Free Printable Easy Sudoku with the Answer #1 - Free Printable
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Step-by-step solution for: Free Printable Easy Sudoku with the Answer #1
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Show Answer Key & Explanations
Step-by-step solution for: Free Printable Easy Sudoku with the Answer #1
To solve this Sudoku puzzle, we need to fill in the empty cells with numbers from 1 to 9. The rules are:
1. Each row must contain the numbers 1–9 exactly once.
2. Each column must contain the numbers 1–9 exactly once.
3. Each of the nine 3x3 boxes must contain the numbers 1–9 exactly once.
Let's solve it step by step, looking for rows, columns, or boxes that are almost full.
Step 1: Look at Row 5 (the middle row)
Current numbers: `2, _, 3, _, 1, 6, 4, 7, 8`
Missing numbers: 5 and 9.
- Look at Column 2 (the second vertical line). It already has a 7, 4, 5... wait, let's look closer.
- Let's check Box 4 (middle-left box). The numbers present are 4, 5, 2, 3, 7, 6. Missing are 1, 8, 9.
- Let's go back to Row 5. The empty spots are at Column 2 and Column 4.
- In Column 4, we see numbers 8, 1, 3, 9, 2. No 5 or 9 yet? Wait, Row 4 Col 4 is 3. Row 6 Col 4 is 9. So Column 4 already has a 9.
- Therefore, the cell at Row 5, Column 4 cannot be 9. It must be 5.
- This means the cell at Row 5, Column 2 must be 9.
*Row 5 is now: 2, 9, 3, 5, 1, 6, 4, 7, 8.*
Step 2: Look at Column 4
Current numbers: `8, 1, _, 3, 5, 9, 2, _, _`
Missing numbers: 4, 6, 7.
- Row 3 Col 4 is empty. Row 8 Col 4 is empty. Row 9 Col 4 is empty.
- Let's look at Row 3. Current: `8, _, _, _, 6, _, _, _, 1`. Missing: 2, 3, 4, 5, 7, 9.
- Let's look at Box 2 (top-middle). Numbers present: 8, 3, 1, 2, 6, 7, 4. Missing: 5, 9.
- The empty cells in Box 2 are Row 1 Col 6 and Row 3 Col 4.
- Row 1 already has a 4, 7, 8, 3.
- Let's look at Row 1 Col 6. Column 6 has 2, 6, 5, 1.
- Let's look at Row 3 Col 4 again. In Box 2, the missing numbers are 5 and 9.
- Row 3 already has a 1, 6, 8.
- Row 1 already has 8, 3, 7, 4.
- Let's check Column 6. It contains 2, 6, 5, 1.
- Actually, let's look at Box 2 again. Cells are R1C4(8), R1C5(3), R1C6(?), R2C4(1), R2C5(2), R2C6(?), R3C4(?), R3C5(6), R3C6(?).
- Wait, R2C6 is empty in the image? No, R2 is `_ _ 4 | 1 2 _ | 9 8 3`. So R2C6 is empty.
- Numbers in Box 2 so far: 8, 3, 1, 2, 6. Missing: 4, 5, 7, 9.
- Empty cells in Box 2: R1C6, R2C6, R3C4, R3C6.
- Let's look at Row 2. Missing numbers: 5, 6, 7. (Has 4,1,2,9,8,3). Empty spots: C1, C2, C6.
- C1 has 8,4,2,7,9,5. Missing 1,3,6. But Row 2 needs 5,6,7. So R2C1 must be 6? No, C1 has 8,4,2,7,9,5. It doesn't have 1,3,6.
- Let's restart with a simpler observation.
Let's try Column 5.
Numbers: 3, 2, 6, 7, 1, 4, 5, _, _.
Missing: 8, 9.
- Row 8 Col 5 is empty. Row 9 Col 5 is empty.
- Row 8 has `_, _, 2, _, _, 1, _, _, _`.
- Row 9 has `5, 7, _, _, _, _, _, _, 4`.
- Look at Row 8. Does it have an 8 or 9? No.
- Look at Row 9. Does it have an 8 or 9? No.
- Look at Box 8 (bottom-middle). Numbers present: 2, 5, 1.
- Let's look at Row 7: `9, _, _, 2, 5, _, _, _, 7`. Missing: 1, 3, 4, 6, 8.
- Let's look at Column 5 again. Missing 8, 9.
- In Row 8, look at Box 7 (bottom-left). Numbers: 9, 2, 5, 7.
- Let's look at Row 9. `5, 7, _`.
- Let's look at Column 1. `_, _, 8, 4, 2, 7, 9, _, 5`. Missing: 1, 3, 6.
- R1C1, R2C1, R8C1 are empty.
- Row 1 has 7,8,3,4.
- Row 2 has 4,1,2,9,8,3.
- Row 8 has 2,5,1,7.
Let's use a standard solver logic path carefully.
Box 5 (Center Box):
Cells:
R4C4=3, R4C5=7, R4C6=2
R5C4=5 (found earlier), R5C5=1, R5C6=6
R6C4=9, R6C5=4, R6C6=?
Missing number in Box 5 is 8.
So R6C6 = 8.
Row 6:
Current: `7, _, 6, 9, 4, 8, _, _, _`
Missing: 1, 2, 3, 5.
Empty cells: C2, C7, C8, C9.
- C2: Column 2 has 9 (from Step 1), 7, 5? Let's check Col 2.
Col 2 values so far: R5=9. R1=?, R2=?, R3=?, R4=?, R6=?, R7=?, R8=?, R9=7.
This is getting complex. Let's look for "naked singles".
Look at Row 4:
`4, _, 5, 3, 7, 2, _, 1, 9`
Missing: 6, 8.
Empty cells: C2, C7.
- Check Column 2. Does it have 6 or 8?
- Check Column 7. Does it have 6 or 8?
- Column 7 has 9, 4.
- Column 2 has 7 (R9), 9 (R5).
- Let's look at Box 4 (Middle Left).
Numbers in Box 4: 4,5,2,3,7,6,9 (R6C4 is 9, but that's Box 5).
Box 4 cells:
R4C1=4, R4C2=?, R4C3=5
R5C1=2, R5C2=9, R5C3=3
R6C1=7, R6C2=?, R6C3=6
Missing in Box 4: 1, 8.
So R4C2 and R6C2 are 1 and 8.
- Look at Row 4. We said R4C2 is either 6 or 8.
- Intersection: R4C2 must be 8 (because Box 4 needs 1 or 8, and Row 4 needs 6 or 8. The common number is 8).
- Therefore, R4C2 = 8.
- Then R4C7 = 6 (last number in Row 4).
- Since R4C2=8, then R6C2 = 1 (last number in Box 4).
Update Row 6:
Current: `7, 1, 6, 9, 4, 8, _, _, _`
Missing: 2, 3, 5.
Empty cells: C7, C8, C9.
- Check Column 7. Has 9, 4, 6, 7.
- Check Column 8. Has 4, 8, 1, 7.
- Check Column 9. Has 3, 1, 9, 8, 7, 4.
Look at Column 2:
Values so far: R4=8, R5=9, R6=1, R9=7.
Missing: 2, 3, 4, 5, 6.
Cells: R1, R2, R3, R7, R8.
- R1C2: Row 1 has 7,8,3,4.
- R2C2: Row 2 has 4,1,2,9,8,3.
- R3C2: Row 3 has 8,6,1.
- R7C2: Row 7 has 9,2,5,7.
- R8C2: Row 8 has 2,5,1,7.
Let's look at Box 1 (Top Left).
Cells:
R1C1=?, R1C2=?, R1C3=7
R2C1=?, R2C2=?, R2C3=4
R3C1=8, R3C2=?, R3C3=?
Numbers present: 7, 4, 8.
Missing: 1, 2, 3, 5, 6, 9.
Let's look at Row 2: `_ _ 4 | 1 2 _ | 9 8 3`
Missing: 5, 6, 7.
Cells: C1, C2, C6.
- C6 is in Box 2.
- C1, C2 are in Box 1.
- In Box 1, we need 1,2,3,5,6,9.
- Row 2 needs 5,6,7 for C1,C2,C6.
- C1 and C2 are in Box 1. So Box 1 must contain two of {5,6,7}.
- But Box 1 already has 4,7,8. So 7 is already in Box 1 (at R1C3).
- Therefore, R2C1 and R2C2 cannot be 7.
- So R2C6 must be 7.
- Now Row 2 missing: 5, 6 for C1, C2.
- Look at Column 1. Has 8,4,2,7,9,5. Missing 1,3,6.
- R2C1 must be 5 or 6. Column 1 needs 1,3,6. So R2C1 can be 6.
- Look at Column 2. Needs 2,3,4,5,6.
- If R2C1 is 6, R2C2 is 5.
- If R2C1 is 5, R2C2 is 6.
- Let's check Column 1 again. Values: R3=8, R4=4, R5=2, R6=7, R7=9, R9=5.
- Missing in Col 1: 1, 3, 6.
- R1C1, R2C1, R8C1 are empty.
- R2C1 is either 5 or 6. But Col 1 needs 1,3,6. So R2C1 MUST be 6.
- Therefore, R2C2 = 5.
- And R2C6 = 7 (confirmed).
Now Col 1 missing: 1, 3. Cells: R1C1, R8C1.
- Row 1 has 7,8,3,4. So R1C1 cannot be 3.
- Therefore, R1C1 = 1.
- Therefore, R8C1 = 3.
Update Box 1:
Present: 1(R1C1), 7(R1C3), 6(R2C1), 5(R2C2), 4(R2C3), 8(R3C1).
Missing: 2, 3, 9.
Cells: R1C2, R3C2, R3C3.
- Row 1: `1, _, 7, 8, 3, _, _, 4, _`. Missing: 2, 5, 6, 9.
- R1C2 is in Box 1. Must be 2, 3, or 9.
- Row 1 already has 3. So R1C2 is 2 or 9.
- Col 2 has 5(R2), 8(R4), 9(R5), 1(R6), 7(R9).
- Col 2 missing: 2, 3, 4, 6.
- R1C2 must be 2 (since 9 is in R5C2). Wait, R5C2 is 9. So Col 2 has 9.
- So R1C2 cannot be 9.
- Therefore, R1C2 = 2.
- Now Box 1 missing: 3, 9. Cells: R3C2, R3C3.
- Row 3: `8, _, _, _, 6, _, _, _, 1`.
- Col 2 missing: 3, 4, 6. (Has 2,5,8,9,1,7).
- R3C2 is in Col 2. Must be 3, 4, or 6.
- Box 1 needs 3 or 9. So R3C2 must be 3.
- Therefore, R3C3 = 9.
Finish Column 2:
Values: 2(R1), 5(R2), 3(R3), 8(R4), 9(R5), 1(R6), 7(R9).
Missing: 4, 6.
Cells: R7C2, R8C2.
- Row 7: `9, _, _, 2, 5, _, _, _, 7`.
- Row 8: `3, _, 2, _, _,
1. Each row must contain the numbers 1–9 exactly once.
2. Each column must contain the numbers 1–9 exactly once.
3. Each of the nine 3x3 boxes must contain the numbers 1–9 exactly once.
Let's solve it step by step, looking for rows, columns, or boxes that are almost full.
Step 1: Look at Row 5 (the middle row)
Current numbers: `2, _, 3, _, 1, 6, 4, 7, 8`
Missing numbers: 5 and 9.
- Look at Column 2 (the second vertical line). It already has a 7, 4, 5... wait, let's look closer.
- Let's check Box 4 (middle-left box). The numbers present are 4, 5, 2, 3, 7, 6. Missing are 1, 8, 9.
- Let's go back to Row 5. The empty spots are at Column 2 and Column 4.
- In Column 4, we see numbers 8, 1, 3, 9, 2. No 5 or 9 yet? Wait, Row 4 Col 4 is 3. Row 6 Col 4 is 9. So Column 4 already has a 9.
- Therefore, the cell at Row 5, Column 4 cannot be 9. It must be 5.
- This means the cell at Row 5, Column 2 must be 9.
*Row 5 is now: 2, 9, 3, 5, 1, 6, 4, 7, 8.*
Step 2: Look at Column 4
Current numbers: `8, 1, _, 3, 5, 9, 2, _, _`
Missing numbers: 4, 6, 7.
- Row 3 Col 4 is empty. Row 8 Col 4 is empty. Row 9 Col 4 is empty.
- Let's look at Row 3. Current: `8, _, _, _, 6, _, _, _, 1`. Missing: 2, 3, 4, 5, 7, 9.
- Let's look at Box 2 (top-middle). Numbers present: 8, 3, 1, 2, 6, 7, 4. Missing: 5, 9.
- The empty cells in Box 2 are Row 1 Col 6 and Row 3 Col 4.
- Row 1 already has a 4, 7, 8, 3.
- Let's look at Row 1 Col 6. Column 6 has 2, 6, 5, 1.
- Let's look at Row 3 Col 4 again. In Box 2, the missing numbers are 5 and 9.
- Row 3 already has a 1, 6, 8.
- Row 1 already has 8, 3, 7, 4.
- Let's check Column 6. It contains 2, 6, 5, 1.
- Actually, let's look at Box 2 again. Cells are R1C4(8), R1C5(3), R1C6(?), R2C4(1), R2C5(2), R2C6(?), R3C4(?), R3C5(6), R3C6(?).
- Wait, R2C6 is empty in the image? No, R2 is `_ _ 4 | 1 2 _ | 9 8 3`. So R2C6 is empty.
- Numbers in Box 2 so far: 8, 3, 1, 2, 6. Missing: 4, 5, 7, 9.
- Empty cells in Box 2: R1C6, R2C6, R3C4, R3C6.
- Let's look at Row 2. Missing numbers: 5, 6, 7. (Has 4,1,2,9,8,3). Empty spots: C1, C2, C6.
- C1 has 8,4,2,7,9,5. Missing 1,3,6. But Row 2 needs 5,6,7. So R2C1 must be 6? No, C1 has 8,4,2,7,9,5. It doesn't have 1,3,6.
- Let's restart with a simpler observation.
Let's try Column 5.
Numbers: 3, 2, 6, 7, 1, 4, 5, _, _.
Missing: 8, 9.
- Row 8 Col 5 is empty. Row 9 Col 5 is empty.
- Row 8 has `_, _, 2, _, _, 1, _, _, _`.
- Row 9 has `5, 7, _, _, _, _, _, _, 4`.
- Look at Row 8. Does it have an 8 or 9? No.
- Look at Row 9. Does it have an 8 or 9? No.
- Look at Box 8 (bottom-middle). Numbers present: 2, 5, 1.
- Let's look at Row 7: `9, _, _, 2, 5, _, _, _, 7`. Missing: 1, 3, 4, 6, 8.
- Let's look at Column 5 again. Missing 8, 9.
- In Row 8, look at Box 7 (bottom-left). Numbers: 9, 2, 5, 7.
- Let's look at Row 9. `5, 7, _`.
- Let's look at Column 1. `_, _, 8, 4, 2, 7, 9, _, 5`. Missing: 1, 3, 6.
- R1C1, R2C1, R8C1 are empty.
- Row 1 has 7,8,3,4.
- Row 2 has 4,1,2,9,8,3.
- Row 8 has 2,5,1,7.
Let's use a standard solver logic path carefully.
Box 5 (Center Box):
Cells:
R4C4=3, R4C5=7, R4C6=2
R5C4=5 (found earlier), R5C5=1, R5C6=6
R6C4=9, R6C5=4, R6C6=?
Missing number in Box 5 is 8.
So R6C6 = 8.
Row 6:
Current: `7, _, 6, 9, 4, 8, _, _, _`
Missing: 1, 2, 3, 5.
Empty cells: C2, C7, C8, C9.
- C2: Column 2 has 9 (from Step 1), 7, 5? Let's check Col 2.
Col 2 values so far: R5=9. R1=?, R2=?, R3=?, R4=?, R6=?, R7=?, R8=?, R9=7.
This is getting complex. Let's look for "naked singles".
Look at Row 4:
`4, _, 5, 3, 7, 2, _, 1, 9`
Missing: 6, 8.
Empty cells: C2, C7.
- Check Column 2. Does it have 6 or 8?
- Check Column 7. Does it have 6 or 8?
- Column 7 has 9, 4.
- Column 2 has 7 (R9), 9 (R5).
- Let's look at Box 4 (Middle Left).
Numbers in Box 4: 4,5,2,3,7,6,9 (R6C4 is 9, but that's Box 5).
Box 4 cells:
R4C1=4, R4C2=?, R4C3=5
R5C1=2, R5C2=9, R5C3=3
R6C1=7, R6C2=?, R6C3=6
Missing in Box 4: 1, 8.
So R4C2 and R6C2 are 1 and 8.
- Look at Row 4. We said R4C2 is either 6 or 8.
- Intersection: R4C2 must be 8 (because Box 4 needs 1 or 8, and Row 4 needs 6 or 8. The common number is 8).
- Therefore, R4C2 = 8.
- Then R4C7 = 6 (last number in Row 4).
- Since R4C2=8, then R6C2 = 1 (last number in Box 4).
Update Row 6:
Current: `7, 1, 6, 9, 4, 8, _, _, _`
Missing: 2, 3, 5.
Empty cells: C7, C8, C9.
- Check Column 7. Has 9, 4, 6, 7.
- Check Column 8. Has 4, 8, 1, 7.
- Check Column 9. Has 3, 1, 9, 8, 7, 4.
Look at Column 2:
Values so far: R4=8, R5=9, R6=1, R9=7.
Missing: 2, 3, 4, 5, 6.
Cells: R1, R2, R3, R7, R8.
- R1C2: Row 1 has 7,8,3,4.
- R2C2: Row 2 has 4,1,2,9,8,3.
- R3C2: Row 3 has 8,6,1.
- R7C2: Row 7 has 9,2,5,7.
- R8C2: Row 8 has 2,5,1,7.
Let's look at Box 1 (Top Left).
Cells:
R1C1=?, R1C2=?, R1C3=7
R2C1=?, R2C2=?, R2C3=4
R3C1=8, R3C2=?, R3C3=?
Numbers present: 7, 4, 8.
Missing: 1, 2, 3, 5, 6, 9.
Let's look at Row 2: `_ _ 4 | 1 2 _ | 9 8 3`
Missing: 5, 6, 7.
Cells: C1, C2, C6.
- C6 is in Box 2.
- C1, C2 are in Box 1.
- In Box 1, we need 1,2,3,5,6,9.
- Row 2 needs 5,6,7 for C1,C2,C6.
- C1 and C2 are in Box 1. So Box 1 must contain two of {5,6,7}.
- But Box 1 already has 4,7,8. So 7 is already in Box 1 (at R1C3).
- Therefore, R2C1 and R2C2 cannot be 7.
- So R2C6 must be 7.
- Now Row 2 missing: 5, 6 for C1, C2.
- Look at Column 1. Has 8,4,2,7,9,5. Missing 1,3,6.
- R2C1 must be 5 or 6. Column 1 needs 1,3,6. So R2C1 can be 6.
- Look at Column 2. Needs 2,3,4,5,6.
- If R2C1 is 6, R2C2 is 5.
- If R2C1 is 5, R2C2 is 6.
- Let's check Column 1 again. Values: R3=8, R4=4, R5=2, R6=7, R7=9, R9=5.
- Missing in Col 1: 1, 3, 6.
- R1C1, R2C1, R8C1 are empty.
- R2C1 is either 5 or 6. But Col 1 needs 1,3,6. So R2C1 MUST be 6.
- Therefore, R2C2 = 5.
- And R2C6 = 7 (confirmed).
Now Col 1 missing: 1, 3. Cells: R1C1, R8C1.
- Row 1 has 7,8,3,4. So R1C1 cannot be 3.
- Therefore, R1C1 = 1.
- Therefore, R8C1 = 3.
Update Box 1:
Present: 1(R1C1), 7(R1C3), 6(R2C1), 5(R2C2), 4(R2C3), 8(R3C1).
Missing: 2, 3, 9.
Cells: R1C2, R3C2, R3C3.
- Row 1: `1, _, 7, 8, 3, _, _, 4, _`. Missing: 2, 5, 6, 9.
- R1C2 is in Box 1. Must be 2, 3, or 9.
- Row 1 already has 3. So R1C2 is 2 or 9.
- Col 2 has 5(R2), 8(R4), 9(R5), 1(R6), 7(R9).
- Col 2 missing: 2, 3, 4, 6.
- R1C2 must be 2 (since 9 is in R5C2). Wait, R5C2 is 9. So Col 2 has 9.
- So R1C2 cannot be 9.
- Therefore, R1C2 = 2.
- Now Box 1 missing: 3, 9. Cells: R3C2, R3C3.
- Row 3: `8, _, _, _, 6, _, _, _, 1`.
- Col 2 missing: 3, 4, 6. (Has 2,5,8,9,1,7).
- R3C2 is in Col 2. Must be 3, 4, or 6.
- Box 1 needs 3 or 9. So R3C2 must be 3.
- Therefore, R3C3 = 9.
Finish Column 2:
Values: 2(R1), 5(R2), 3(R3), 8(R4), 9(R5), 1(R6), 7(R9).
Missing: 4, 6.
Cells: R7C2, R8C2.
- Row 7: `9, _, _, 2, 5, _, _, _, 7`.
- Row 8: `3, _, 2, _, _,
Parent Tip: Review the logic above to help your child master the concept of printable sudoku puzzles easy 1 answers.