Imprimir sudokus para niños - Free Printable
Educational worksheet: Imprimir sudokus para niños. Download and print for classroom or home learning activities.
JPG
474×657
42.4 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1861329
⭐
Show Answer Key & Explanations
Step-by-step solution for: Imprimir sudokus para niños
▼
Show Answer Key & Explanations
Step-by-step solution for: Imprimir sudokus para niños
To solve these puzzles, we need to fill in the empty squares so that every row, every column, and every 2x2 block contains the numbers 1, 2, 3, and 4 exactly once.
Here are the solutions for each puzzle, going from left to right, top to bottom.
Puzzle 1 (Top Left):
* Row 1: The missing numbers are 1 and 3. Looking at the first column, it already has a 1 in Row 3. So, R1C1 must be 3, and R1C2 is 1. -> `3 1 | 4 2`
* Row 2: Missing 1 and 3. Column 1 needs a 1 (since we just put 3 there). So R2C1 is 1, R2C2 is 3. -> `1 3 | 4 2` (Wait, let's re-check constraints. Col 1 has 2,4. Needs 1,3. Row 2 has 4,2. Needs 1,3. Block TL has 4,2,3,1. Let's restart systematically.)
Let's solve Puzzle 1 carefully:
Grid:
`. . | 4 .`
`. 4 | . 2`
`-----+-----`
`2 3 | 1 4`
`4 . | . .`
1. Row 3 is complete: `2 3 1 4`.
2. Col 1 has 2, 4. Needs 1, 3.
3. Col 2 has 4, 3. Needs 1, 2.
4. Block Top-Left has 4, 2, 3. Needs 1. The empty spots are R1C1, R1C2, R2C1. Wait, R2C2 is 4. R3C1=2, R3C2=3. R4C1=4.
* Let's look at Col 1: Cells are R1, R2, R3(2), R4(4). Missing 1, 3.
* Let's look at Row 2: Cells are R2C1, R2C2(4), R2C3, R2C4(2). Missing 1, 3.
* Let's look at Block Top-Right: Has 4, 2. Needs 1, 3. Cells R1C3(4), R1C4, R2C3, R2C4(2).
* R1C3 is 4. R2C4 is 2.
* Row 1 needs 1, 2, 3. It has 4.
* Let's look at Col 4: Has 2, 4. Needs 1, 3.
* Let's look at Row 4: Has 4. Needs 1, 2, 3.
Let's try filling logically:
* R3 is `2 3 1 4`.
* Col 1: Needs 1, 3. R1C1 and R2C1.
* Col 2: Has 4, 3. Needs 1, 2. R1C2 and R4C2.
* Block Bottom-Left: Has 2, 3, 4. Needs 1. The only empty spot in this block is R4C2? No, R4C1 is 4, R3C1 is 2, R3C2 is 3. The block is R3C1, R3C2, R4C1, R4C2. Values present: 2, 3, 4. So R4C2 must be 1.
* Since R4C2 is 1, then R1C2 must be 2 (to complete Col 2 which needs 1,2).
* Now Row 1: Has 2, 4. Needs 1, 3.
* Now Col 1: Needs 1, 3.
* Look at Block Top-Left: Cells R1C1, R1C2(2), R2C1, R2C2(4). Present: 2, 4. Needs 1, 3.
* Look at Row 2: Has 4, 2. Needs 1, 3.
* Look at Col 4: Has 2, 4. Needs 1, 3.
* Look at Row 4: Has 4, 1. Needs 2, 3.
* Let's look at Col 3: Has 1, 4. Needs 2, 3.
* In Row 1, we need 1, 3 for R1C1 and R1C4? No, R1C3 is 4. So R1 is `? 2 | 4 ?`. Needs 1, 3.
* In Col 1, we need 1, 3 for R1C1 and R2C1.
* If R1C1 is 1, then R1C4 is 3. Then R2C1 is 3. Then R2C3 is 1.
* Check Row 2: `3 4 | 1 2`. Valid.
* Check Col 1: `1 3 2 4`. Valid.
* Check Col 4: `3 2 4 ?`. R4C4 needs to be 1? Row 4 is `4 1 | ? ?`. Needs 2, 3. Col 4 has 3, 2, 4. So R4C4 must be 1? But Row 4 already has 1 at R4C2. Contradiction.
* Let's re-evaluate.
* Col 4 has R2C4=2, R3C4=4. Needs 1, 3.
* Row 4 has R4C1=4, R4C2=1. Needs 2, 3.
* So R4C4 cannot be 1. It must be 2 or 3.
* Col 4 needs 1 or 3. So R4C4 must be 3 (intersection of {2,3} and {1,3}).
* Therefore, R4C4 = 3.
* Then R4C3 = 2 (to complete Row 4: `4 1 2 3`).
* Then R1C4 = 1 (to complete Col 4: `1 2 4 3`).
* Then R1C1 = 3 (to complete Row 1: `3 2 4 1`).
* Then R2C1 = 1 (to complete Col 1: `3 1 2 4`).
* Then R2C3 = 3 (to complete Row 2: `1 4 3 2`).
* Check Col 3: `4 3 1 2`. Valid.
Solution 1:
3 2 | 4 1
1 4 | 3 2
-----+-----
2 3 | 1 4
4 1 | 2 3
Puzzle 2 (Top Middle):
Grid:
`2 4 | 1 .`
`. . | . .`
`-----+-----`
`1 3 | 4 2`
`4 . | . .`
1. Row 3 is `1 3 4 2`.
2. Row 1: Has 2, 4, 1. Needs 3. So R1C4 = 3.
3. Col 1: Has 2, 1, 4. Needs 3. So R2C1 = 3.
4. Col 2: Has 4, 3. Needs 1, 2.
5. Block Bottom-Left: Has 1, 3, 4. Needs 2. So R4C2 = 2.
6. Then R1C2 is already 4. Wait, Col 2 needs 1, 2. R4C2=2. So R2C2 = 1? No, R1C2 is 4. R3C2 is 3. R4C2 is 2. So R2C2 = 1 is wrong because Col 2 needs 1? Yes. Col 2 cells: R1(4), R2(?), R3(3), R4(2). Missing 1. So R2C2 = 1.
7. Row 2: Has 3, 1. Needs 2, 4.
8. Col 4: Has 3, 2. Needs 1, 4.
9. Row 4: Has 4, 2. Needs 1, 3.
10. Col 3: Has 1, 4. Needs 2, 3.
11. Look at R4C3. Row 4 needs 1, 3. Col 3 needs 2, 3. Intersection is 3. So R4C3 = 3.
12. Then R4C4 = 1 (complete Row 4: `4 2 3 1`).
13. Then R2C3 = 2 (complete Col 3: `1 2 4 3`).
14. Then R2C4 = 4 (complete Row 2: `3 1 2 4`).
Solution 2:
2 4 | 1 3
3 1 | 2 4
-----+-----
1 3 | 4 2
4 2 | 3 1
Puzzle 3 (Top Right):
Grid:
`4 . | 3 1`
`1 . | . .`
`-----+-----`
`. . | . .`
`2 4 | 1 3`
1. Row 4 is `2 4 1 3`.
2. Row 1: Has 4, 3, 1. Needs 2. So R1C2 = 2.
3. Col 1: Has 4, 1, 2. Needs 3. So R3C1 = 3.
4. Col 2: Has 2, 4. Needs 1, 3.
5. Block Bottom-Left: Has 3, 2, 4. Needs 1. So R3C2 = 1.
6. Then R2C2 = 3 (complete Col 2: `2 3 1 4`).
7. Row 2: Has 1, 3. Needs 2, 4.
8. Col 4: Has 1, 3. Needs 2, 4.
9. Col 3: Has 3, 1. Needs 2, 4.
10. Look at R2C3. Row 2 needs 2, 4. Col 3 needs 2, 4.
11. Look at R3C3. Row 3 needs 2, 4 (has 3, 1). Col 3 needs 2, 4.
12. Look at R2C4. Row 2 needs 2, 4. Col 4 needs 2, 4.
13. Look at R3C4. Row 3 needs 2, 4. Col 4 needs 2, 4.
14. Let's check blocks.
* Block Top-Right: Has 3, 1. Needs 2, 4. Cells R1C3(3), R1C4(1), R2C3, R2C4.
* Block Bottom-Right: Has 1, 3. Needs 2, 4. Cells R3C3, R3C4, R4C3(1), R4C4(3).
* Wait, R4C3 is 1, R4C4 is 3.
* Col 3 has R1C3=3, R4C3=1. Needs 2, 4.
* Col 4 has R1C4=1, R4C4=3. Needs 2, 4.
* Row 2 has R2C1=1, R2C2=3. Needs 2, 4.
* Row 3 has R3C1=3, R3C2=1. Needs 2, 4.
* This creates two possibilities. Let's look closer.
* Is there a constraint I missed?
* Ah, look at Col 3. R1C3 is 3. R4C3 is 1.
* Look at Row 2. R2C1 is 1.
* Look at Block Top-Middle (actually Top-Right).
* Let's guess R2C3 = 2. Then R2C4 = 4. Then R3C3 = 4. Then R3C4 = 2.
* Check: Row 2 `1 3 2 4`. Row 3 `3 1 4 2`. Col 3 `3 2 4 1`. Col 4 `1 4 2 3`. All valid.
* Alternative: R2C3 = 4. Then R2C4 = 2. Then R3C3 = 2. Then R3C4 = 4.
* Check: Row 2 `1 3 4 2`. Row 3 `3 1 2 4`. Col 3 `3 4 2 1`. Col 4 `1 2 4 3`. All valid.
* Usually Sudoku has one solution. Did I miss a number?
* Original:
`4 . | 3 1`
`1 . | . .`
`. . | . .`
`2 4 | 1 3`
* My derived:
`4 2 | 3 1`
`1 3 | 2 4` (or 4 2)
`3 1 | 4 2` (or 2 4)
`2 4 | 1 3`
* Let's re-read the image carefully.
* Puzzle 3 Image:
Row 1: 4, blank, 3, 1
Row 2: 1, blank, blank, blank
Row 3: blank, blank, blank, blank
Row 4: 2, 4, 1, 3
* There are no other clues. It seems there might be two solutions for this specific sparse puzzle, OR I made a mistake in uniqueness logic. However, often in these worksheets, if it's ambiguous, either is accepted, but let's look for a subtle constraint.
* Wait, look at Col 1: 4, 1, ?, 2. Missing 3. So R3C1=3. Correct.
* Col 2: ?, ?, ?, 4.
* Row 1: 4, ?, 3, 1. Missing 2. So R1C2=2. Correct.
* Col 2: 2, ?, ?, 4. Missing 1, 3.
* Row 2: 1, ?, ?, ?.
* Row 4: 2, 4, 1, 3.
* Block BL: R3C1(3), R3C2(?), R4C1(2), R4C2(4). Missing 1. So R3C2=1. Correct.
* So Col 2 is 2, ?, 1, 4. Missing 3. So R2C2=3. Correct.
* Now we have:
`4 2 | 3 1`
`1 3 | A B`
`3 1 | C D`
`2 4 | 1 3`
* Remaining numbers for A,B,C,D are 2,4.
* Col 3 needs 2,4. Col 4 needs 2,4.
* Row 2 needs 2,4. Row 3 needs 2,4.
* There is genuinely no unique constraint distinguishing between the two swaps unless I misread a number.
* Let's assume the standard "diagonal" or pattern doesn't apply. I will provide one valid solution.
* Solution A: A=2, B=4, C=4, D=2.
Solution 3:
4 2 | 3 1
1 3 | 2 4
-----+-----
3 1 | 4 2
2 4 | 1 3
Puzzle 4 (Middle Left):
Grid:
`. 4 | . 1`
`. . | 3 4`
`-----+-----`
`1 2 | . .`
`. 3 | . 2`
1. Col 2: Has 4, 2, 3. Needs 1. So R2C2 = 1.
2. Row 2: Has 1, 3, 4. Needs 2. So R2C1 = 2.
3. Col 1: Has 2, 1. Needs 3, 4.
4. Row 1: Has 4, 1. Needs 2, 3.
5. Block Top-Left: Has 4, 1, 2. Needs 3. So R1C1 = 3.
6. Then R4C1 = 4 (complete Col 1: `3 2 1 4`).
7. Then R1C3 = 2 (complete Row 1: `3 4 2 1`).
8. Col 3: Has 2, 3. Needs 1, 4.
9. Row 4: Has 4, 3, 2. Needs 1. So R4C3 = 1.
10. Then R3C3 = 4 (complete Col 3: `2 3 4 1`).
11. Row 3: Has 1, 2, 4. Needs 3. So R3C4 = 3.
12. Row 4: Has 4, 3, 1, 2. Complete.
13. Check Col 4: 1, 4, 3, 2. Valid.
Solution 4:
3 4 | 2 1
2 1 | 3 4
-----+-----
1 2 | 4 3
4 3 | 1 2
Puzzle 5 (Middle Center):
Grid:
`. . | 1 .`
`3 . | . 4`
`-----+-----`
`. . | . 1`
`1 3 | 4 2`
1. Row 4 is `1 3 4 2`.
2. Col 1: Has 3, 1. Needs 2, 4.
3. Col 2: Has 3. Needs 1, 2, 4.
4. Col 3: Has 1, 4. Needs 2, 3.
5. Col 4: Has 4, 1, 2. Needs 3. So R1C4 = 3.
6. Row 1: Has 1, 3. Needs 2, 4.
7. Block Top-Right: Has 1, 4, 3. Needs 2. So R2C3 = 2.
8. Then R3C3 = 3 (complete Col 3: `1 2 3 4`).
9. Row 2: Has 3, 2, 4. Needs 1. So R2C2 = 1.
10. Col 2: Has 1, 3. Needs 2, 4.
11. Row 1: Needs 2, 4 for R1C1, R1C2.
12. Row 3: Needs 2, 4 for R3C1, R3C2 (has 3, 1 in C3, C4).
13. Col 1: Needs 2, 4 for R1C1, R3C1 (has 3, 1 in R2, R4).
14. Look at Block Bottom-Left: Has 1, 3, 4. Needs 2. So R3C2 = 2? No, R4C1=1, R4C2=3. R3C1=?, R3C2=?. Block is R3C1, R3C2, R4C1, R4C2. Values present in block: 1, 3. Needs 2, 4.
15. Look at Row 3: `? ? 3 1`. Needs 2, 4.
16. Look at Col 1: `? 3 ? 1`. Needs 2, 4.
17. Look at Col 2: `? 1 ? 3`. Needs 2, 4.
18. If R1C1=2, R1C2=4. Then R3C1=4, R3C2=2.
* Check Col 1: 2, 3, 4, 1. OK.
* Check Col 2: 4, 1, 2, 3. OK.
* Check Row 1: 2, 4, 1, 3. OK.
* Check Row 3: 4, 2, 3, 1. OK.
* This works.
Solution 5:
2 4 | 1 3
3 1 | 2 4
-----+-----
4 2 | 3 1
1 3 | 4 2
Puzzle 6 (Middle Right):
Grid:
`. 1 | 4 3`
`. . | 3 2`
`-----+-----`
`3 4 | . .`
`. 2 | . .`
1. Row 1: Has 1, 4, 3. Needs 2. So R1C1 = 2.
2. Col 1: Has 2, 3. Needs 1, 4.
3. Row 2: Has 3, 2. Needs 1, 4.
4. Block Top-Left: Has 2, 1, 3, 4? No. R1C1=2, R1C2=1. R2C1=?, R2C2=?. Block needs 3, 4? No, 1, 2 are present. Needs 3, 4.
* Wait, R2C3=3, R2C4=2.
* Row 2 needs 1, 4.
* Col 1 needs 1, 4.
* If R2C1=1, then R2C2=4. Then R4C1=4? No, Col 1 needs 1, 4. If R2C1=1, R4C1=4.
* If R2C1=4, then R2C2=1. Then R4C1=1.
* Let's check Col 2: Has 1, 2. Needs 3, 4.
* If R2C2=4, then R4C2=2 (already 2). Conflict? No, R4C2 is 2. So Col 2 has 1, ?, 4, 2. Needs 3. So R2C2=3? No, Row 2 has 3.
* Let's restart Puzzle 6.
* R1: `2 1 4 3`.
* Col 2: `1, ?, 4, 2`. Needs 3. So R2C2 = 3.
* Row 2: `? 3 3 2`? No, R2C3 is 3. So R2C2 cannot be 3.
* Wait, look at image again.
* Puzzle 6:
`. 1 | 4 3`
`. . | 3 2`
`3 4 | . .`
`. 2 | . .`
* Col 2 has 1, 2. And R3C2=4. So Col 2 has 1, 4, 2. Needs 3. So R2C2 = 3.
* But Row 2 has a 3 at R2C3. Contradiction.
* Did I read R3C2 correctly? Yes, `3 4`.
* Did I read R2C3 correctly? Yes, `3 2`.
* Did I read R1C2 correctly? Yes, `1`.
* Did I read R4C2 correctly? Yes, `2`.
* So Col 2 contains: R1=1, R3=4, R4=2. The missing number is 3. So R2C2 MUST be 3.
* But Row 2 contains: R2C3=3, R2C4=2. So R2C2 CANNOT be 3.
* Is it possible R3C1 is not 3? Image says `3 4`.
* Is it possible R2C3 is not 3? Image says `3 2`.
* Let me re-examine the image for Puzzle 6.
* Row 1: blank, 1, 4, 3.
* Row 2: blank, blank, 3, 2.
* Row 3: 3, 4, blank, blank.
* Row 4: blank, 2, blank, blank.
* Okay, Col 2: 1, ?, 4, 2. Missing 3. So R2C2=3.
* Row 2: ?, 3, 3, 2. Two 3s.
* There is an error in my reading or the puzzle.
* Let's look really closely at Crop 6.
* Row 1: `. 1 | 4 3`
* Row 2: `. . | 3 2` -> Wait, is that a 3? Or a 5? No, 4x4 sudoku.
* Maybe R3C1 is not 3? It looks like a 3.
* Maybe R2C3 is not 3? It looks like a 3.
* Let's check if R2C2 could be something else.
* Col 2: 1, X, 4, 2. X must be 3.
* Row 2: Y, 3, 3, 2. Invalid.
* Is it possible R4C2 is not 2? It looks like a 2.
* Is it possible R1C2 is not 1? It looks like a 1.
* Is it possible R3C2 is not 4? It looks like a 4.
* Let's assume I misidentified a number.
* What if R2C3 is a 1?
* Then Row 2 needs 4. R2C2=4? Col 2 needs 3. Conflict.
* What if R2C3 is a 4?
* Then Row 2 needs 1. R2C2=1? Col 2 has 1. Conflict.
* What if R3C2 is 2?
* Then Col 2: 1, ?, 2, 2. Conflict.
* What if R3C2 is 1?
* Then Col 2: 1, ?, 1, 2. Conflict.
* What if R3C2 is 3?
* Then Col 2: 1, ?, 3, 2. Missing 4. So R2C2=4.
* Row 2: ?, 4, 3, 2. Missing 1. So R2C1=1.
* Col 1: ?, 1, 3, ?. Needs 2, 4.
* Row 1: ?, 1, 4, 3. Missing 2. So R1C1=2.
* Then R4C1=4.
* Row 4: 4, 2, ?, ?. Needs 1, 3.
* Col 3: 4, 3, ?, ?. Needs 1, 2.
* R3C3? Row 3: 3, 3... wait, if R3C2=3, Row 3 has 3,3. Conflict.
* Okay, let's look at the image again very carefully.
* Puzzle 6 is the top right of the second row.
* Row 1: `. 1 | 4 3`
* Row 2: `. . | 3 2`
* Row 3: `3 4 | . .`
* Row 4: `. 2 | . .`
* There is definitely a conflict if interpreted literally.
* HOWEVER, looking at the third crop (middle right), the number in R2C3 might be a 1? No, it has the flat top of a 3 or 5. In 4x4, it's a 3.
* Is it possible R3C1 is a 2?
* If R3C1=2, R3C2=4.
* Col 2: 1, ?, 4, 2. Missing 3. R2C2=3.
* Row 2: ?, 3, 3, 2. Still conflict.
* Is it possible R4C2 is 1?
* Col 2: 1, ?, 4, 1. Conflict.
* Is it possible R1C2 is 4?
* Col 2: 4, ?, 4, 2. Conflict.
* Let's assume the puzzle in the image has a typo or I am blind.
* Let's try swapping R2C3 to 1.
* R2: `. . 1 2`. Needs 3, 4.
* Col 2: `1, ?, 4, 2`. Needs 3. R2C2=3.
* R2: `4 3 1 2`.
* Col 1: `?, 4, 3, ?`. Needs 1, 2.
* R1: `? 1 4 3`. Needs 2. R1C1=2.
* R4C1=1.
* R4: `1 2 ? ?`. Needs 3, 4.
* Col 3: `4 1 ? ?`. Needs 2, 3.
* R3C3? Row 3: `3 4 ? ?`. Needs 1, 2.
* Col 3 needs 2, 3. Row 3 needs 1, 2. Intersection 2. So R3C3=2.
* R3C4=1.
* Col 4: `3 2 1 ?`. Needs 4. R4C4=4.
* R4C3=3.
* Check:
`2 1 | 4 3`
`4 3 | 1 2`
`3 4 | 2 1`
`1 2 | 3 4`
* This is a valid solution if R2C3 is 1. The digit in the image looks like a 3, but 1 makes it solvable. I will proceed with this assumption as it's the most likely intended puzzle structure.
Solution 6:
2 1 | 4 3
4 3 | 1 2
-----+-----
3 4 | 2 1
1 2 | 3 4
Puzzle 7 (Bottom Left of Middle Row - actually 3rd row, 1st col):
Grid:
`. 2 | 1 4`
`. 1 | . .`
`-----+-----`
`. . | 2 3`
`2 3 | . .`
1. Row 1: Has 2, 1, 4. Needs 3. So R1C1 = 3.
2. Col 1: Has 3, 2. Needs 1, 4.
3. Row 4: Has 2, 3. Needs 1, 4.
4. Col 4: Has 4, 3. Needs 1, 2.
5. Row 2: Has 1. Needs 2, 3, 4.
6. Block Bottom-Right: Has 2, 3. Needs 1, 4.
7. Col 3: Has 1, 2. Needs 3, 4.
8. Row 3: Has 2, 3. Needs 1, 4.
9. Look at R4C3. Row 4 needs 1, 4. Col 3 needs 3, 4. Intersection 4. So R4C3 = 4.
10. Then R4C4 = 1 (complete Row 4: `2 3 4 1`).
11. Then R3C3 = 3 (complete Col 3: `1 ? 3 4` -> R2C3?). Wait. Col 3 has R1C3=1, R4C3=4. Needs 2, 3.
* R3C3 is in Row 3 (`? ? 2 3`). R3C3 cannot be 2 or 3? No, R3C3 is blank. R3C3 is part of Col 3.
* Col 3: R1=1, R4=4. Needs 2, 3.
* Row 3: R3C3, R3C4(3). So R3C3 cannot be 3. So R3C3 = 2? But R3C3 is in the block with R3C4=3.
* Wait, R3 is `. . | 2 3`. So R3C3=2, R3C4=3.
* So Col 3 has 1, ?, 2, 4. Needs 3. So R2C3 = 3.
12. Row 2: Has 1, 3. Needs 2, 4.
13. Col 4: Has 4, 3, 1. Needs 2. So R2C4 = 2.
14. Then R2C1 = 4 (complete Row 2: `4 1 3 2`).
15. Col 1: Has 3, 4, 2. Needs 1. So R3C1 = 1.
16. Then R3C2 = 4 (complete Row 3: `1 4 2 3`).
Solution 7:
3 2 | 1 4
4 1 | 3 2
-----+-----
1 4 | 2 3
2 3 | 4 1
Puzzle 8 (Bottom Middle of Middle Row - 3rd row, 2nd col):
Grid:
`4 . | 2 3`
`. 2 | . .`
`-----+-----`
`1 . | . 2`
`. . | 4 1`
1. Row 1: Has 4, 2, 3. Needs 1. So R1C2 = 1.
2. Col 2: Has 1, 2. Needs 3, 4.
3. Col 1: Has 4, 1. Needs 2, 3.
4. Row 4: Has 4, 1. Needs 2, 3.
5. Block Bottom-Right: Has 2, 4, 1. Needs 3. So R3C3 = 3.
6. Col 3: Has 2, 3, 4. Needs 1. So R2C3 = 1.
7. Row 2: Has 2, 1. Needs 3, 4.
8. Col 4: Has 3, 2, 1. Needs 4. So R2C4 = 4.
9. Then R2C1 = 3 (complete Row 2: `3 2 1 4`).
10. Col 1: Has 4, 3, 1. Needs 2. So R4C1 = 2.
11. Row 4: Has 2, 4, 1. Needs 3. So R4C2 = 3.
12. Col 2: Has 1, 2, 3. Needs 4. So R3C2 = 4.
13. Row 3: Has 1, 4, 3, 2. Complete.
Solution 8:
4 1 | 2 3
3 2 | 1 4
-----+-----
1 4 | 3 2
2 3 | 4 1
Puzzle 9 (Bottom Right of Middle Row - 3rd row, 3rd col):
Grid:
`. 2 | 4 .`
`4 . | 1 2`
`-----+-----`
`. 1 | . 4`
`. 4 | . .`
1. Row 2: Has 4, 1, 2. Needs 3. So R2C2 = 3.
2. Col 2: Has 2, 3, 1, 4. Complete.
3. Col 1: Has 4. Needs 1, 2, 3.
4. Row 1: Has 2, 4. Needs 1, 3.
5. Block Top-Left: Has 2, 4, 3. Needs 1. So R1C1 = 1.
6. Then R1C4 = 3 (complete Row 1: `1 2 4 3`).
7. Col 1: Has 1, 4. Needs 2, 3.
8. Row 3: Has 1, 4. Needs 2, 3.
9. Row 4: Has 4. Needs 1, 2, 3.
10. Col 4: Has 3, 2, 4. Needs 1. So R4C4 = 1.
11. Row 4: Has 4, 1. Needs 2, 3.
12. Col 3: Has 4, 1. Needs 2, 3.
13. Block Bottom-Right: Has 4, 1. Needs 2, 3.
14. Look at R3C3. Row 3 needs 2, 3. Col 3 needs 2, 3.
15. Look at R4C3. Row 4 needs 2, 3. Col 3 needs 2, 3.
16. Look at R3C1. Row 3 needs 2, 3. Col 1 needs 2, 3.
17. Look at R4C1. Row 4 needs 2, 3. Col 1 needs 2, 3.
18. Another ambiguous one?
* If R3C1=2, R3C3=3. Then R4C1=3, R4C3=2.
* Check: R3 `2 1 3 4`. R4 `3 4 2 1`.
* Col 1: 1, 4, 2, 3. OK.
* Col 3: 4, 1, 3, 2. OK.
* This works.
Solution 9:
1 2 | 4 3
4 3 | 1 2
-----+-----
2 1 | 3 4
3 4 | 2 1
Puzzle 10 (Bottom Left):
Grid:
`3 4 | . .`
`1 . | . .`
`-----+-----`
`2 1 | . 3`
`. 3 | 2 .`
1. Row 3: Has 2, 1, 3. Needs 4. So R3C3 = 4.
2. Col 3: Has 4, 2. Needs 1, 3.
3. Row 4: Has 3, 2. Needs 1, 4.
4. Col 1: Has 3,
Here are the solutions for each puzzle, going from left to right, top to bottom.
Row 1
Puzzle 1 (Top Left):
* Row 1: The missing numbers are 1 and 3. Looking at the first column, it already has a 1 in Row 3. So, R1C1 must be 3, and R1C2 is 1. -> `3 1 | 4 2`
* Row 2: Missing 1 and 3. Column 1 needs a 1 (since we just put 3 there). So R2C1 is 1, R2C2 is 3. -> `1 3 | 4 2` (Wait, let's re-check constraints. Col 1 has 2,4. Needs 1,3. Row 2 has 4,2. Needs 1,3. Block TL has 4,2,3,1. Let's restart systematically.)
Let's solve Puzzle 1 carefully:
Grid:
`. . | 4 .`
`. 4 | . 2`
`-----+-----`
`2 3 | 1 4`
`4 . | . .`
1. Row 3 is complete: `2 3 1 4`.
2. Col 1 has 2, 4. Needs 1, 3.
3. Col 2 has 4, 3. Needs 1, 2.
4. Block Top-Left has 4, 2, 3. Needs 1. The empty spots are R1C1, R1C2, R2C1. Wait, R2C2 is 4. R3C1=2, R3C2=3. R4C1=4.
* Let's look at Col 1: Cells are R1, R2, R3(2), R4(4). Missing 1, 3.
* Let's look at Row 2: Cells are R2C1, R2C2(4), R2C3, R2C4(2). Missing 1, 3.
* Let's look at Block Top-Right: Has 4, 2. Needs 1, 3. Cells R1C3(4), R1C4, R2C3, R2C4(2).
* R1C3 is 4. R2C4 is 2.
* Row 1 needs 1, 2, 3. It has 4.
* Let's look at Col 4: Has 2, 4. Needs 1, 3.
* Let's look at Row 4: Has 4. Needs 1, 2, 3.
Let's try filling logically:
* R3 is `2 3 1 4`.
* Col 1: Needs 1, 3. R1C1 and R2C1.
* Col 2: Has 4, 3. Needs 1, 2. R1C2 and R4C2.
* Block Bottom-Left: Has 2, 3, 4. Needs 1. The only empty spot in this block is R4C2? No, R4C1 is 4, R3C1 is 2, R3C2 is 3. The block is R3C1, R3C2, R4C1, R4C2. Values present: 2, 3, 4. So R4C2 must be 1.
* Since R4C2 is 1, then R1C2 must be 2 (to complete Col 2 which needs 1,2).
* Now Row 1: Has 2, 4. Needs 1, 3.
* Now Col 1: Needs 1, 3.
* Look at Block Top-Left: Cells R1C1, R1C2(2), R2C1, R2C2(4). Present: 2, 4. Needs 1, 3.
* Look at Row 2: Has 4, 2. Needs 1, 3.
* Look at Col 4: Has 2, 4. Needs 1, 3.
* Look at Row 4: Has 4, 1. Needs 2, 3.
* Let's look at Col 3: Has 1, 4. Needs 2, 3.
* In Row 1, we need 1, 3 for R1C1 and R1C4? No, R1C3 is 4. So R1 is `? 2 | 4 ?`. Needs 1, 3.
* In Col 1, we need 1, 3 for R1C1 and R2C1.
* If R1C1 is 1, then R1C4 is 3. Then R2C1 is 3. Then R2C3 is 1.
* Check Row 2: `3 4 | 1 2`. Valid.
* Check Col 1: `1 3 2 4`. Valid.
* Check Col 4: `3 2 4 ?`. R4C4 needs to be 1? Row 4 is `4 1 | ? ?`. Needs 2, 3. Col 4 has 3, 2, 4. So R4C4 must be 1? But Row 4 already has 1 at R4C2. Contradiction.
* Let's re-evaluate.
* Col 4 has R2C4=2, R3C4=4. Needs 1, 3.
* Row 4 has R4C1=4, R4C2=1. Needs 2, 3.
* So R4C4 cannot be 1. It must be 2 or 3.
* Col 4 needs 1 or 3. So R4C4 must be 3 (intersection of {2,3} and {1,3}).
* Therefore, R4C4 = 3.
* Then R4C3 = 2 (to complete Row 4: `4 1 2 3`).
* Then R1C4 = 1 (to complete Col 4: `1 2 4 3`).
* Then R1C1 = 3 (to complete Row 1: `3 2 4 1`).
* Then R2C1 = 1 (to complete Col 1: `3 1 2 4`).
* Then R2C3 = 3 (to complete Row 2: `1 4 3 2`).
* Check Col 3: `4 3 1 2`. Valid.
Solution 1:
3 2 | 4 1
1 4 | 3 2
-----+-----
2 3 | 1 4
4 1 | 2 3
Puzzle 2 (Top Middle):
Grid:
`2 4 | 1 .`
`. . | . .`
`-----+-----`
`1 3 | 4 2`
`4 . | . .`
1. Row 3 is `1 3 4 2`.
2. Row 1: Has 2, 4, 1. Needs 3. So R1C4 = 3.
3. Col 1: Has 2, 1, 4. Needs 3. So R2C1 = 3.
4. Col 2: Has 4, 3. Needs 1, 2.
5. Block Bottom-Left: Has 1, 3, 4. Needs 2. So R4C2 = 2.
6. Then R1C2 is already 4. Wait, Col 2 needs 1, 2. R4C2=2. So R2C2 = 1? No, R1C2 is 4. R3C2 is 3. R4C2 is 2. So R2C2 = 1 is wrong because Col 2 needs 1? Yes. Col 2 cells: R1(4), R2(?), R3(3), R4(2). Missing 1. So R2C2 = 1.
7. Row 2: Has 3, 1. Needs 2, 4.
8. Col 4: Has 3, 2. Needs 1, 4.
9. Row 4: Has 4, 2. Needs 1, 3.
10. Col 3: Has 1, 4. Needs 2, 3.
11. Look at R4C3. Row 4 needs 1, 3. Col 3 needs 2, 3. Intersection is 3. So R4C3 = 3.
12. Then R4C4 = 1 (complete Row 4: `4 2 3 1`).
13. Then R2C3 = 2 (complete Col 3: `1 2 4 3`).
14. Then R2C4 = 4 (complete Row 2: `3 1 2 4`).
Solution 2:
2 4 | 1 3
3 1 | 2 4
-----+-----
1 3 | 4 2
4 2 | 3 1
Puzzle 3 (Top Right):
Grid:
`4 . | 3 1`
`1 . | . .`
`-----+-----`
`. . | . .`
`2 4 | 1 3`
1. Row 4 is `2 4 1 3`.
2. Row 1: Has 4, 3, 1. Needs 2. So R1C2 = 2.
3. Col 1: Has 4, 1, 2. Needs 3. So R3C1 = 3.
4. Col 2: Has 2, 4. Needs 1, 3.
5. Block Bottom-Left: Has 3, 2, 4. Needs 1. So R3C2 = 1.
6. Then R2C2 = 3 (complete Col 2: `2 3 1 4`).
7. Row 2: Has 1, 3. Needs 2, 4.
8. Col 4: Has 1, 3. Needs 2, 4.
9. Col 3: Has 3, 1. Needs 2, 4.
10. Look at R2C3. Row 2 needs 2, 4. Col 3 needs 2, 4.
11. Look at R3C3. Row 3 needs 2, 4 (has 3, 1). Col 3 needs 2, 4.
12. Look at R2C4. Row 2 needs 2, 4. Col 4 needs 2, 4.
13. Look at R3C4. Row 3 needs 2, 4. Col 4 needs 2, 4.
14. Let's check blocks.
* Block Top-Right: Has 3, 1. Needs 2, 4. Cells R1C3(3), R1C4(1), R2C3, R2C4.
* Block Bottom-Right: Has 1, 3. Needs 2, 4. Cells R3C3, R3C4, R4C3(1), R4C4(3).
* Wait, R4C3 is 1, R4C4 is 3.
* Col 3 has R1C3=3, R4C3=1. Needs 2, 4.
* Col 4 has R1C4=1, R4C4=3. Needs 2, 4.
* Row 2 has R2C1=1, R2C2=3. Needs 2, 4.
* Row 3 has R3C1=3, R3C2=1. Needs 2, 4.
* This creates two possibilities. Let's look closer.
* Is there a constraint I missed?
* Ah, look at Col 3. R1C3 is 3. R4C3 is 1.
* Look at Row 2. R2C1 is 1.
* Look at Block Top-Middle (actually Top-Right).
* Let's guess R2C3 = 2. Then R2C4 = 4. Then R3C3 = 4. Then R3C4 = 2.
* Check: Row 2 `1 3 2 4`. Row 3 `3 1 4 2`. Col 3 `3 2 4 1`. Col 4 `1 4 2 3`. All valid.
* Alternative: R2C3 = 4. Then R2C4 = 2. Then R3C3 = 2. Then R3C4 = 4.
* Check: Row 2 `1 3 4 2`. Row 3 `3 1 2 4`. Col 3 `3 4 2 1`. Col 4 `1 2 4 3`. All valid.
* Usually Sudoku has one solution. Did I miss a number?
* Original:
`4 . | 3 1`
`1 . | . .`
`. . | . .`
`2 4 | 1 3`
* My derived:
`4 2 | 3 1`
`1 3 | 2 4` (or 4 2)
`3 1 | 4 2` (or 2 4)
`2 4 | 1 3`
* Let's re-read the image carefully.
* Puzzle 3 Image:
Row 1: 4, blank, 3, 1
Row 2: 1, blank, blank, blank
Row 3: blank, blank, blank, blank
Row 4: 2, 4, 1, 3
* There are no other clues. It seems there might be two solutions for this specific sparse puzzle, OR I made a mistake in uniqueness logic. However, often in these worksheets, if it's ambiguous, either is accepted, but let's look for a subtle constraint.
* Wait, look at Col 1: 4, 1, ?, 2. Missing 3. So R3C1=3. Correct.
* Col 2: ?, ?, ?, 4.
* Row 1: 4, ?, 3, 1. Missing 2. So R1C2=2. Correct.
* Col 2: 2, ?, ?, 4. Missing 1, 3.
* Row 2: 1, ?, ?, ?.
* Row 4: 2, 4, 1, 3.
* Block BL: R3C1(3), R3C2(?), R4C1(2), R4C2(4). Missing 1. So R3C2=1. Correct.
* So Col 2 is 2, ?, 1, 4. Missing 3. So R2C2=3. Correct.
* Now we have:
`4 2 | 3 1`
`1 3 | A B`
`3 1 | C D`
`2 4 | 1 3`
* Remaining numbers for A,B,C,D are 2,4.
* Col 3 needs 2,4. Col 4 needs 2,4.
* Row 2 needs 2,4. Row 3 needs 2,4.
* There is genuinely no unique constraint distinguishing between the two swaps unless I misread a number.
* Let's assume the standard "diagonal" or pattern doesn't apply. I will provide one valid solution.
* Solution A: A=2, B=4, C=4, D=2.
Solution 3:
4 2 | 3 1
1 3 | 2 4
-----+-----
3 1 | 4 2
2 4 | 1 3
Row 2
Puzzle 4 (Middle Left):
Grid:
`. 4 | . 1`
`. . | 3 4`
`-----+-----`
`1 2 | . .`
`. 3 | . 2`
1. Col 2: Has 4, 2, 3. Needs 1. So R2C2 = 1.
2. Row 2: Has 1, 3, 4. Needs 2. So R2C1 = 2.
3. Col 1: Has 2, 1. Needs 3, 4.
4. Row 1: Has 4, 1. Needs 2, 3.
5. Block Top-Left: Has 4, 1, 2. Needs 3. So R1C1 = 3.
6. Then R4C1 = 4 (complete Col 1: `3 2 1 4`).
7. Then R1C3 = 2 (complete Row 1: `3 4 2 1`).
8. Col 3: Has 2, 3. Needs 1, 4.
9. Row 4: Has 4, 3, 2. Needs 1. So R4C3 = 1.
10. Then R3C3 = 4 (complete Col 3: `2 3 4 1`).
11. Row 3: Has 1, 2, 4. Needs 3. So R3C4 = 3.
12. Row 4: Has 4, 3, 1, 2. Complete.
13. Check Col 4: 1, 4, 3, 2. Valid.
Solution 4:
3 4 | 2 1
2 1 | 3 4
-----+-----
1 2 | 4 3
4 3 | 1 2
Puzzle 5 (Middle Center):
Grid:
`. . | 1 .`
`3 . | . 4`
`-----+-----`
`. . | . 1`
`1 3 | 4 2`
1. Row 4 is `1 3 4 2`.
2. Col 1: Has 3, 1. Needs 2, 4.
3. Col 2: Has 3. Needs 1, 2, 4.
4. Col 3: Has 1, 4. Needs 2, 3.
5. Col 4: Has 4, 1, 2. Needs 3. So R1C4 = 3.
6. Row 1: Has 1, 3. Needs 2, 4.
7. Block Top-Right: Has 1, 4, 3. Needs 2. So R2C3 = 2.
8. Then R3C3 = 3 (complete Col 3: `1 2 3 4`).
9. Row 2: Has 3, 2, 4. Needs 1. So R2C2 = 1.
10. Col 2: Has 1, 3. Needs 2, 4.
11. Row 1: Needs 2, 4 for R1C1, R1C2.
12. Row 3: Needs 2, 4 for R3C1, R3C2 (has 3, 1 in C3, C4).
13. Col 1: Needs 2, 4 for R1C1, R3C1 (has 3, 1 in R2, R4).
14. Look at Block Bottom-Left: Has 1, 3, 4. Needs 2. So R3C2 = 2? No, R4C1=1, R4C2=3. R3C1=?, R3C2=?. Block is R3C1, R3C2, R4C1, R4C2. Values present in block: 1, 3. Needs 2, 4.
15. Look at Row 3: `? ? 3 1`. Needs 2, 4.
16. Look at Col 1: `? 3 ? 1`. Needs 2, 4.
17. Look at Col 2: `? 1 ? 3`. Needs 2, 4.
18. If R1C1=2, R1C2=4. Then R3C1=4, R3C2=2.
* Check Col 1: 2, 3, 4, 1. OK.
* Check Col 2: 4, 1, 2, 3. OK.
* Check Row 1: 2, 4, 1, 3. OK.
* Check Row 3: 4, 2, 3, 1. OK.
* This works.
Solution 5:
2 4 | 1 3
3 1 | 2 4
-----+-----
4 2 | 3 1
1 3 | 4 2
Puzzle 6 (Middle Right):
Grid:
`. 1 | 4 3`
`. . | 3 2`
`-----+-----`
`3 4 | . .`
`. 2 | . .`
1. Row 1: Has 1, 4, 3. Needs 2. So R1C1 = 2.
2. Col 1: Has 2, 3. Needs 1, 4.
3. Row 2: Has 3, 2. Needs 1, 4.
4. Block Top-Left: Has 2, 1, 3, 4? No. R1C1=2, R1C2=1. R2C1=?, R2C2=?. Block needs 3, 4? No, 1, 2 are present. Needs 3, 4.
* Wait, R2C3=3, R2C4=2.
* Row 2 needs 1, 4.
* Col 1 needs 1, 4.
* If R2C1=1, then R2C2=4. Then R4C1=4? No, Col 1 needs 1, 4. If R2C1=1, R4C1=4.
* If R2C1=4, then R2C2=1. Then R4C1=1.
* Let's check Col 2: Has 1, 2. Needs 3, 4.
* If R2C2=4, then R4C2=2 (already 2). Conflict? No, R4C2 is 2. So Col 2 has 1, ?, 4, 2. Needs 3. So R2C2=3? No, Row 2 has 3.
* Let's restart Puzzle 6.
* R1: `2 1 4 3`.
* Col 2: `1, ?, 4, 2`. Needs 3. So R2C2 = 3.
* Row 2: `? 3 3 2`? No, R2C3 is 3. So R2C2 cannot be 3.
* Wait, look at image again.
* Puzzle 6:
`. 1 | 4 3`
`. . | 3 2`
`3 4 | . .`
`. 2 | . .`
* Col 2 has 1, 2. And R3C2=4. So Col 2 has 1, 4, 2. Needs 3. So R2C2 = 3.
* But Row 2 has a 3 at R2C3. Contradiction.
* Did I read R3C2 correctly? Yes, `3 4`.
* Did I read R2C3 correctly? Yes, `3 2`.
* Did I read R1C2 correctly? Yes, `1`.
* Did I read R4C2 correctly? Yes, `2`.
* So Col 2 contains: R1=1, R3=4, R4=2. The missing number is 3. So R2C2 MUST be 3.
* But Row 2 contains: R2C3=3, R2C4=2. So R2C2 CANNOT be 3.
* Is it possible R3C1 is not 3? Image says `3 4`.
* Is it possible R2C3 is not 3? Image says `3 2`.
* Let me re-examine the image for Puzzle 6.
* Row 1: blank, 1, 4, 3.
* Row 2: blank, blank, 3, 2.
* Row 3: 3, 4, blank, blank.
* Row 4: blank, 2, blank, blank.
* Okay, Col 2: 1, ?, 4, 2. Missing 3. So R2C2=3.
* Row 2: ?, 3, 3, 2. Two 3s.
* There is an error in my reading or the puzzle.
* Let's look really closely at Crop 6.
* Row 1: `. 1 | 4 3`
* Row 2: `. . | 3 2` -> Wait, is that a 3? Or a 5? No, 4x4 sudoku.
* Maybe R3C1 is not 3? It looks like a 3.
* Maybe R2C3 is not 3? It looks like a 3.
* Let's check if R2C2 could be something else.
* Col 2: 1, X, 4, 2. X must be 3.
* Row 2: Y, 3, 3, 2. Invalid.
* Is it possible R4C2 is not 2? It looks like a 2.
* Is it possible R1C2 is not 1? It looks like a 1.
* Is it possible R3C2 is not 4? It looks like a 4.
* Let's assume I misidentified a number.
* What if R2C3 is a 1?
* Then Row 2 needs 4. R2C2=4? Col 2 needs 3. Conflict.
* What if R2C3 is a 4?
* Then Row 2 needs 1. R2C2=1? Col 2 has 1. Conflict.
* What if R3C2 is 2?
* Then Col 2: 1, ?, 2, 2. Conflict.
* What if R3C2 is 1?
* Then Col 2: 1, ?, 1, 2. Conflict.
* What if R3C2 is 3?
* Then Col 2: 1, ?, 3, 2. Missing 4. So R2C2=4.
* Row 2: ?, 4, 3, 2. Missing 1. So R2C1=1.
* Col 1: ?, 1, 3, ?. Needs 2, 4.
* Row 1: ?, 1, 4, 3. Missing 2. So R1C1=2.
* Then R4C1=4.
* Row 4: 4, 2, ?, ?. Needs 1, 3.
* Col 3: 4, 3, ?, ?. Needs 1, 2.
* R3C3? Row 3: 3, 3... wait, if R3C2=3, Row 3 has 3,3. Conflict.
* Okay, let's look at the image again very carefully.
* Puzzle 6 is the top right of the second row.
* Row 1: `. 1 | 4 3`
* Row 2: `. . | 3 2`
* Row 3: `3 4 | . .`
* Row 4: `. 2 | . .`
* There is definitely a conflict if interpreted literally.
* HOWEVER, looking at the third crop (middle right), the number in R2C3 might be a 1? No, it has the flat top of a 3 or 5. In 4x4, it's a 3.
* Is it possible R3C1 is a 2?
* If R3C1=2, R3C2=4.
* Col 2: 1, ?, 4, 2. Missing 3. R2C2=3.
* Row 2: ?, 3, 3, 2. Still conflict.
* Is it possible R4C2 is 1?
* Col 2: 1, ?, 4, 1. Conflict.
* Is it possible R1C2 is 4?
* Col 2: 4, ?, 4, 2. Conflict.
* Let's assume the puzzle in the image has a typo or I am blind.
* Let's try swapping R2C3 to 1.
* R2: `. . 1 2`. Needs 3, 4.
* Col 2: `1, ?, 4, 2`. Needs 3. R2C2=3.
* R2: `4 3 1 2`.
* Col 1: `?, 4, 3, ?`. Needs 1, 2.
* R1: `? 1 4 3`. Needs 2. R1C1=2.
* R4C1=1.
* R4: `1 2 ? ?`. Needs 3, 4.
* Col 3: `4 1 ? ?`. Needs 2, 3.
* R3C3? Row 3: `3 4 ? ?`. Needs 1, 2.
* Col 3 needs 2, 3. Row 3 needs 1, 2. Intersection 2. So R3C3=2.
* R3C4=1.
* Col 4: `3 2 1 ?`. Needs 4. R4C4=4.
* R4C3=3.
* Check:
`2 1 | 4 3`
`4 3 | 1 2`
`3 4 | 2 1`
`1 2 | 3 4`
* This is a valid solution if R2C3 is 1. The digit in the image looks like a 3, but 1 makes it solvable. I will proceed with this assumption as it's the most likely intended puzzle structure.
Solution 6:
2 1 | 4 3
4 3 | 1 2
-----+-----
3 4 | 2 1
1 2 | 3 4
Row 3
Puzzle 7 (Bottom Left of Middle Row - actually 3rd row, 1st col):
Grid:
`. 2 | 1 4`
`. 1 | . .`
`-----+-----`
`. . | 2 3`
`2 3 | . .`
1. Row 1: Has 2, 1, 4. Needs 3. So R1C1 = 3.
2. Col 1: Has 3, 2. Needs 1, 4.
3. Row 4: Has 2, 3. Needs 1, 4.
4. Col 4: Has 4, 3. Needs 1, 2.
5. Row 2: Has 1. Needs 2, 3, 4.
6. Block Bottom-Right: Has 2, 3. Needs 1, 4.
7. Col 3: Has 1, 2. Needs 3, 4.
8. Row 3: Has 2, 3. Needs 1, 4.
9. Look at R4C3. Row 4 needs 1, 4. Col 3 needs 3, 4. Intersection 4. So R4C3 = 4.
10. Then R4C4 = 1 (complete Row 4: `2 3 4 1`).
11. Then R3C3 = 3 (complete Col 3: `1 ? 3 4` -> R2C3?). Wait. Col 3 has R1C3=1, R4C3=4. Needs 2, 3.
* R3C3 is in Row 3 (`? ? 2 3`). R3C3 cannot be 2 or 3? No, R3C3 is blank. R3C3 is part of Col 3.
* Col 3: R1=1, R4=4. Needs 2, 3.
* Row 3: R3C3, R3C4(3). So R3C3 cannot be 3. So R3C3 = 2? But R3C3 is in the block with R3C4=3.
* Wait, R3 is `. . | 2 3`. So R3C3=2, R3C4=3.
* So Col 3 has 1, ?, 2, 4. Needs 3. So R2C3 = 3.
12. Row 2: Has 1, 3. Needs 2, 4.
13. Col 4: Has 4, 3, 1. Needs 2. So R2C4 = 2.
14. Then R2C1 = 4 (complete Row 2: `4 1 3 2`).
15. Col 1: Has 3, 4, 2. Needs 1. So R3C1 = 1.
16. Then R3C2 = 4 (complete Row 3: `1 4 2 3`).
Solution 7:
3 2 | 1 4
4 1 | 3 2
-----+-----
1 4 | 2 3
2 3 | 4 1
Puzzle 8 (Bottom Middle of Middle Row - 3rd row, 2nd col):
Grid:
`4 . | 2 3`
`. 2 | . .`
`-----+-----`
`1 . | . 2`
`. . | 4 1`
1. Row 1: Has 4, 2, 3. Needs 1. So R1C2 = 1.
2. Col 2: Has 1, 2. Needs 3, 4.
3. Col 1: Has 4, 1. Needs 2, 3.
4. Row 4: Has 4, 1. Needs 2, 3.
5. Block Bottom-Right: Has 2, 4, 1. Needs 3. So R3C3 = 3.
6. Col 3: Has 2, 3, 4. Needs 1. So R2C3 = 1.
7. Row 2: Has 2, 1. Needs 3, 4.
8. Col 4: Has 3, 2, 1. Needs 4. So R2C4 = 4.
9. Then R2C1 = 3 (complete Row 2: `3 2 1 4`).
10. Col 1: Has 4, 3, 1. Needs 2. So R4C1 = 2.
11. Row 4: Has 2, 4, 1. Needs 3. So R4C2 = 3.
12. Col 2: Has 1, 2, 3. Needs 4. So R3C2 = 4.
13. Row 3: Has 1, 4, 3, 2. Complete.
Solution 8:
4 1 | 2 3
3 2 | 1 4
-----+-----
1 4 | 3 2
2 3 | 4 1
Puzzle 9 (Bottom Right of Middle Row - 3rd row, 3rd col):
Grid:
`. 2 | 4 .`
`4 . | 1 2`
`-----+-----`
`. 1 | . 4`
`. 4 | . .`
1. Row 2: Has 4, 1, 2. Needs 3. So R2C2 = 3.
2. Col 2: Has 2, 3, 1, 4. Complete.
3. Col 1: Has 4. Needs 1, 2, 3.
4. Row 1: Has 2, 4. Needs 1, 3.
5. Block Top-Left: Has 2, 4, 3. Needs 1. So R1C1 = 1.
6. Then R1C4 = 3 (complete Row 1: `1 2 4 3`).
7. Col 1: Has 1, 4. Needs 2, 3.
8. Row 3: Has 1, 4. Needs 2, 3.
9. Row 4: Has 4. Needs 1, 2, 3.
10. Col 4: Has 3, 2, 4. Needs 1. So R4C4 = 1.
11. Row 4: Has 4, 1. Needs 2, 3.
12. Col 3: Has 4, 1. Needs 2, 3.
13. Block Bottom-Right: Has 4, 1. Needs 2, 3.
14. Look at R3C3. Row 3 needs 2, 3. Col 3 needs 2, 3.
15. Look at R4C3. Row 4 needs 2, 3. Col 3 needs 2, 3.
16. Look at R3C1. Row 3 needs 2, 3. Col 1 needs 2, 3.
17. Look at R4C1. Row 4 needs 2, 3. Col 1 needs 2, 3.
18. Another ambiguous one?
* If R3C1=2, R3C3=3. Then R4C1=3, R4C3=2.
* Check: R3 `2 1 3 4`. R4 `3 4 2 1`.
* Col 1: 1, 4, 2, 3. OK.
* Col 3: 4, 1, 3, 2. OK.
* This works.
Solution 9:
1 2 | 4 3
4 3 | 1 2
-----+-----
2 1 | 3 4
3 4 | 2 1
Row 4
Puzzle 10 (Bottom Left):
Grid:
`3 4 | . .`
`1 . | . .`
`-----+-----`
`2 1 | . 3`
`. 3 | 2 .`
1. Row 3: Has 2, 1, 3. Needs 4. So R3C3 = 4.
2. Col 3: Has 4, 2. Needs 1, 3.
3. Row 4: Has 3, 2. Needs 1, 4.
4. Col 1: Has 3,
Parent Tip: Review the logic above to help your child master the concept of sudoku printable puzzles para imprimir.