Sudoku puzzle worksheet for beginners, Level 1.1, from Superstar Worksheets.
Sudoku puzzle worksheet from Superstar Worksheets, Level 1.1, with a 9x9 grid partially filled, requiring numbers 1-9 in each row, column, and 3x3 box.
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Show Answer Key & Explanations
Step-by-step solution for: Sudoku Puzzles -Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Sudoku Puzzles -Worksheets Library
Let’s solve this Sudoku puzzle step by step.
We are given a 9x9 grid, divided into nine 3x3 boxes. The goal is to fill each row, each column, and each 3x3 box with the numbers 1 through 9 — no repeats allowed in any row, column, or box.
We’ll go row by row, looking for missing numbers and using logic to figure out where they go.
---
Row 1:
Given: _ 7 _ | 3 _ _ | 5 _ 6
Missing numbers: 1, 2, 4, 8, 9
Look at columns and boxes to eliminate possibilities.
- Column 1: already has 5, 9, 2, 6, 1 → so can’t be those → possible: 3,4,7,8 → but 3 and 7 are used in row → so only 4 or 8? Wait, let’s check box 1 (top-left 3x3).
Box 1 (rows 1–3, cols 1–3):
Current:
_ 7 _
5 1 _
_ _ 4
So in Box 1, we have: 1,4,5,7 → missing: 2,3,6,8,9
But Row 1 already has 3,5,6,7 → so in Row 1, Box 1 cells (col1, col3) must be from {1,2,4,8,9} minus what’s in box.
Actually, maybe better to look for rows/columns/boxes that are almost full.
---
Let’s try Row 9 — it’s completely filled!
1 8 5 | 2 4 3 | 9 6 7 → Good, valid.
Row 8:
6 9 7 | _ 8 5 | _ 4 3
Missing: 1,2
Check column 4: has 3,6,5,8,4,9,7,2 → wait, let’s list column 4:
Col 4:
Row1: 3
Row2: 6
Row3: 5
Row4: 8
Row5: 4
Row6: 9
Row7: 7
Row8: ?
Row9: 2
So Col 4 has: 2,3,4,5,6,7,8,9 → missing 1 → So Row8, Col4 = 1
Then Row8, Col7 must be 2 (only one left)
So Row8 becomes:
6 9 7 | 1 8 5 | 2 4 3 ✔
---
Row 7:
2 4 _ | 7 _ 9 | 8 5 1
Missing: 3,6
Check Col3:
Row1: ?
Row2: ?
Row3: 4
Row4: ?
Row5: 8
Row6: 6
Row7: ?
Row8: 7
Row9: 5
So Col3 has: 4,5,6,7,8 → missing 1,2,3,9
In Row7, Col3 must be 3 or 6.
But Box 7 (bottom-left 3x3):
Rows 7–9, Cols 1–3:
2 4 ?
6 9 7
1 8 5
Already has: 1,2,4,5,6,7,8,9 → missing 3 → So Row7, Col3 = 3
Then Row7, Col5 = 6 (only one left)
So Row7:
2 4 3 | 7 6 9 | 8 5 1 ✔
---
Row 6:
_ _ 6 | 9 2 7 | 1 _ _
Missing: 3,4,5,8
Check Box 6 (middle-right 3x3):
Rows 4–6, Cols 7–9:
3 7 4
6 _ _
1 _ _
Wait, Row4: ... 3 7 4
Row5: ... 6 _ _
Row6: ... 1 _ _
So Box 6 currently has: 1,3,4,6,7 → missing 2,5,8,9
But Row6 already has 1,2,6,7,9 → so in Row6, cols 8 and 9 must be from {3,4,5,8} minus what’s in box.
Also, Col8:
Row1: ?
Row2: 3
Row3: ?
Row4: 7
Row5: ?
Row6: ?
Row7: 5
Row8: 4
Row9: 6
So Col8 has: 3,4,5,6,7 → missing 1,2,8,9
Row6, Col8: cannot be 1,2,6,7,9 (already in row) → so possible 3,4,5,8 → but 3,4,5 may be blocked by box or column.
This is getting messy. Let’s try another approach.
Look at Box 5 (center 3x3):
Rows 4–6, Cols 4–6:
8 5 _
4 3 1
9 2 7
So current: 1,2,3,4,5,7,8,9 → missing 6 → So Row4, Col6 = 6
Update Row4:
9 2 _ | 8 5 6 | 3 7 4 → Now missing only Col3
Row4: 9,2,?,8,5,6,3,7,4 → missing 1 → So Row4, Col3 = 1
Row4 complete:
9 2 1 | 8 5 6 | 3 7 4 ✔
---
Now Row 5:
_ _ 8 | 4 3 1 | 6 _ _
Missing: 2,5,7,9
Box 4 (middle-left 3x3):
Rows 4–6, Cols 1–3:
9 2 1
_ _ 8
_ _ 6
Has: 1,2,6,8,9 → missing 3,4,5,7
Row5, Cols1-2 must be from missing in row: 2,5,7,9 → but 2 is already in box → so possible 5,7,9
Col1:
Row1: ?
Row2: 5
Row3: ?
Row4: 9
Row5: ?
Row6: ?
Row7: 2
Row8: 6
Row9: 1
So Col1 has: 1,2,5,6,9 → missing 3,4,7,8
Row5, Col1: must be from {2,5,7,9} ∩ {3,4,7,8} → only 7
So Row5, Col1 = 7
Then Row5: 7 _ 8 | 4 3 1 | 6 _ _
Now missing: 2,5,9 for Cols2,8,9
Col2:
Row1: 7
Row2: 1
Row3: ?
Row4: 2
Row5: ?
Row6: ?
Row7: 4
Row8: 9
Row9: 8
Has: 1,2,4,7,8,9 → missing 3,5,6
Row5, Col2: must be from {2,5,9} ∩ {3,5,6} → only 5
So Row5, Col2 = 5
Now Row5: 7 5 8 | 4 3 1 | 6 _ _
Missing: 2,9 for Cols8,9
Col8: has 3,4,5,6,7 → missing 1,2,8,9 → so 2 or 9 ok
Col9:
Row1: 6
Row2: 8
Row3: ?
Row4: 4
Row5: ?
Row6: ?
Row7: 1
Row8: 3
Row9: 7
Has: 1,3,4,6,7,8 → missing 2,5,9
So both 2 and 9 are possible in Col8 and Col9.
But look at Box 6 (right-middle 3x3):
Rows 4–6, Cols 7–9:
3 7 4
6 _ _
1 _ _
Has: 1,3,4,6,7 → missing 2,5,8,9
Row5, Cols8-9 must be 2 and 9 → which fits.
Now check Row6 to see if we can resolve.
Row6: _ _ 6 | 9 2 7 | 1 _ _
We know from earlier, Box 6 needs 2,5,8,9 — but Row6 already has 1,2,6,7,9 → so in Row6, Cols8-9 must be from {3,4,5,8} minus what’s in box.
Wait, Row6 missing: 3,4,5,8 (since 1,2,6,7,9 present)
But Box 6 missing: 2,5,8,9 — but 2 and 9 are already in Row6? No, Row6 has 2 and 9? Let's check:
Row6: positions: Col3=6, Col4=9, Col5=2, Col6=7, Col7=1 → so yes, 1,2,6,7,9 present → so Cols1,2,8,9 need 3,4,5,8
In Box 6, Row6 Cols8-9 must be two of 3,4,5,8 — but Box 6 already has 1,3,4,6,7 → so missing 2,5,8,9 — but 2 and 9 are not available in Row6 → contradiction?
Wait, I think I made a mistake.
Box 6: Rows 4-6, Cols 7-9
Row4: Col7=3, Col8=7, Col9=4
Row5: Col7=6, Col8=?, Col9=?
Row6: Col7=1, Col8=?, Col9=?
So current numbers in Box 6: 1,3,4,6,7 → missing 2,5,8,9
Row5 Cols8-9: must be 2 and 9 (as we said)
Then Row6 Cols8-9 must be 5 and 8 (since 2 and 9 taken by Row5)
And Row6 missing numbers are 3,4,5,8 — so 5 and 8 fit.
Now, which is which?
Col8: has 3,4,5,6,7 → missing 1,2,8,9
If Row6, Col8 = 5 → but 5 is already in Col8? Row7 Col8=5 → yes! So Col8 already has 5 → so Row6, Col8 cannot be 5 → must be 8
Then Row6, Col9 = 5
So Row6: _ _ 6 | 9 2 7 | 1 8 5
Now missing for Row6: Cols1-2: 3,4
Col1: has 1,2,5,6,7,9 → missing 3,4,8
Col2: has 1,2,4,5,7,8,9 → missing 3,6
So Row6, Col1: must be 3 or 4
Row6, Col2: must be 3 or 4
But Col2 missing 3,6 — and 6 is not in Row6 missing → so Row6, Col2 must be 3
Then Row6, Col1 = 4
So Row6: 4 3 6 | 9 2 7 | 1 8 5 ✔
Now back to Row5: we had 7 5 8 | 4 3 1 | 6 _ _
With Cols8-9 = 2 and 9
Col8: now has Row6=8, Row7=5, Row8=4, Row9=6, Row2=3, Row4=7 → so has 3,4,5,6,7,8 → missing 1,2,9
So Row5, Col8 can be 2 or 9
Col9: has Row1=6, Row2=8, Row4=4, Row6=5, Row7=1, Row8=3, Row9=7 → has 1,3,4,5,6,7,8 → missing 2,9
Same.
But look at Box 6: after placing Row5 Cols8-9 as 2 and 9, and Row6 as 8 and 5, then Box 6 will have all.
No conflict yet.
But let’s check Row3 to help.
Perhaps easier to fill in what we have so far.
Let me write down the grid as we have it now.
After solving Rows 4,5,6,7,8,9 partially:
Row1: _ 7 _ | 3 _ _ | 5 _ 6
Row2: 5 1 _ | 6 7 2 | 4 3 8
Row3: _ _ 4 | 5 9 8 | 7 _ _
Row4: 9 2 1 | 8 5 6 | 3 7 4
Row5: 7 5 8 | 4 3 1 | 6 ? ? → ? are 2,9
Row6: 4 3 6 | 9 2 7 | 1 8 5
Row7: 2 4 3 | 7 6 9 | 8 5 1
Row8: 6 9 7 | 1 8 5 | 2 4 3
Row9: 1 8 5 | 2 4 3 | 9 6 7
Now Row5 Cols8-9: 2 and 9
Look at Col8:
Row1: ?
Row2: 3
Row3: ?
Row4: 7
Row5: ?
Row6: 8
Row7: 5
Row8: 4
Row9: 6
So missing in Col8: 1,2,9
Row5 Col8 can be 2 or 9
Similarly, Col9:
Row1: 6
Row2: 8
Row3: ?
Row4: 4
Row5: ?
Row6: 5
Row7: 1
Row8: 3
Row9: 7
Missing: 2,9
Same.
But in Box 6, if we put Row5 Col8=2, Col9=9, or vice versa.
Check Row3 Col9: might help.
Row3: _ _ 4 | 5 9 8 | 7 _ _
Missing: 1,2,3,6
Col9 missing 2,9 — so Row3 Col9 could be 2 (since 9 is in row already? Row3 has 4,5,7,8,9 → yes, 9 is there, so Col9 for Row3 cannot be 9 → must be 2? But 2 is also in row? Row3 has 5,9,8,7,4 — no 2 yet.
Row3: values present: 4,5,7,8,9 → so missing 1,2,3,6
Col9 missing 2,9 — but 9 is in row, so Row3 Col9 = 2
Then Col9 has 2 placed.
Then for Row5, Col9 cannot be 2 → must be 9
Then Row5 Col8 = 2
So Row5: 7 5 8 | 4 3 1 | 6 2 9 ✔
Now Col9: Row3=2, Row5=9, others known → complete.
Col8: Row5=2, so missing 1,9 for Row1 and Row3
Col8: has Row2=3, Row4=7, Row5=2, Row6=8, Row7=5, Row8=4, Row9=6 → so has 2,3,4,5,6,7,8 → missing 1,9
Row1 and Row3 need to fill Col8 with 1 and 9
Now Row1: _ 7 _ | 3 _ _ | 5 _ 6
Missing: 1,2,4,8,9
Col8 for Row1: must be 1 or 9
Similarly, Row3: _ _ 4 | 5 9 8 | 7 _ _
Missing: 1,2,3,6 (but 2 is now in Col9, so for Row3, missing 1,3,6 for Cols1,2,8)
Col8 for Row3: must be 1 or 9 — but 9 is in row (Col5=9), so cannot be 9 → must be 1
Then Row3 Col8 = 1
Then Row1 Col8 = 9
So update:
Row3: _ _ 4 | 5 9 8 | 7 1 _
Now missing for Row3: Cols1,2,9: but Col9 is already set to 2? Earlier we said Row3 Col9=2
Yes, so Row3: Cols1,2 missing, and Col9=2
So Row3: _ _ 4 | 5 9 8 | 7 1 2
Missing: 3,6 for Cols1,2
Col1: has Row2=5, Row4=9, Row5=7, Row6=4, Row7=2, Row8=6, Row9=1 → has 1,2,4,5,6,7,9 → missing 3,8
So Row3 Col1: must be 3 or 6, but Col1 missing 3,8 → so must be 3
Then Row3 Col2 = 6
So Row3: 3 6 4 | 5 9 8 | 7 1 2 ✔
Now Row1: _ 7 _ | 3 _ _ | 5 9 6 (since Col8=9)
Missing: 1,2,4,8 for Cols1,3,5,6
Col1: missing 8 (since has 1,2,3,4,5,6,7,9) → only 8 missing? Let's list Col1:
Row1: ?
Row2: 5
Row3: 3
Row4: 9
Row5: 7
Row6: 4
Row7: 2
Row8: 6
Row9: 1
So has: 1,2,3,4,5,6,7,9 → missing 8 → so Row1 Col1 = 8
Then Row1: 8 7 _ | 3 _ _ | 5 9 6
Missing: 1,2,4 for Cols3,5,6
Col3:
Row1: ?
Row2: ?
Row3: 4
Row4: 1
Row5: 8
Row6: 6
Row7: 3
Row8: 7
Row9: 5
Has: 1,3,4,5,6,7,8 → missing 2,9
So Row1 Col3: must be 2 (since 9 not in missing for row)
Row1 missing 1,2,4 — Col3 missing 2,9 → so only 2 possible → Row1 Col3 = 2
Then Row1: 8 7 2 | 3 _ _ | 5 9 6
Missing: 1,4 for Cols5,6
Col5:
Row1: ?
Row2: 7
Row3: 9
Row4: 5
Row5: 3
Row6: 2
Row7: 6
Row8: 8
Row9: 4
Has: 2,3,4,5,6,7,8,9 → missing 1 → so Row1 Col5 = 1
Then Row1 Col6 = 4
So Row1: 8 7 2 | 3 1 4 | 5 9 6 ✔
Now last, Row2: 5 1 _ | 6 7 2 | 4 3 8
Missing only Col3
Col3: has Row1=2, Row3=4, Row4=1, Row5=8, Row6=6, Row7=3, Row8=7, Row9=5 → has 1,2,3,4,5,6,7,8 → missing 9
So Row2 Col3 = 9
Row2: 5 1 9 | 6 7 2 | 4 3 8 ✔
All rows filled!
Let me verify the entire grid:
Row1: 8 7 2 | 3 1 4 | 5 9 6
Row2: 5 1 9 | 6 7 2 | 4 3 8
Row3: 3 6 4 | 5 9 8 | 7 1 2
Row4: 9 2 1 | 8 5 6 | 3 7 4
Row5: 7 5 8 | 4 3 1 | 6 2 9
Row6: 4 3 6 | 9 2 7 | 1 8 5
Row7: 2 4 3 | 7 6 9 | 8 5 1
Row8: 6 9 7 | 1 8 5 | 2 4 3
Row9: 1 8 5 | 2 4 3 | 9 6 7
Check a few things:
- Each row has 1-9? Yes, by construction.
- Columns: e.g., Col1: 8,5,3,9,7,4,2,6,1 → all unique.
Col2: 7,1,6,2,5,3,4,9,8 → good.
Col3: 2,9,4,1,8,6,3,7,5 → good.
Boxes: e.g., Box1 (top-left):
8 7 2
5 1 9
3 6 4 → has 1-9? 1,2,3,4,5,6,7,8,9 → yes.
Box5 (center):
8 5 6
4 3 1
9 2 7 → 1,2,3,4,5,6,7,8,9 → yes.
All good.
Final Answer:
8 7 2 | 3 1 4 | 5 9 6
5 1 9 | 6 7 2 | 4 3 8
3 6 4 | 5 9 8 | 7 1 2
------+-------+------
9 2 1 | 8 5 6 | 3 7 4
7 5 8 | 4 3 1 | 6 2 9
4 3 6 | 9 2 7 | 1 8 5
------+-------+------
2 4 3 | 7 6 9 | 8 5 1
6 9 7 | 1 8 5 | 2 4 3
1 8 5 | 2 4 3 | 9 6 7
We are given a 9x9 grid, divided into nine 3x3 boxes. The goal is to fill each row, each column, and each 3x3 box with the numbers 1 through 9 — no repeats allowed in any row, column, or box.
We’ll go row by row, looking for missing numbers and using logic to figure out where they go.
---
Row 1:
Given: _ 7 _ | 3 _ _ | 5 _ 6
Missing numbers: 1, 2, 4, 8, 9
Look at columns and boxes to eliminate possibilities.
- Column 1: already has 5, 9, 2, 6, 1 → so can’t be those → possible: 3,4,7,8 → but 3 and 7 are used in row → so only 4 or 8? Wait, let’s check box 1 (top-left 3x3).
Box 1 (rows 1–3, cols 1–3):
Current:
_ 7 _
5 1 _
_ _ 4
So in Box 1, we have: 1,4,5,7 → missing: 2,3,6,8,9
But Row 1 already has 3,5,6,7 → so in Row 1, Box 1 cells (col1, col3) must be from {1,2,4,8,9} minus what’s in box.
Actually, maybe better to look for rows/columns/boxes that are almost full.
---
Let’s try Row 9 — it’s completely filled!
1 8 5 | 2 4 3 | 9 6 7 → Good, valid.
Row 8:
6 9 7 | _ 8 5 | _ 4 3
Missing: 1,2
Check column 4: has 3,6,5,8,4,9,7,2 → wait, let’s list column 4:
Col 4:
Row1: 3
Row2: 6
Row3: 5
Row4: 8
Row5: 4
Row6: 9
Row7: 7
Row8: ?
Row9: 2
So Col 4 has: 2,3,4,5,6,7,8,9 → missing 1 → So Row8, Col4 = 1
Then Row8, Col7 must be 2 (only one left)
So Row8 becomes:
6 9 7 | 1 8 5 | 2 4 3 ✔
---
Row 7:
2 4 _ | 7 _ 9 | 8 5 1
Missing: 3,6
Check Col3:
Row1: ?
Row2: ?
Row3: 4
Row4: ?
Row5: 8
Row6: 6
Row7: ?
Row8: 7
Row9: 5
So Col3 has: 4,5,6,7,8 → missing 1,2,3,9
In Row7, Col3 must be 3 or 6.
But Box 7 (bottom-left 3x3):
Rows 7–9, Cols 1–3:
2 4 ?
6 9 7
1 8 5
Already has: 1,2,4,5,6,7,8,9 → missing 3 → So Row7, Col3 = 3
Then Row7, Col5 = 6 (only one left)
So Row7:
2 4 3 | 7 6 9 | 8 5 1 ✔
---
Row 6:
_ _ 6 | 9 2 7 | 1 _ _
Missing: 3,4,5,8
Check Box 6 (middle-right 3x3):
Rows 4–6, Cols 7–9:
3 7 4
6 _ _
1 _ _
Wait, Row4: ... 3 7 4
Row5: ... 6 _ _
Row6: ... 1 _ _
So Box 6 currently has: 1,3,4,6,7 → missing 2,5,8,9
But Row6 already has 1,2,6,7,9 → so in Row6, cols 8 and 9 must be from {3,4,5,8} minus what’s in box.
Also, Col8:
Row1: ?
Row2: 3
Row3: ?
Row4: 7
Row5: ?
Row6: ?
Row7: 5
Row8: 4
Row9: 6
So Col8 has: 3,4,5,6,7 → missing 1,2,8,9
Row6, Col8: cannot be 1,2,6,7,9 (already in row) → so possible 3,4,5,8 → but 3,4,5 may be blocked by box or column.
This is getting messy. Let’s try another approach.
Look at Box 5 (center 3x3):
Rows 4–6, Cols 4–6:
8 5 _
4 3 1
9 2 7
So current: 1,2,3,4,5,7,8,9 → missing 6 → So Row4, Col6 = 6
Update Row4:
9 2 _ | 8 5 6 | 3 7 4 → Now missing only Col3
Row4: 9,2,?,8,5,6,3,7,4 → missing 1 → So Row4, Col3 = 1
Row4 complete:
9 2 1 | 8 5 6 | 3 7 4 ✔
---
Now Row 5:
_ _ 8 | 4 3 1 | 6 _ _
Missing: 2,5,7,9
Box 4 (middle-left 3x3):
Rows 4–6, Cols 1–3:
9 2 1
_ _ 8
_ _ 6
Has: 1,2,6,8,9 → missing 3,4,5,7
Row5, Cols1-2 must be from missing in row: 2,5,7,9 → but 2 is already in box → so possible 5,7,9
Col1:
Row1: ?
Row2: 5
Row3: ?
Row4: 9
Row5: ?
Row6: ?
Row7: 2
Row8: 6
Row9: 1
So Col1 has: 1,2,5,6,9 → missing 3,4,7,8
Row5, Col1: must be from {2,5,7,9} ∩ {3,4,7,8} → only 7
So Row5, Col1 = 7
Then Row5: 7 _ 8 | 4 3 1 | 6 _ _
Now missing: 2,5,9 for Cols2,8,9
Col2:
Row1: 7
Row2: 1
Row3: ?
Row4: 2
Row5: ?
Row6: ?
Row7: 4
Row8: 9
Row9: 8
Has: 1,2,4,7,8,9 → missing 3,5,6
Row5, Col2: must be from {2,5,9} ∩ {3,5,6} → only 5
So Row5, Col2 = 5
Now Row5: 7 5 8 | 4 3 1 | 6 _ _
Missing: 2,9 for Cols8,9
Col8: has 3,4,5,6,7 → missing 1,2,8,9 → so 2 or 9 ok
Col9:
Row1: 6
Row2: 8
Row3: ?
Row4: 4
Row5: ?
Row6: ?
Row7: 1
Row8: 3
Row9: 7
Has: 1,3,4,6,7,8 → missing 2,5,9
So both 2 and 9 are possible in Col8 and Col9.
But look at Box 6 (right-middle 3x3):
Rows 4–6, Cols 7–9:
3 7 4
6 _ _
1 _ _
Has: 1,3,4,6,7 → missing 2,5,8,9
Row5, Cols8-9 must be 2 and 9 → which fits.
Now check Row6 to see if we can resolve.
Row6: _ _ 6 | 9 2 7 | 1 _ _
We know from earlier, Box 6 needs 2,5,8,9 — but Row6 already has 1,2,6,7,9 → so in Row6, Cols8-9 must be from {3,4,5,8} minus what’s in box.
Wait, Row6 missing: 3,4,5,8 (since 1,2,6,7,9 present)
But Box 6 missing: 2,5,8,9 — but 2 and 9 are already in Row6? No, Row6 has 2 and 9? Let's check:
Row6: positions: Col3=6, Col4=9, Col5=2, Col6=7, Col7=1 → so yes, 1,2,6,7,9 present → so Cols1,2,8,9 need 3,4,5,8
In Box 6, Row6 Cols8-9 must be two of 3,4,5,8 — but Box 6 already has 1,3,4,6,7 → so missing 2,5,8,9 — but 2 and 9 are not available in Row6 → contradiction?
Wait, I think I made a mistake.
Box 6: Rows 4-6, Cols 7-9
Row4: Col7=3, Col8=7, Col9=4
Row5: Col7=6, Col8=?, Col9=?
Row6: Col7=1, Col8=?, Col9=?
So current numbers in Box 6: 1,3,4,6,7 → missing 2,5,8,9
Row5 Cols8-9: must be 2 and 9 (as we said)
Then Row6 Cols8-9 must be 5 and 8 (since 2 and 9 taken by Row5)
And Row6 missing numbers are 3,4,5,8 — so 5 and 8 fit.
Now, which is which?
Col8: has 3,4,5,6,7 → missing 1,2,8,9
If Row6, Col8 = 5 → but 5 is already in Col8? Row7 Col8=5 → yes! So Col8 already has 5 → so Row6, Col8 cannot be 5 → must be 8
Then Row6, Col9 = 5
So Row6: _ _ 6 | 9 2 7 | 1 8 5
Now missing for Row6: Cols1-2: 3,4
Col1: has 1,2,5,6,7,9 → missing 3,4,8
Col2: has 1,2,4,5,7,8,9 → missing 3,6
So Row6, Col1: must be 3 or 4
Row6, Col2: must be 3 or 4
But Col2 missing 3,6 — and 6 is not in Row6 missing → so Row6, Col2 must be 3
Then Row6, Col1 = 4
So Row6: 4 3 6 | 9 2 7 | 1 8 5 ✔
Now back to Row5: we had 7 5 8 | 4 3 1 | 6 _ _
With Cols8-9 = 2 and 9
Col8: now has Row6=8, Row7=5, Row8=4, Row9=6, Row2=3, Row4=7 → so has 3,4,5,6,7,8 → missing 1,2,9
So Row5, Col8 can be 2 or 9
Col9: has Row1=6, Row2=8, Row4=4, Row6=5, Row7=1, Row8=3, Row9=7 → has 1,3,4,5,6,7,8 → missing 2,9
Same.
But look at Box 6: after placing Row5 Cols8-9 as 2 and 9, and Row6 as 8 and 5, then Box 6 will have all.
No conflict yet.
But let’s check Row3 to help.
Perhaps easier to fill in what we have so far.
Let me write down the grid as we have it now.
After solving Rows 4,5,6,7,8,9 partially:
Row1: _ 7 _ | 3 _ _ | 5 _ 6
Row2: 5 1 _ | 6 7 2 | 4 3 8
Row3: _ _ 4 | 5 9 8 | 7 _ _
Row4: 9 2 1 | 8 5 6 | 3 7 4
Row5: 7 5 8 | 4 3 1 | 6 ? ? → ? are 2,9
Row6: 4 3 6 | 9 2 7 | 1 8 5
Row7: 2 4 3 | 7 6 9 | 8 5 1
Row8: 6 9 7 | 1 8 5 | 2 4 3
Row9: 1 8 5 | 2 4 3 | 9 6 7
Now Row5 Cols8-9: 2 and 9
Look at Col8:
Row1: ?
Row2: 3
Row3: ?
Row4: 7
Row5: ?
Row6: 8
Row7: 5
Row8: 4
Row9: 6
So missing in Col8: 1,2,9
Row5 Col8 can be 2 or 9
Similarly, Col9:
Row1: 6
Row2: 8
Row3: ?
Row4: 4
Row5: ?
Row6: 5
Row7: 1
Row8: 3
Row9: 7
Missing: 2,9
Same.
But in Box 6, if we put Row5 Col8=2, Col9=9, or vice versa.
Check Row3 Col9: might help.
Row3: _ _ 4 | 5 9 8 | 7 _ _
Missing: 1,2,3,6
Col9 missing 2,9 — so Row3 Col9 could be 2 (since 9 is in row already? Row3 has 4,5,7,8,9 → yes, 9 is there, so Col9 for Row3 cannot be 9 → must be 2? But 2 is also in row? Row3 has 5,9,8,7,4 — no 2 yet.
Row3: values present: 4,5,7,8,9 → so missing 1,2,3,6
Col9 missing 2,9 — but 9 is in row, so Row3 Col9 = 2
Then Col9 has 2 placed.
Then for Row5, Col9 cannot be 2 → must be 9
Then Row5 Col8 = 2
So Row5: 7 5 8 | 4 3 1 | 6 2 9 ✔
Now Col9: Row3=2, Row5=9, others known → complete.
Col8: Row5=2, so missing 1,9 for Row1 and Row3
Col8: has Row2=3, Row4=7, Row5=2, Row6=8, Row7=5, Row8=4, Row9=6 → so has 2,3,4,5,6,7,8 → missing 1,9
Row1 and Row3 need to fill Col8 with 1 and 9
Now Row1: _ 7 _ | 3 _ _ | 5 _ 6
Missing: 1,2,4,8,9
Col8 for Row1: must be 1 or 9
Similarly, Row3: _ _ 4 | 5 9 8 | 7 _ _
Missing: 1,2,3,6 (but 2 is now in Col9, so for Row3, missing 1,3,6 for Cols1,2,8)
Col8 for Row3: must be 1 or 9 — but 9 is in row (Col5=9), so cannot be 9 → must be 1
Then Row3 Col8 = 1
Then Row1 Col8 = 9
So update:
Row3: _ _ 4 | 5 9 8 | 7 1 _
Now missing for Row3: Cols1,2,9: but Col9 is already set to 2? Earlier we said Row3 Col9=2
Yes, so Row3: Cols1,2 missing, and Col9=2
So Row3: _ _ 4 | 5 9 8 | 7 1 2
Missing: 3,6 for Cols1,2
Col1: has Row2=5, Row4=9, Row5=7, Row6=4, Row7=2, Row8=6, Row9=1 → has 1,2,4,5,6,7,9 → missing 3,8
So Row3 Col1: must be 3 or 6, but Col1 missing 3,8 → so must be 3
Then Row3 Col2 = 6
So Row3: 3 6 4 | 5 9 8 | 7 1 2 ✔
Now Row1: _ 7 _ | 3 _ _ | 5 9 6 (since Col8=9)
Missing: 1,2,4,8 for Cols1,3,5,6
Col1: missing 8 (since has 1,2,3,4,5,6,7,9) → only 8 missing? Let's list Col1:
Row1: ?
Row2: 5
Row3: 3
Row4: 9
Row5: 7
Row6: 4
Row7: 2
Row8: 6
Row9: 1
So has: 1,2,3,4,5,6,7,9 → missing 8 → so Row1 Col1 = 8
Then Row1: 8 7 _ | 3 _ _ | 5 9 6
Missing: 1,2,4 for Cols3,5,6
Col3:
Row1: ?
Row2: ?
Row3: 4
Row4: 1
Row5: 8
Row6: 6
Row7: 3
Row8: 7
Row9: 5
Has: 1,3,4,5,6,7,8 → missing 2,9
So Row1 Col3: must be 2 (since 9 not in missing for row)
Row1 missing 1,2,4 — Col3 missing 2,9 → so only 2 possible → Row1 Col3 = 2
Then Row1: 8 7 2 | 3 _ _ | 5 9 6
Missing: 1,4 for Cols5,6
Col5:
Row1: ?
Row2: 7
Row3: 9
Row4: 5
Row5: 3
Row6: 2
Row7: 6
Row8: 8
Row9: 4
Has: 2,3,4,5,6,7,8,9 → missing 1 → so Row1 Col5 = 1
Then Row1 Col6 = 4
So Row1: 8 7 2 | 3 1 4 | 5 9 6 ✔
Now last, Row2: 5 1 _ | 6 7 2 | 4 3 8
Missing only Col3
Col3: has Row1=2, Row3=4, Row4=1, Row5=8, Row6=6, Row7=3, Row8=7, Row9=5 → has 1,2,3,4,5,6,7,8 → missing 9
So Row2 Col3 = 9
Row2: 5 1 9 | 6 7 2 | 4 3 8 ✔
All rows filled!
Let me verify the entire grid:
Row1: 8 7 2 | 3 1 4 | 5 9 6
Row2: 5 1 9 | 6 7 2 | 4 3 8
Row3: 3 6 4 | 5 9 8 | 7 1 2
Row4: 9 2 1 | 8 5 6 | 3 7 4
Row5: 7 5 8 | 4 3 1 | 6 2 9
Row6: 4 3 6 | 9 2 7 | 1 8 5
Row7: 2 4 3 | 7 6 9 | 8 5 1
Row8: 6 9 7 | 1 8 5 | 2 4 3
Row9: 1 8 5 | 2 4 3 | 9 6 7
Check a few things:
- Each row has 1-9? Yes, by construction.
- Columns: e.g., Col1: 8,5,3,9,7,4,2,6,1 → all unique.
Col2: 7,1,6,2,5,3,4,9,8 → good.
Col3: 2,9,4,1,8,6,3,7,5 → good.
Boxes: e.g., Box1 (top-left):
8 7 2
5 1 9
3 6 4 → has 1-9? 1,2,3,4,5,6,7,8,9 → yes.
Box5 (center):
8 5 6
4 3 1
9 2 7 → 1,2,3,4,5,6,7,8,9 → yes.
All good.
Final Answer:
8 7 2 | 3 1 4 | 5 9 6
5 1 9 | 6 7 2 | 4 3 8
3 6 4 | 5 9 8 | 7 1 2
------+-------+------
9 2 1 | 8 5 6 | 3 7 4
7 5 8 | 4 3 1 | 6 2 9
4 3 6 | 9 2 7 | 1 8 5
------+-------+------
2 4 3 | 7 6 9 | 8 5 1
6 9 7 | 1 8 5 | 2 4 3
1 8 5 | 2 4 3 | 9 6 7
Parent Tip: Review the logic above to help your child master the concept of soduko worksheet.