3 2 | 4 |
| 1 4 | 3 |
+-----+-----+
```
Let’s fill in.
Start with Box 2 (top-right): R1C3=3, R1C4=4, R2C3=1, R2C4=2 → all filled → good.
Now Row 1: R1 = [?, ?, 3, 4] → missing 1,2
So R1C1 and R1C2 = 1 and 2
Now Box 1 (top-left): R1C1=?, R1C2=?, R2C1=?, R2C2=3
Numbers: ?, ?, ?, 3 → missing 1,2,4
But R1C1 and R1C2 are 1 and 2 → so R2C1 must be 4 (only missing number)
So R2C1 = 4
Now Row 2: R2 = [4,3,1,2] → complete.
Now Column 1: R1C1=?, R2C1=4, R3C1=3, R4C1=1 → missing 2 → so R1C1 = 2
Then R1C2 = 1 (since row 1 needs 1,2)
So R1 = [2,1,3,4]
Now Box 1: R1C1=2, R1C2=1, R2C1=4, R2C2=3 → all good.
Now Row 3: R3 = [3,2,4,?] → missing 1 → R3C4 = 1
Now Column 4: R1C4=4, R2C4=2, R3C4=1, R4C4=3 → complete.
Now Row 4: R4 = [1,4,?,3] → missing 2 → R4C3 = 2
Now Box 4 (bottom-right): R3C3=4, R3C4=1, R4C3=2, R4C4=3 → all good.
Check Column 3: R1C3=3, R2C3=1, R3C3=4, R4C3=2 → all good.
All boxes:
- Box 1: 2,1,4,3 → good
- Box 2: 3,4,1,2 → good
- Box 3: 3,2,4,1 → good
- Box 4: 4,1,2,3 → good
✔ Puzzle 4 Solved
Final grid:
```
+-----+-----+
| 2 1 | 3 4 |
| 4 3 | 1 2 |
+-----+-----+
| 3 2 | 4 1 |
| 1 4 | 2 3 |
+-----+-----+
```
Wait — same as Puzzle 3?
No, different positions.
Wait:
Puzzle 3:
```
| 2 1 | 3 4 |
| 4 3 | 1 2 |
| 3 2 | 4 1 |
| 1 4 | 2 3 |
```
Puzzle 4:
```
| 2 1 | 3 4 |
| 4 3 | 1 2 |
| 3 2 | 4 1 |
| 1 4 | 2 3 |
```
Same grid? Yes — both solved to same configuration.
But initial clues were different.
Let’s verify Puzzle 4 initial clues:
Given:
- R1C3=3, R1C4=4
- R2C2=3, R2C3=1, R2C4=2
- R3C1=3, R3C2=2, R3C3=4
- R4C1=1, R4C2=4, R4C4=3
In our solution:
- R1C1=2, R1C2=1 → not given → okay
- R2C1=4 → not given → okay
- R3C4=1 → not given → okay
- R4C3=2 → not given → okay
So yes, consistent.
So Puzzle 4 is solvable.
---
## 🚫 Back to Puzzle 2
We found a contradiction.
Let’s list all clues:
Puzzle 2:
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
So:
- R1C2=3, R1C4=1
- R2C1=1, R2C2=4, R2C3=3
- R3C1=1, R3C2=4, R3C3=3
- R4C1=3, R4C3=1, R4C4=4
Now try to deduce:
Box 1 (top-left): R1C1=?, R1C2=3, R2C1=1, R2C2=4 → missing 2 → R1C1=2
Row 1: R1 = [2,3,?,1] → missing 4 → R1C3=4
Box 2 (top-right): R1C3=4, R1C4=1, R2C3=3, R2C4=? → missing 2 → R2C4=2
Row 2: R2 = [1,4,3,2] → good
Column 4: R1C4=1, R2C4=2, R3C4=?, R4C4=4 → missing 3 → R3C4=3
Row 3: R3 = [1,4,3,3] → two 3s → invalid
No way to fix.
So Puzzle 2 is unsolvable under standard Sudoku rules.
Possibility: typo in puzzle?
For example, if R3C3 were 2 instead of 3, it might work.
But as given, it's inconsistent.
---
## ✔ Final Answers
```
+-----+-----+
| 2 3 | 4 1 |
| 4 1 | 2 3 |
+-----+-----+
| 3 4 | 1 2 |
| 1 2 | 3 4 |
+-----+-----+
```
```
+-----+-----+
| 2 1 | 3 4 |
| 4 3 | 1 2 |
+-----+-----+
| 3 2 | 4 1 |
| 1 4 | 2 3 |
+-----+-----+
```
```
+-----+-----+
| 2 1 | 3 4 |
| 4 3 | 1 2 |
+-----+-----+
| 3 2 | 4 1 |
| 1 4 | 2 3 |
+-----+-----+
```
Note: Puzzles 3 and 4 have the same solution, but different clues.
---
## 📝 Summary
- Puzzle 1: Solvable — completed.
- Puzzle 2: Unsolvable due to conflicting constraints (duplicate 3 in row 3).
- Puzzle 3: Solvable.
- Puzzle 4: Solvable.
If Puzzle 2 was intended to be solvable, likely a typo in the input (e.g., R3C3 should be 2 instead of 3).
Let me know if you'd like a visual explanation or want to try fixing Puzzle 2.
Let’s solve each puzzle step by step.
---
🔍 General Rules:
- Each row must contain numbers 1–4, no repeats.
- Each column must contain numbers 1–4, no repeats.
- Each 2×2 box (there are four of them) must contain numbers 1–4, no repeats.
We’ll go one by one.
---
## ✔ Puzzle 1
```
+-----+-----+
| 2 3 | 4 |
| 4 | 2 |
+-----+-----+
| 3 4 | 2 |
| 2 | 3 4 |
+-----+-----+
```
Let’s label rows R1 to R4 and columns C1 to C4.
Step 1: Look at missing values
We’ll start filling in what we can.
#### Box 1 (Top-left): R1C1, R1C2, R2C1, R2C2
Current:
- R1C1 = 2
- R1C2 = 3
- R2C1 = 4
- R2C2 = ?
So missing: 1
→ So R2C2 = 1
Update:
```
+-----+-----+
| 2 3 | 4 |
| 4 1 | 2 |
+-----+-----+
| 3 4 | 2 |
| 2 | 3 4 |
+-----+-----+
```
#### Box 2 (Top-right): R1C3, R1C4, R2C3, R2C4
Current:
- R1C3 = 4
- R1C4 = ?
- R2C3 = 2
- R2C4 = ?
Missing: 1, 3
Now look at Row 1: has 2,3,4 → missing 1 → so R1C4 = 1
Then R2C4 must be 3 (since 1 and 3 left, but 1 used in row)
So:
- R1C4 = 1
- R2C4 = 3
Update:
```
+-----+-----+
| 2 3 | 4 1 |
| 4 1 | 2 3 |
+-----+-----+
| 3 4 | 2 |
| 2 | 3 4 |
+-----+-----+
```
#### Box 3 (Bottom-left): R3C1, R3C2, R4C1, R4C2
Current:
- R3C1 = 3
- R3C2 = 4
- R4C1 = ?
- R4C2 = 2
Missing: 1, 4? Wait — numbers needed: 1, 2, 3, 4 → already have 3,4,2 → missing 1
So only missing number is 1 → R4C1 = 1
But R4C1 is also part of Column 1: current values:
- R1C1 = 2
- R2C1 = 4
- R3C1 = 3
- R4C1 = ?
So missing: 1 → yes, confirms R4C1 = 1
So R4C1 = 1
Now R4C2 = 2 → okay.
Now update:
```
+-----+-----+
| 2 3 | 4 1 |
| 4 1 | 2 3 |
+-----+-----+
| 3 4 | 2 |
| 1 2 | 3 4 |
+-----+-----+
```
Now Box 4 (Bottom-right): R3C3, R3C4, R4C3, R4C4
Current:
- R3C3 = ?
- R3C4 = 2
- R4C3 = 3
- R4C4 = 4
So missing: 1, 4? Wait: numbers: 1,2,3,4 → present: 2,3,4 → missing: 1 → so R3C3 = 1
Now check Row 3: R3 = [3,4,?,2] → missing 1 → so R3C3 = 1 → matches.
So R3C3 = 1
Now only missing is R3C4 → wait, R3C4 is already 2.
Wait — R3C3 is now 1, R3C4 is 2 → row 3: 3,4,1,2 → complete.
Now Column 3:
- R1C3 = 4
- R2C3 = 2
- R3C3 = 1
- R4C3 = 3 → all good.
Column 4:
- R1C4 = 1
- R2C4 = 3
- R3C4 = 2
- R4C4 = 4 → complete.
Now check Box 3 (bottom-left): R3C1=3, R3C2=4, R4C1=1, R4C2=2 → has 1,2,3,4 → good.
All boxes and rows/columns seem satisfied.
✔ Puzzle 1 Solved
Final grid:
```
+-----+-----+
| 2 3 | 4 1 |
| 4 1 | 2 3 |
+-----+-----+
| 3 4 | 1 2 |
| 1 2 | 3 4 |
+-----+-----+
```
---
## ✔ Puzzle 2
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
Let’s analyze.
Start with Box 1 (top-left): R1C1=?, R1C2=3, R2C1=1, R2C2=4
So values: ?,3,1,4 → missing 2 → so R1C1 = 2
Now Row 1: R1 = [2,3,?,1] → missing 4 → so R1C3 = 4
Now Box 2 (top-right): R1C3=4, R1C4=1, R2C3=3, R2C4=?
So values: 4,1,3,? → missing 2 → R2C4 = 2
Now Row 2: R2 = [1,4,3,2] → complete.
Now Column 4: R1C4=1, R2C4=2, R3C4=?, R4C4=4 → missing 3 → R3C4 = 3
Now Row 3: R3 = [1,4,3,3] → wait! Two 3s → conflict?
Wait: R3C1=1, R3C2=4, R3C3=3, R3C4=3 → two 3s → invalid!
But we just set R3C4=3, but R3C3=3 already.
So contradiction.
Wait — let's double-check.
Wait, original Puzzle 2:
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
So:
- R3C1 = 1
- R3C2 = 4
- R3C3 = 3
- R3C4 = ?
So R3 = [1,4,3,?] → missing 2 → so R3C4 = 2
Ah! I made a mistake earlier.
Column 4:
- R1C4 = 1
- R2C4 = ?
- R3C4 = 2
- R4C4 = 4
So missing: 3 → so R2C4 = 3
But earlier we had R2C4 = ? from Box 2.
Let’s restart carefully.
Step-by-step:
Box 1 (top-left): R1C1=?, R1C2=3, R2C1=1, R2C2=4 → missing 2 → R1C1 = 2
Row 1: R1 = [2,3,?,1] → missing 4 → R1C3 = 4
Box 2 (top-right): R1C3=4, R1C4=1, R2C3=3, R2C4=? → values: 4,1,3,? → missing 2 → R2C4 = 2
But now Row 2: R2 = [1,4,3,2] → valid.
Column 4: R1C4=1, R2C4=2, R3C4=?, R4C4=4 → missing 3 → R3C4 = 3
But Row 3: R3 = [1,4,3,3] → two 3s → invalid!
Contradiction.
Wait — R3C3 is given as 3, R3C4 = 3 → duplicate → impossible.
But R3C3 = 3 is given, R3C4 = ? → if R3C4 = 3, then duplicate.
But Column 4 needs 3 → so R3C4 must be 3 → contradiction.
So this puzzle seems unsolvable?
Wait — maybe I misread.
Let me recheck the original:
Puzzle 2:
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
So:
- R3C3 = 3
- R3C4 = ?
And Column 4: R1C4=1, R2C4=?, R3C4=?, R4C4=4
We need to place 2 and 3 in R2C4 and R3C4.
But Row 3: R3 = [1,4,3,?] → missing 2 → so R3C4 = 2
Then Column 4: R1C4=1, R2C4=?, R3C4=2, R4C4=4 → missing 3 → so R2C4 = 3
Now Row 2: R2 = [1,4,3,3] → wait! R2C3=3, R2C4=3 → duplicate!
Oh! R2C3 = 3 is given, so R2C4 cannot be 3.
Conflict.
So R2C4 cannot be 3, but must be 3 from column → contradiction.
Thus, no solution exists for Puzzle 2?
Wait — is there a typo?
Let’s list all constraints.
R2C3 = 3 (given), R2C4 = ? → so R2C4 ≠ 3
Column 4: R1C4=1, R2C4=?, R3C4=?, R4C4=4
Values needed: 2 and 3
But R2C4 ≠ 3 → so R2C4 = 2 → then R3C4 = 3
But Row 3: R3 = [1,4,3,3] → R3C3=3, R3C4=3 → duplicate → invalid.
No way out.
So Puzzle 2 has no valid solution.
But maybe I missed something.
Wait — is it possible that R3C3 is not 3?
Look again:
Puzzle 2:
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
Yes, R3C3 = 3 is given.
So unless the puzzle is invalid, it's unsolvable.
Alternatively, perhaps the regions are different?
Wait — maybe these aren't standard Sudoku? But they are 4x4 with 2x2 boxes.
Alternatively, maybe the rules are different?
But based on standard logic, Puzzle 2 is unsolvable due to contradiction.
Let’s move on and come back.
---
## ✔ Puzzle 3
```
+-----+-----+
| 1 | 3 4 |
| 4 | 1 |
+-----+-----+
| 3 2 | 1 |
| 1 | 2 3 |
+-----+-----+
```
Let’s solve.
Box 1 (top-left): R1C1=?, R1C2=1, R2C1=4, R2C2=?
Numbers: ?,1,4,? → missing 2,3
So R1C1 and R2C2 must be 2 and 3 in some order.
Now Row 1: R1 = [?,1,3,4] → missing 2 → so R1C1 = 2
Then R2C2 = 3 (from box 1)
Now R1 = [2,1,3,4] → complete.
R2 = [4,3,1,?] → missing 2 → R2C4 = 2
Now Box 2 (top-right): R1C3=3, R1C4=4, R2C3=1, R2C4=2 → all filled → good.
Now Column 4: R1C4=4, R2C4=2, R3C4=1, R4C4=3 → all good.
Now Row 3: R3 = [3,2,?,1] → missing 4 → R3C3 = 4
Now Box 3 (bottom-left): R3C1=3, R3C2=2, R4C1=1, R4C2=?
Numbers: 3,2,1,? → missing 4 → R4C2 = 4
Now Row 4: R4 = [1,4,2,3] → complete.
Now Box 4 (bottom-right): R3C3=4, R3C4=1, R4C3=2, R4C4=3 → all good.
Now check columns:
- C1: 2,4,3,1 → all good
- C2: 1,3,2,4 → good
- C3: 3,1,4,2 → good
- C4: 4,2,1,3 → good
All boxes:
- Box 1: 2,1,4,3 → good
- Box 2: 3,4,1,2 → good
- Box 3: 3,2,1,4 → good
- Box 4: 4,1,2,3 → good
✔ Puzzle 3 Solved
Final grid:
```
+-----+-----+
| 2 1 | 3 4 |
| 4 3 | 1 2 |
+-----+-----+
| 3 2 | 4 1 |
| 1 4 | 2 3 |
+-----+-----+
```
---
## ✔ Puzzle 4
```
+-----+-----+
| | 3 4 |
| 3 | 1 2 |
+-----+-----+
| 3 2 | 4 |
| 1 4 | 3 |
+-----+-----+
```
Let’s fill in.
Start with Box 2 (top-right): R1C3=3, R1C4=4, R2C3=1, R2C4=2 → all filled → good.
Now Row 1: R1 = [?, ?, 3, 4] → missing 1,2
So R1C1 and R1C2 = 1 and 2
Now Box 1 (top-left): R1C1=?, R1C2=?, R2C1=?, R2C2=3
Numbers: ?, ?, ?, 3 → missing 1,2,4
But R1C1 and R1C2 are 1 and 2 → so R2C1 must be 4 (only missing number)
So R2C1 = 4
Now Row 2: R2 = [4,3,1,2] → complete.
Now Column 1: R1C1=?, R2C1=4, R3C1=3, R4C1=1 → missing 2 → so R1C1 = 2
Then R1C2 = 1 (since row 1 needs 1,2)
So R1 = [2,1,3,4]
Now Box 1: R1C1=2, R1C2=1, R2C1=4, R2C2=3 → all good.
Now Row 3: R3 = [3,2,4,?] → missing 1 → R3C4 = 1
Now Column 4: R1C4=4, R2C4=2, R3C4=1, R4C4=3 → complete.
Now Row 4: R4 = [1,4,?,3] → missing 2 → R4C3 = 2
Now Box 4 (bottom-right): R3C3=4, R3C4=1, R4C3=2, R4C4=3 → all good.
Check Column 3: R1C3=3, R2C3=1, R3C3=4, R4C3=2 → all good.
All boxes:
- Box 1: 2,1,4,3 → good
- Box 2: 3,4,1,2 → good
- Box 3: 3,2,4,1 → good
- Box 4: 4,1,2,3 → good
✔ Puzzle 4 Solved
Final grid:
```
+-----+-----+
| 2 1 | 3 4 |
| 4 3 | 1 2 |
+-----+-----+
| 3 2 | 4 1 |
| 1 4 | 2 3 |
+-----+-----+
```
Wait — same as Puzzle 3?
No, different positions.
Wait:
Puzzle 3:
```
| 2 1 | 3 4 |
| 4 3 | 1 2 |
| 3 2 | 4 1 |
| 1 4 | 2 3 |
```
Puzzle 4:
```
| 2 1 | 3 4 |
| 4 3 | 1 2 |
| 3 2 | 4 1 |
| 1 4 | 2 3 |
```
Same grid? Yes — both solved to same configuration.
But initial clues were different.
Let’s verify Puzzle 4 initial clues:
Given:
- R1C3=3, R1C4=4
- R2C2=3, R2C3=1, R2C4=2
- R3C1=3, R3C2=2, R3C3=4
- R4C1=1, R4C2=4, R4C4=3
In our solution:
- R1C1=2, R1C2=1 → not given → okay
- R2C1=4 → not given → okay
- R3C4=1 → not given → okay
- R4C3=2 → not given → okay
So yes, consistent.
So Puzzle 4 is solvable.
---
## 🚫 Back to Puzzle 2
We found a contradiction.
Let’s list all clues:
Puzzle 2:
```
+-----+-----+
| 3 | 1 |
| 1 4 | 3 |
+-----+-----+
| 1 4 | 3 |
| 3 | 1 4 |
+-----+-----+
```
So:
- R1C2=3, R1C4=1
- R2C1=1, R2C2=4, R2C3=3
- R3C1=1, R3C2=4, R3C3=3
- R4C1=3, R4C3=1, R4C4=4
Now try to deduce:
Box 1 (top-left): R1C1=?, R1C2=3, R2C1=1, R2C2=4 → missing 2 → R1C1=2
Row 1: R1 = [2,3,?,1] → missing 4 → R1C3=4
Box 2 (top-right): R1C3=4, R1C4=1, R2C3=3, R2C4=? → missing 2 → R2C4=2
Row 2: R2 = [1,4,3,2] → good
Column 4: R1C4=1, R2C4=2, R3C4=?, R4C4=4 → missing 3 → R3C4=3
Row 3: R3 = [1,4,3,3] → two 3s → invalid
No way to fix.
So Puzzle 2 is unsolvable under standard Sudoku rules.
Possibility: typo in puzzle?
For example, if R3C3 were 2 instead of 3, it might work.
But as given, it's inconsistent.
---
## ✔ Final Answers
Puzzle 1:
```
+-----+-----+
| 2 3 | 4 1 |
| 4 1 | 2 3 |
+-----+-----+
| 3 4 | 1 2 |
| 1 2 | 3 4 |
+-----+-----+
```
Puzzle 2: ✘ No solution (contradiction in row 3)
Puzzle 3:
```
+-----+-----+
| 2 1 | 3 4 |
| 4 3 | 1 2 |
+-----+-----+
| 3 2 | 4 1 |
| 1 4 | 2 3 |
+-----+-----+
```
Puzzle 4:
```
+-----+-----+
| 2 1 | 3 4 |
| 4 3 | 1 2 |
+-----+-----+
| 3 2 | 4 1 |
| 1 4 | 2 3 |
+-----+-----+
```
Note: Puzzles 3 and 4 have the same solution, but different clues.
---
## 📝 Summary
- Puzzle 1: Solvable — completed.
- Puzzle 2: Unsolvable due to conflicting constraints (duplicate 3 in row 3).
- Puzzle 3: Solvable.
- Puzzle 4: Solvable.
If Puzzle 2 was intended to be solvable, likely a typo in the input (e.g., R3C3 should be 2 instead of 3).
Let me know if you'd like a visual explanation or want to try fixing Puzzle 2.
Parent Tip: Review the logic above to help your child master the concept of printable sudoku directions.