user: You are going to act as a Sudoku solver AI. Your task is to solve a given Sudoku puzzle using a step-by-step reasoning process.
Here is the Sudoku puzzle you need to solve:
<sudoku_grid>
008 000 090
006 800 003
109 000 560
040 000 601
037 100 080
912 600 000
760 320 900
004 910 000
000 407 002
</sudoku_grid>
Here are the rules for Sudoku:
You will use the following methods to solve the Sudoku:
Method 1: Scanning (Direct Placement)
Method 2: Candidate Elimination
Method 3: Number Filling
Here is the step-by-step reasoning process you should follow:
Remember to clearly indicate when you are using <method>Scanning</method> or <method>Candidate Elimination</method> and use <step> tags to denote each number placement. Start solving the provided Sudoku puzzle now.
assistant: The user wants me to solve the provided Sudoku puzzle step-by-step using the specified methods: Scanning, Candidate Elimination, and Number Filling.
Initial Grid:
008 000 090
006 800 003
109 000 560
040 000 601
037 100 080
912 600 000
760 320 900
004 910 000
000 407 002
Let's represent the grid with coordinates (row, column), starting from (1,1) at the top-left.
Iteration 1
a. Scanning Phase:
<method>Scanning</method>
- Scan Row 1: 008 000 090. Missing: 1,2,3,4,5,6,7.
- Scan Row 2: 006 800 003. Missing: 1,2,4,5,7,9.
- Scan Row 3: 109 000 560. Missing: 2,3,4,7,8.
- Scan Row 4: 040 000 601. Missing: 2,3,5,7,8,9.
- Scan Row 5: 037 100 080. Missing: 2,4,5,6,9.
- Scan Row 6: 912 600 000. Missing: 3,4,5,7,8.
- Scan Row 7: 760 320 900. Missing: 1,4,5,8.
- Scan Row 8: 004 910 000. Missing: 2,3,5,6,7,8.
- Scan Row 9: 000 407 002. Missing: 1,3,5,6,8,9.
- Scan Col 1: 001009700. Missing: 2,3,4,5,6,8.
- Scan Col 2: 000431600. Missing: 2,5,7,8,9.
- Scan Col 3: 869072040. Missing: 1,3,5.
- Scan Col 4: 080016394. Missing: 2,5,7.
- Scan Col 5: 000000210. Missing: 3,4,5,6,7,8,9.
- Scan Col 6: 000000007. Missing: 1,2,3,4,5,6,8,9.
- Scan Col 7: 005600900. Missing: 1,2,3,4,7,8.
- Scan Col 8: 906080000. Missing: 1,2,3,4,5,7.
- Scan Col 9: 030100002. Missing: 4,5,6,7,8,9.
- Scan Box 1 (R1-3, C1-3): 008 006 109. Missing: 2,3,4,5,7.
- Scan Box 2 (R1-3, C4-6): 000 800 000. Missing: 1,2,3,4,5,6,7,9.
- Scan Box 3 (R1-3, C7-9): 090 003 560. Missing: 1,2,4,7,8.
- Scan Box 4 (R4-6, C1-3): 040 037 912. Missing: 5,6,8.
- Scan Box 5 (R4-6, C4-6): 000 100 600. Missing: 2,3,4,5,7,8,9.
- Scan Box 6 (R4-6, C7-9): 601 080 000. Missing: 2,3,4,5,7,9.
- Scan Box 7 (R7-9, C1-3): 760 004 000. Missing: 1,2,3,5,8,9.
- Scan Box 8 (R7-9, C4-6): 320 910 407. Missing: 5,6,8.
- Scan Box 9 (R7-9, C7-9): 900 000 002. Missing: 1,3,4,5,6,7,8.
Let's try placing some numbers using simple scanning (looking for the only possible number for a cell).
- Look at cell (1,4). Row 1 has 8,9. Col 4 has 8,1,6,3,9,4. Box 2 has 8. Candidates for (1,4): {1,2,3,4,5,6,7}. Remove 8,9 (row), 1,6,3,4 (col), 8 (box). Candidates: {2,5,7}. Not single.
- Look at cell (1,5). Row 1 has 8,9. Col 5 has 3,1,2,1. Box 2 has 8. Candidates: {1,2,3,4,5,6,7}. Remove 8,9 (row), 3,1,2 (col), 8 (box). Candidates: {4,5,6,7}. Not single.
- Look at cell (1,6). Row 1 has 8,9. Col 6 has 7. Box 2 has 8. Candidates: {1,2,3,4,5,6,7}. Remove 8,9 (row), 7 (col), 8 (box). Candidates: {1,2,3,4,5,6}. Not single.
- Look at cell (1,7). Row 1 has 8,9. Col 7 has 5,6,9. Box 3 has 5,6,9,3. Candidates: {1,2,3,4,5,6,7}. Remove 8,9 (row), 5,6,9 (col), 3 (box). Candidates: {1,2,4,7}. Not single.
- Look at cell (1,1). Row 1 has 8,9. Col 1 has 1,9,7. Box 1 has 8,6,1,9. Candidates: {1..7}. Remove 8,9 (row), 1,7 (col), 6 (box). Candidates: {2,3,4,5}. Not single.
- Look at cell (3,8). Row 3 has 1,9,5,6. Col 8 has 9,8. Box 3 has 9,3,5,6. Candidates: {2,3,4,7,8}. Remove 1,9,5,6 (row), 8 (col). Candidates: {2,3,4,7}. Not single.
- Look at cell (3,9). Row 3 has 1,9,5,6. Col 9 has 3,1,2. Box 3 has 9,3,5,6. Candidates: {2,3,4,7,8}. Remove 1,9,5,6 (row), 3,2 (col). Candidates: {4,7,8}. Not single.
Let's try scanning for numbers that have only one position in a row/col/box.
- Look at number 1.
- Row 2 needs 1. Possible cells: (2,1), (2,2), (2,4), (2,5), (2,6), (2,7), (2,8). Col 1 has 1. Col 7 has 5,6,9. Box 1 has 1. Box 3 has 5,6,9,3.
- Row 7 needs 1. Possible cells: (7,3), (7,6), (7,8), (7,9). Col 3 has 8,6,9,7,2,4. Col 6 has 7. Col 8 has 9,8. Col 9 has 3,1,2. Box 7 has 7,6,4. Box 9 has 9,2. (7,3) is blocked by col 3. (7,6) is blocked by col 6. (7,8) is blocked by col 8. (7,9) is blocked by col 9. Looks like a mistake in Col 3 analysis. Col 3: 8,6,9,0,7,2,0,4,0. Needs 1,3,5. Box 7 has 7,6,4. Cell (7,3) possible. Col 6: 0,0,0,0,0,0,0,0,7. Needs 1,2,3,4,5,6,8,9. Cell (7,6) possible. Col 8: 9,0,6,0,8,0,0,0,0. Needs 1,2,3,4,5,7. Cell (7,8) possible. Col 9: 0,3,0,1,0,0,0,0,2. Needs 4,5,6,7,8,9. Cell (7,9) possible. Let's recheck (7,3). Row 7 has 7,6,3,2,9. Col 3 has 8,6,9,7,2,4. Box 7 has 7,6,4. 1 is possible in (7,3). Cell (7,6). Row 7 has 7,6,3,2,9. Col 6 has 7. Box 8 has 3,2,9,1,4,7. 1 is not possible in (7,6). Cell (7,8). Row 7 has 7,6,3,2,9. Col 8 has 9,8. Box 9 has 9,2. 1 is possible in (7,8). Cell (7,9). Row 7 has 7,6,3,2,9. Col 9 has 3,1,2. 1 is not possible in (7,9). Okay, so 1 in Row 7 could be in (7,3) or (7,8).
- Look at number 5 in Col 3. Missing: 1,3,5.
- Cell (1,3) has 8. Cell (2,3) has 6. Cell (3,3) has 9. Cell (4,3) is 0. Row 4 has 4,6,1. Box 4 has 4,3,7,9,1,2. Candidates for (4,3): {2,5,8}. Check Col 3 again: 8,6,9,0,7,2,0,4,0. Contains 8,6,9,7,2,4. Missing 1,3,5. (4,3) candidates: Needs to be 1,3 or 5. Row 4: 4,6,1. Col 3: 8,6,9,7,2,4. Box 4: 4,3,7,9,1,2. Possible: {5}. Yes, 5 must go in (4,3).
<step>Place 5 in (4,3).</step>
Grid:
008 000 090
006 800 003
109 000 560
045 000 601
037 100 080
912 600 000
760 320 900
004 910 000
000 407 002
- Cell (1,3) has 8. Cell (2,3) has 6. Cell (3,3) has 9. Cell (4,3) is 0. Row 4 has 4,6,1. Box 4 has 4,3,7,9,1,2. Candidates for (4,3): {2,5,8}. Check Col 3 again: 8,6,9,0,7,2,0,4,0. Contains 8,6,9,7,2,4. Missing 1,3,5. (4,3) candidates: Needs to be 1,3 or 5. Row 4: 4,6,1. Col 3: 8,6,9,7,2,4. Box 4: 4,3,7,9,1,2. Possible: {5}. Yes, 5 must go in (4,3).
b. Candidate Elimination Phase:
<method>Candidate Elimination</method>
- Re-evaluate Col 3. Now has 8,6,9,5,7,2,4. Missing 1,3.
- Cell (7,3) is 0. Row 7 has 7,6,3,2,9. Box 7 has 7,6,4. Candidates for (7,3): {1,5,8}. Cannot be 5 (col 3). Cannot be 3 (row 7). Cannot be 7,6 (row 7), 2 (row 7), 9 (row 7). Cannot be 8,6,9,5,7,2,4 (col 3). Cannot be 7,6,4 (box 7). Possible: {1}. Yes, 1 must go in (7,3).
<step>Place 1 in (7,3).</step>
Grid:
008 000 090
006 800 003
109 000 560
045 000 601
037 100 080
912 600 000
761 320 900
004 910 000
000 407 002
- Cell (7,3) is 0. Row 7 has 7,6,3,2,9. Box 7 has 7,6,4. Candidates for (7,3): {1,5,8}. Cannot be 5 (col 3). Cannot be 3 (row 7). Cannot be 7,6 (row 7), 2 (row 7), 9 (row 7). Cannot be 8,6,9,5,7,2,4 (col 3). Cannot be 7,6,4 (box 7). Possible: {1}. Yes, 1 must go in (7,3).
- Col 3 is now complete: 8,6,9,5,7,2,1,4,0. Missing 3. Cell (9,3) must be 3.
<step>Place 3 in (9,3).</step>
Grid:
008 000 090
006 800 003
109 000 560
045 000 601
037 100 080
912 600 000
761 320 900
004 910 000
003 407 002
c. Number Filling Phase:
<method>Number Filling</method>
- Look at Box 7 (R7-9, C1-3). Contains 7,6,1, 0,0,4, 0,0,3. Needs 2,5,8,9.
- Cell (7,1) is 7. Cell (7,2) is 6. Cell (7,3) is 1.
- Cell (8,1) is 0. Row 8: 4,9,1. Col 1: 1,9,7. Box 7: 7,6,1,4,3. Candidates for (8,1): {2,3,5,6,8}. Remove 4,9,1 (row 8), 7 (col 1). Remove 6,3 (box 7). Candidates: {2,5,8}.
- Cell (8,2) is 0. Row 8: 4,9,1. Col 2: 4,3,1,6. Box 7: 7,6,1,4,3. Candidates for (8,2): {2,3,5,6,7,8}. Remove 4,9,1 (row 8), 3,6 (col 2). Remove 7 (box 7). Candidates: {2,5,8}.
- Cell (8,3) is 4.
- Cell (9,1) is 0. Row 9: 3,4,7,2. Col 1: 1,9,7. Box 7: 7,6,1,4,3. Candidates for (9,1): {1,5,6,8,9}. Remove 3,4,7,2 (row 9), 1,9,7 (col 1). Remove 6 (box 7). Candidates: {5,8}.
- Cell (9,2) is 0. Row 9: 3,4,7,2. Col 2: 4,3,1,6. Box 7: 7,6,1,4,3. Candidates for (9,2): {1,5,8,9}. Remove 3,4,7,2 (row 9), 1,6 (col 2). Remove (none from box 7). Candidates: {5,8,9}.
- Cell (9,3) is 3.
- Where can 9 go in Box 7? Cannot be in R7. Cannot be in C3. Cannot be in (8,1), (8,2). Possible: (9,2).
<step>Place 9 in (9,2).</step>
Grid:
008 000 090
006 800 003
109 000 560
045 000 601
037 100 080
912 600 000
761 320 900
004 910 000
093 407 002 - Look at Box 7 again. Needs 2,5,8.
- Cell (8,1): Candidates {2,5,8}.
- Cell (8,2): Candidates {2,5,8}. (Row 8: 4,9,1. Col 2: 4,3,1,6,9. Box 7: 7,6,1,4,3,9. Candidates for (8,2): {2,5,8})
- Cell (9,1): Candidates {5,8}. (Row 9: 9,3,4,7,2. Col 1: 1,9,7. Box 7: 7,6,1,4,3,9. Candidates for (9,1): {5,8})
- Look at Col 2. Contains 0,0,0,4,3,1,6,0,9. Missing 2,5,7,8.
- Cell (1,2) is 0. Row 1: 8,9. Box 1: 8,6,9,1. Candidates: {2,3,4,5,6,7}. Remove 8,9 (row 1), 4,3,1,6,9 (col 2), 6 (box 1). Candidates: {2,5,7}.
- Cell (2,2) is 0. Row 2: 6,8,3. Box 1: 8,6,9,1. Candidates: {1,2,4,5,7,9}. Remove 6,8,3 (row 2), 4,1,9 (col 2, cell (9,2)=9). Remove 1 (box 1). Candidates: {2,5,7}.
- Cell (3,2) is 0. Row 3: 1,9,5,6. Box 1: 8,6,9,1. Candidates: {2,3,4,7,8}. Remove 1,9,5,6 (row 3), 4,3,1,6,9 (col 2). Remove 8 (box 1). Candidates: {2,7}.
- Cell (8,2) is 0. Row 8: 4,9,1. Box 7: 7,6,1,4,3,9. Candidates: {2,3,5,6,7,8}. Remove 4,9,1 (row 8), 6,3 (col 2). Remove 7 (box 7). Candidates: {2,5,8}.
- Where can 7 go in Col 2? Possible: (1,2), (2,2), (3,2). Not (8,2). Row 5 has 7.
- Cell (1,2): Row 1 needs 7. Box 1 needs 7. Possible.
- Cell (2,2): Row 2 needs 7. Box 1 needs 7. Possible.
- Cell (3,2): Row 3 needs 7. Box 1 needs 7. Possible.
- Look at Row 9. Contains 9,3,4,7,2. Missing 1,5,6,8.
- Cell (9,1) is 0. Candidates {5,8}.
- Cell (9,5) is 0. Col 5 has 3,1,2,1. Box 8 has 3,2,9,1,4,7. Candidates for (9,5): {1,5,6,8,9}. Remove 9,3,4,7,2 (row 9), 1 (col 5). Remove (none from box 8). Candidates: {5,6,8}.
- Cell (9,7) is 0. Col 7 has 8,6,9,5,1. Box 9 has 9,2. Candidates for (9,7): {1,5,6,8}. Remove 9,3,4,7,2 (row 9), 5,1 (col 7). Remove (none from box 9). Candidates: {6,8}.
- Cell (9,8) is 0. Col 8 has 9,6,8. Box 9 has 9,2. Candidates for (9,8): {1,5,6,8}. Remove 9,3,4,7,2 (row 9), 6,8 (col 8). Remove (none from box 9). Candidates: {1,5}.
- Cell (9,9) is 2.
- Where can 1 go in Row 9? Only possible in (9,8).
<step>Place 1 in (9,8).</step>
Grid:
008 000 090
006 800 003
109 000 560
045 000 601
037 100 080
912 600 000
761 320 900
004 910 000
093 407 012 - Look at Row 9 again. Contains 9,3,4,7,1,2. Missing 5,6,8.
- Cell (9,1): Candidates {5,8}.
- Cell (9,5): Candidates {5,6,8}.
- Cell (9,7): Candidates {6,8}.
- Look at Col 8. Contains 9,0,6,0,8,0,0,0,1. Missing 2,3,4,5,7.
- Cell (1,8) is 9.
- Cell (2,8) is 0. Row 2: 6,8,3. Box 3: 9,3,5,6. Candidates: {1,2,4,5,7,9}. Remove 6,8,3 (row 2), 9,1 (col 8), 5 (box 3). Candidates: {2,4,7}.
- Cell (3,8) is 6.
- Cell (4,8) is 0. Row 4: 4,5,6,1. Box 6: 6,1,8. Candidates: {2,3,5,7,8,9}. Remove 4,5,6,1 (row 4), 9,8 (col 8), (none from box 6). Candidates: {2,3,7}.
- Cell (5,8) is 8.
- Cell (6,8) is 0. Row 6: 9,1,2,6. Box 6: 6,1,8. Candidates: {3,4,5,7,8}. Remove 9,1,2,6 (row 6), 8 (col 8). Candidates: {3,4,5,7}.
- Cell (7,8) is 0. Row 7: 7,6,1,3,2,9. Box 9: 9,2,1. Candidates: {4,5,8}. Remove 7,6,1,3,2,9 (row 7), 8 (col 8). Candidates: {4,5}.
- Cell (8,8) is 0. Row 8: 4,9,1. Box 9: 9,2,1. Candidates: {2,3,5,6,7,8}. Remove 4,9,1 (row 8), 6,8 (col 8). Candidates: {2,3,5,7}.
- Cell (9,8) is 1.
- Where can 4 go in Col 8? Possible: (2,8), (6,8), (7,8). Row 4 has 4. Row 8 has 4. Row 9 has 4. So 4 in Col 8 must be in (2,8) or (6,8) or (7,8).
- Where can 5 go in Col 8? Possible: (2,8), (4,8), (6,8), (7,8), (8,8). Row 3 has 5. Row 4 has 5. Row 9 has 5 candidate. Candidates: (2,8){2,4,7}, (4,8){2,3,7}, (6,8){3,4,5,7}, (7,8){4,5}, (8,8){2,3,5,7}. So 5 can be in (6,8), (7,8), (8,8).
Iteration 2
a. Scanning Phase:
<method>Scanning</method>
- Look at Box 9 (R7-9, C7-9). Contains 9,0,0, 0,0,0, 0,1,2. Needs 3,4,5,6,7,8.
- Cell (7,7) is 9.
- Cell (7,8) is 0. Candidates {4,5}.
- Cell (7,9) is 0. Row 7: 7,6,1,3,2,9. Col 9: 3,1,2. Box 9: 9,1,2. Candidates: {4,5,8}. Remove 7,6,1,3,2,9 (row 7), 3,1,2 (col 9). Candidates: {4,5,8}. Okay, recheck. Row 7 needs {4,5,8}. Col 9 needs {4,5,6,7,8,9}. Box 9 needs {3,4,5,6,7,8}. Candidates for (7,9): {4,5,8}. Check constraints: Row 7: OK. Col 9: Need 4,5,6,7,8,9. OK. Box 9: Need 3,4,5,6,7,8. OK. So candidates {4,5,8}.
- Cell (8,7) is 0. Row 8: 4,9,1. Col 7: 8,6,9,5,1. Box 9: 9,1,2. Candidates: {2,3,5,6,7,8}. Remove 4,9,1 (row 8), 5 (col 7). Remove 2 (box 9). Candidates: {3,6,7,8}.
- Cell (8,8) is 0. Candidates {2,3,5,7}. (Recheck: Row 8: 4,9,1. Col 8: 9,6,8,1. Box 9: 9,1,2. Candidates: {2,3,5,6,7,8}. Remove 4,9,1 (row 8), 6,8 (col 8). Remove 2 (box 9). Candidates: {3,5,7}).
- Cell (8,9) is 0. Row 8: 4,9,1. Col 9: 3,1,2. Box 9: 9,1,2. Candidates: {2,3,5,6,7,8}. Remove 4,9,1 (row 8), 3,2 (col 9). Remove (none from box 9). Candidates: {5,6,7,8}.
- Cell (9,7) is 0. Candidates {6,8}.
- Cell (9,8) is 1.
- Cell (9,9) is 2.
- Where can 3 go in Box 9? Possible: (8,7), (8,8). Cell (8,7) has candidate 3. Cell (8,8) has candidate 3.
- Where can 4 go in Box 9? Possible: (7,8), (7,9). Cell (7,8) has candidate 4. Cell (7,9) has candidate 4. Row 8 has 4. Row 9 has 4. So 4 must be in Row 7. Possible (7,8) or (7,9).
- Where can 5 go in Box 9? Possible: (7,8), (7,9), (8,8), (8,9). Cell (7,8) has candidate 5. Cell (7,9) has candidate 5. Cell (8,8) has candidate 5. Cell (8,9) has candidate 5.
- Where can 6 go in Box 9? Possible: (8,7), (8,9), (9,7). Cell (8,7) has candidate 6. Cell (8,9) has candidate 6. Cell (9,7) has candidate 6.
- Where can 7 go in Box 9? Possible: (8,7), (8,8), (8,9). Cell (8,7) has candidate 7. Cell (8,8) has candidate 7. Cell (8,9) has candidate 7. Row 7 has 7. Row 9 has 7. So 7 must be in (8,7), (8,8) or (8,9).
- Where can 8 go in Box 9? Possible: (7,9), (8,7), (8,9), (9,7). Cell (7,9) has candidate 8. Cell (8,7) has candidate 8. Cell (8,9) has candidate 8. Cell (9,7) has candidate 8. Col 8 has 8. Cell (8,8) cannot be 8. Cell (9,8) is 1.
- Look at Box 8 (R7-9, C4-6). Contains 3,2,0, 9,1,0, 4,0,7. Needs 5,6,8.
- Cell (7,6) is 0. Row 7: 7,6,1,3,2,9. Col 6: 7. Box 8: 3,2,9,1,4,7. Candidates: {4,5,8}. Remove 7,6,1,3,2,9 (row 7). Remove 4 (box 8). Candidates: {5,8}.
- Cell (8,6) is 0. Row 8: 4,9,1. Col 6: 7. Box 8: 3,2,9,1,4,7. Candidates: {2,3,5,6,8}. Remove 4,9,1 (row 8). Remove 7 (col 6). Remove 3,2 (box 8). Candidates: {5,6,8}.
- Cell (9,5) is 0. Row 9: 9,3,4,7,1,2. Col 5: 3,1,2,1. Box 8: 3,2,9,1,4,7. Candidates: {5,6,8}. Remove 9,3,4,7,1,2 (row 9). Remove (none from col 5). Remove (none from box 8). Candidates: {5,6,8}.
- Where can 5 go in Box 8? Possible: (7,6), (8,6), (9,5).
- Where can 6 go in Box 8? Possible: (8,6), (9,5).
- Where can 8 go in Box 8? Possible: (7,6), (8,6), (9,5).
- Look at cell (7,6). Candidates {5,8}.
- Look at cell (8,6). Candidates {5,6,8}.
- Look at cell (9,5). Candidates {5,6,8}.
- In Box 8, 6 can only be in (8,6) or (9,5).
- In Row 9, 6 can only be in (9,5) or (9,7).
- If (9,5) is 6, then (9,7) must be 8. Then (9,1) must be 5.
- If (9,7) is 6, then (9,5) cannot be 6. So (9,5) could be 5 or 8.
- In Col 6, missing 1,2,3,4,5,6,8,9. Contains 7.
- (1,6) is 0. Row 1: 8,9. Box 2: 8. Candidates: {1,2,3,4,5,6}.
- (2,6) is 0. Row 2: 6,8,3. Box 2: 8. Candidates: {1,2,4,5,7,9}. Remove 7 (col 6). Candidates: {1,2,4,5,9}.
- (3,6) is 0. Row 3: 1,9,5,6. Box 2: 8. Candidates: {2,3,4,7,8}. Remove 7 (col 6). Candidates: {2,3,4,8}.
- (4,6) is 0. Row 4: 4,5,6,1. Box 5: 1,6. Candidates: {2,3,7,8,9}. Remove 7 (col 6). Candidates: {2,3,8,9}.
- (5,6) is 0. Row 5: 3,7,1,8. Box 5: 1,6. Candidates: {2,4,5,6,9}. Remove 7 (col 6). Candidates: {2,4,5,9}.
- (6,6) is 0. Row 6: 9,1,2,6. Box 5: 1,6. Candidates: {3,4,5,7,8}. Remove 7 (col 6). Candidates: {3,4,5,8}.
- (7,6) is 0. Candidates {5,8}.
- (8,6) is 0. Candidates {5,6,8}.
- (9,6) is 7.
- Where can 6 go in Col 6? Possible: (1,6), (8,6). (Row 2 has 6, Row 3 has 6, Row 4 has 6, Row 5 has candidate 6?, Row 6 has 6, Row 7 has 6, Row 9 has candidate 6?). Let's check candidates for 6 in Col 6. (1,6){1,2,3,4,5,6}, (2,6){1,2,4,5,9}, (3,6){2,3,4,8}, (4,6){2,3,8,9}, (5,6){2,4,5,9}, (6,6){3,4,5,8}, (7,6){5,8}, (8,6){5,6,8}. So 6 can be in (1,6) or (8,6).
- Look at Box 2 (R1-3, C4-6). Contains 8. Needs 1,2,3,4,5,6,7,9.
- Cell (1,4) {2,5,7} (Recheck: Row 1: 8,9. Col 4: 8,1,6,3,9,4. Box 2: 8. Candidates: {1,2,3,4,5,6,7}. Remove 8,9 (row), 1,6,3,4 (col). Candidates: {2,5,7}). OK.
- Cell (1,5) {4,5,6,7} (Recheck: Row 1: 8,9. Col 5: 3,1,2. Box 2: 8. Candidates: {1..7}. Remove 8,9(row), 3,1,2(col). Candidates: {4,5,6,7}). OK.
- Cell (1,6) {1,2,3,4,5,6} (Recheck: Row 1: 8,9. Col 6: 7. Box 2: 8. Candidates: {1..7}. Remove 8,9(row), 7(col). Candidates: {1,2,3,4,5,6}). OK.
- Cell (2,4) {2,5,7,9} (Recheck: Row 2: 6,8,3. Col 4: 8,1,6,3,9,4. Box 2: 8. Candidates: {1,2,4,5,7,9}. Remove 6,8,3(row), 1,9,4(col). Candidates: {2,5,7}). ERROR in COL 4 check. Col 4: 080016394. Has 8,1,6,3,9,4. Missing 2,5,7. Check cell (2,4). Row 2: 6,8,3. Col 4: 1,6,3,9,4. Box 2: 8. Candidates: {1,2,4,5,7,9}. Remove 6,8,3(row), 1,9,4(col). Candidates: {2,5,7}. OK.
- Cell (2,5) {2,4,5,7,9} (Recheck: Row 2: 6,8,3. Col 5: 3,1,2. Box 2: 8. Candidates: {1,2,4,5,7,9}. Remove 6,8,3(row), 1,2(col). Candidates: {4,5,7,9}). OK.
- Cell (2,6) {1,2,4,5,9}. OK.
- Cell (3,4) {2,3,4,7,8} (Recheck: Row 3: 1,9,5,6. Col 4: 8,1,6,3,9,4. Box 2: 8. Candidates: {2,3,4,7,8}. Remove 1,9,5,6(row), 3,4(col). Candidates: {2,7,8}). OK.
- Cell (3,5) {2,3,4,7,8} (Recheck: Row 3: 1,9,5,6. Col 5: 3,1,2. Box 2: 8. Candidates: {2,3,4,7,8}. Remove 1,9,5,6(row), 3,2(col). Candidates: {4,7,8}). OK.
- Cell (3,6) {2,3,4,8}. OK.
- Where can 7 go in Box 2? Possible: (1,4), (1,5), (2,4), (2,5), (3,4), (3,5). Row 5 has 7. Row 9 has 7. Col 6 has 7. Cell (1,6) cannot be 7.
Candidates with 7: (1,4){2,5,7}, (1,5){4,5,6,7}, (2,4){2,5,7}, (2,5){4,5,7,9}, (3,4){2,7,8}, (3,5){4,7,8}.
Col 4 missing 2,5,7. Possible (1,4), (2,4), (3,4).
Col 5 missing 4,5,6,7,8,9. Possible (1,5), (2,5), (3,5).
In Box 2, 7 can only be in (1,4), (1,5), (2,4), (2,5), (3,4), (3,5). - Look at Col 4. Missing 2,5,7.
- Cell (1,4) {2,5,7}
- Cell (2,4) {2,5,7}
- Cell (3,4) {2,7,8} -> cannot be 5. Corrected: {2,7,8}. Still wrong. Row 3: 1,9,5,6. Col 4: 8,1,6,3,9,4. Box 2: 8. Possible: 2,7. Correct candidate set {2,7}.
- Cell (4,4) is 0. Row 4: 4,5,6,1. Box 5: 1,6. Col 4: 8,1,6,3,9,4. Candidates {2,3,7,8,9}. Remove 4,5,6,1 (row), 3,9 (col). Remove (none from box). Candidates {2,7,8}.
- Cell (5,4) is 1.
- Cell (6,4) is 6.
- Cell (7,4) is 3.
- Cell (8,4) is 9.
- Cell (9,4) is 4.
- In Col 4, missing 2,5,7. Candidates are: (1,4){2,5,7}, (2,4){2,5,7}, (3,4){2,7}, (4,4){2,7,8}. So 5 can only be in (1,4) or (2,4).
- Look at Row 1. Missing 1,2,3,4,5,6,7.
- (1,1){2,3,4,5}. (1,2){2,5,7}. (1,4){2,5,7}. (1,5){4,5,6,7}. (1,6){1,2,3,4,5,6}. (1,7){1,2,4,7}.
- Where can 3 go in Row 1? Possible: (1,1), (1,6). Box 1 needs 3. Col 1 needs 3. Col 6 needs 3.
- Where can 6 go in Row 1? Possible: (1,1), (1,5), (1,6). Row 1 has 8,9. Col 1 has 1,9,7. Col 2 has 4,3,1,6,9. Col 4 has 8,1,6,3,9,4. Col 5 has 3,1,2. Col 6 has 7. Col 7 has 5,6,9,1,4,3. Col 8 has 9,6,8,1. Col 9 has 3,1,2. Box 1 has 8,6,9,1,5. Box 2 has 8. Box 3 has 9,3,5,6.
- (1,1) {2,3,4,5}. No 6.
- (1,2) {2,5,7}. No 6.
- (1,4) {2,5,7}. No 6.
- (1,5) {4,5,6,7}. Yes 6.
- (1,6) {1,2,3,4,5,6}. Yes 6.
- (1,7) {1,2,4,7}. No 6.
Okay, where can 6 go in Row 1? Cell (1,5) or (1,6).
- Look at cell (5,5). Row 5: 3,7,1,8. Col 5: 3,1,2. Box 5: 1,6. Candidates: {2,4,5,6,9}. Remove 3,7,1,8 (row), (none from col 5), 6 (box 5). Candidates: {2,4,5,9}.
- Look at cell (5,6). Row 5: 3,7,1,8. Col 6: 7. Box 5: 1,6. Candidates: {2,4,5,9}. OK.
- Look at cell (5,7). Row 5: 3,7,1,8. Col 7: 8,6,9,5,1. Box 6: 6,1,8. Candidates: {2,4,5,6,9}. Remove 3,7,1,8 (row), 5,9 (col), 6 (box 6). Candidates: {2,4}.
- Look at cell (5,9). Row 5: 3,7,1,8. Col 9: 3,1,2. Box 6: 6,1,8. Candidates: {2,4,5,6,9}. Remove 3,7,1,8 (row), 2 (col), 6 (box 6). Candidates: {4,5,9}.
- Look at cell (4,5). Row 4: 4,5,6,1. Col 5: 3,1,2. Box 5: 1,6. Candidates: {2,3,7,8,9}. Remove 4,5,6,1 (row), 3,2 (col). Candidates: {7,8,9}.
- Look at cell (4,6). Candidates {2,3,8,9}. OK.
- Look at cell (4,7). Cell is 6.
- Look at cell (4,8). Candidates {2,3,7}. OK.
- Look at cell (4,9). Cell is 1.
- Look at cell (6,5). Row 6: 9,1,2,6. Col 5: 3,1,2. Box 5: 1,6. Candidates: {3,4,5,7,8}. Remove 9,1,2,6 (row), 3 (col). Candidates: {4,5,7,8}.
- Look at cell (6,6). Candidates {3,4,5,8}. OK.
- Look at cell (6,7). Row 6: 9,1,2,6. Col 7: 8,6,9,5,1. Box 6: 6,1,8. Candidates: {3,4,5,7,8}. Remove 9,1,2,6 (row), 5 (col), 8 (box 6). Candidates: {3,4,7}.
- Look at cell (6,8). Candidates {3,4,5,7}. OK.
- Look at cell (6,9). Row 6: 9,1,2,6. Col 9: 3,1,2. Box 6: 6,1,8. Candidates: {3,4,5,7,8}. Remove 9,1,2,6 (row), 3 (col), 8 (box 6). Candidates: {4,5,7}.
- Consider Box 5 (R4-6, C4-6). Contains 1,6. Needs 2,3,4,5,7,8,9.
- (4,4){2,7,8}
- (4,5){7,8,9}
- (4,6){2,3,8,9}
- (5,4)=1
- (5,5){2,4,5,9}
- (5,6){2,4,5,9}
- (6,4)=6
- (6,5){4,5,7,8}
- (6,6){3,4,5,8}
- Where can 3 go in Box 5? Possible: (4,6), (6,6).
- Where can 4 go in Box 5? Possible: (5,5), (5,6), (6,5), (6,6).
- Where can 5 go in Box 5? Possible: (5,5), (5,6), (6,5), (6,6).
- Where can 7 go in Box 5? Possible: (4,4), (4,5), (6,5).
- Where can 8 go in Box 5? Possible: (4,4), (4,5), (4,6), (6,5), (6,6).
- Where can 9 go in Box 5? Possible: (4,5), (4,6), (5,5), (5,6).
- Hidden Single: Look at number 7 in Col 4. Candidates: (1,4){2,5,7}, (2,4){2,5,7}, (3,4){2,7}, (4,4){2,7,8}. It can be in any of these cells.
- Hidden Single: Look at number 2 in Col 4. Candidates: (1,4){2,5,7}, (2,4){2,5,7}, (3,4){2,7}, (4,4){2,7,8}. Can be in any of these cells.
- Hidden Single: Look at number 5 in Col 4. Candidates: (1,4){2,5,7}, (2,4){2,5,7}. Must be in (1,4) or (2,4).
- Let's try Number Filling again.
<method>Number Filling</method> - Number 2 in Box 1 (R1-3, C1-3). Needs 2,3,4,5,7. Box contains 8,6,1,9. Col 1 has 7. Col 2 has 4,3,1,6,9. Col 3 has 8,6,9,5,7,2,1,4,3. Row 1 has 8,9. Row 2 has 6,8,3. Row 3 has 1,9,5,6.
- (1,1){2,3,4,5}. Needs 2,4. OK {2,4}. Col 1 has 7,1,9. Row 1 has 8,9. Box has 8,6,1,9. Candidates {2,3,4,5,7}. Remove 7 (col 1). Remove 3 (cell (9,3)=3). Candidates {2,4,5}.
- (1,2){2,5,7}. OK.
- (2,1){2,4,5,7,9}. Row 2: 6,8,3. Col 1: 1,9,7. Box 1: 8,6,1,9. Candidates {2,4,5}.
- (2,2){2,5,7}. OK.
- (3,1) is 1.
- (3,2){2,7}. OK.
- Where can 2 go in Box 1? Possible: (1,1), (1,2), (2,1), (2,2), (3,2).
- Where can 4 go in Box 1? Possible: (1,1), (2,1). Cell (1,1){2,4,5}, (2,1){2,4,5}. Row 3 has no 4. Row 4 has 4. Col 2 has 4. Col 3 has 4. So 4 in Box 1 must be in C1. Either (1,1) or (2,1).
- Where can 5 go in Box 1? Possible: (1,1), (1,2), (2,1), (2,2). Cell (1,1){2,4,5}, (1,2){2,5,7}, (2,1){2,4,5}, (2,2){2,5,7}. Col 3 has 5. Row 3 has 5. Row 4 has 5. So 5 must be in (1,1), (1,2), (2,1), (2,2).
- Where can 7 go in Box 1? Possible: (1,2), (2,2), (3,2). Cell (1,2){2,5,7}, (2,2){2,5,7}, (3,2){2,7}. Row 5 has 7. Row 7 has 7. Row 9 has 7. Col 1 has 7. Col 6 has 7. Col 9 has 7 candidate. OK.
- Look at number 8 in Box 7 (R7-9, C1-3). Needs 2,5,8.
- (8,1){2,5,8}.
- (8,2){2,5,8}.
- (9,1){5,8}.
- 8 must be in (8,1), (8,2), or (9,1). Col 8 has 8. Row 5 has 8.
- Look at number 5 in Row 9. Needs 5,6,8.
- (9,1){5,8}.
- (9,5){5,6,8}.
- (9,7){6,8}.
- 5 in Row 9 must be in (9,1) or (9,5).
- Look at number 8 in Row 9. Needs 5,6,8.
- (9,1){5,8}.
- (9,5){5,6,8}.
- (9,7){6,8}.
- 8 in Row 9 must be in (9,1), (9,5) or (9,7).
- Look at number 6 in Row 9. Needs 5,6,8.
- (9,5){5,6,8}.
- (9,7){6,8}.
- 6 in Row 9 must be in (9,5) or (9,7).
- Look at number 5 in Col 1. Needs 2,3,4,5,6,8. Contains 1,9,7.
- (1,1){2,4,5}.
- (2,1){2,4,5}.
- (4,1) 0. Row 4: 4,5,6,1. Box 4: 4,5,3,7,9,1,2. Candidates {2,3,7,8,9}. Remove 4,5,6,1 (row), 7,9 (col). Remove 3 (Box 4 contains 3,7,9,1,2 and 5 from cell 4,3). Box 4: 5,4,?, 7,3,?, 2,1,9. Check Box 4 (R4-6, C1-3): 045, 037, 912. Needs 6,8. Cell (4,1) is 0. Candidates: {2,3,8}. Remove 5(row 4). {2,3,8}. Col 1 has 1,9,7. Needs 2,3,4,5,6,8. Candidates {2,3,8}. Cell (5,1) is 0. Row 5: 3,7,1,8. Box 4: 5,4,7,9,1,2. Candidates {2,4,5,6,9}. Remove 3,7,1,8(row), 9(col). Remove 5,4,2(box 4). Need to recompute Box 4 candidates.
- Let's restart candidate computation for some areas after placing 5 at (4,3), 1 at (7,3), 3 at (9,3), 9 at (9,2), 1 at (9,8).
Grid:
008 000 090
006 800 003
109 000 560
045 000 601
037 100 080
912 600 000
761 320 900
004 910 000
093 407 012 - Box 4 (R4-6, C1-3): 045, 037, 912. Needs 6,8.
- Cell (4,1). Row 4: 4,5,6,1. Col 1: 1,9,7. Box 4: 4,5,3,7,9,1,2. Needs 6,8. Candidates {2,3,8}. Remove 4,5,6,1 (row), 7,9 (col), 3,7,2 (box). Candidates {8}.
<step>Place 8 in (4,1).</step>
Grid:
008 000 090
006 800 003
109 000 560
845 000 601
037 100 080
912 600 000
761 320 900
004 910 000
093 407 012
- Cell (4,1). Row 4: 4,5,6,1. Col 1: 1,9,7. Box 4: 4,5,3,7,9,1,2. Needs 6,8. Candidates {2,3,8}. Remove 4,5,6,1 (row), 7,9 (col), 3,7,2 (box). Candidates {8}.
- Box 4 now needs 6. Cell (5,1) is the only empty cell left in Box 4's C1. It must be 6.
- Cell (5,1). Row 5: 3,7,1,8. Col 1: 1,9,7,8. Box 4: 4,5,3,7,9,1,2,8. Needs 6. Candidates {2,4,5,6,9}. Remove 3,7,1,8 (row), 9 (col), 4,5,2 (box). Candidate {6}.
<step>Place 6 in (5,1).</step>
Grid:
008 000 090
006 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
004 910 000
093 407 012
- Cell (5,1). Row 5: 3,7,1,8. Col 1: 1,9,7,8. Box 4: 4,5,3,7,9,1,2,8. Needs 6. Candidates {2,4,5,6,9}. Remove 3,7,1,8 (row), 9 (col), 4,5,2 (box). Candidate {6}.
- Col 1 is now complete: 8,0,1,8,6,9,7,0,0. Missing 2,3,4,5. Col 1: 8,0,1,8,6,9,7,0,0. ERROR! (4,1)=8. (5,1)=6. (6,1)=9. (7,1)=7. (8,1)=0. (9,1)=0. Col 1 has 8,1,8,6,9,7. ERROR - duplicate 8. Let's retrace.
- Placement of 8 in (4,1). Check candidates again. Row 4: 4,5,6,1. Col 1: 1,9,7. Box 4: 4,5,3,7,9,1,2. Needs 6,8. Candidates {2,3,8}. Remove 4,5,6,1 (row 4). This means candidate cannot be 6. OK. Candidates {2,3,8}. Remove 1,9,7 (col 1). OK. Candidates {2,3,8}. Remove 4,5,3,7,9,1,2 (box 4). Cannot be 3,7,2. Candidates {8}. Yes, 8 in (4,1) seems correct.
- Placement of 6 in (5,1). Check candidates again. Row 5: 3,7,1,8. Col 1: 1,9,7,8. Box 4: 4,5,3,7,9,1,2,8. Needs 6. Candidates {2,4,5,6,9}. Remove 3,7,1,8 (row 5). Candidates {2,4,5,6,9}. Remove 1,9,7,8 (col 1). Candidate {2,4,5,6}. Remove 4,5,3,7,9,1,2,8 (box 4). Cannot be 4,5,7,9,1,2,8. OK. Candidate {6}. Seems correct.
Let's check Col 1 again: Cell (1,1)=0, (2,1)=0, (3,1)=1, (4,1)=8, (5,1)=6, (6,1)=9, (7,1)=7, (8,1)=0, (9,1)=0. Missing 2,3,4,5.
Let's check Box 4 again: R4-6, C1-3: 845, 637, 912. This box is complete. No errors here.
Let's check Row 4 again: 845 000 601. Contains 8,4,5,6,1. Needs 2,3,7,9.
Let's check Row 5 again: 637 100 080. Contains 6,3,7,1,8. Needs 2,4,5,9.
The placements of 8 at (4,1) and 6 at (5,1) seem correct based on the state before placing them.
Continue Iteration 2
- Col 1 is 8,0,1,8,6,9,7,0,0. Where is the error? Let me check the initial grid.
008 000 090
006 800 003
109 000 560
040 000 601 <- (4,3) is 0 initially. I placed 5 here. 845 000 601.
037 100 080
912 600 000
760 320 900 <- (7,3) is 0 initially. I placed 1 here. 761 320 900.
004 910 000
000 407 002 <- (9,3) is 0 initially. I placed 3 here. (9,2)=9. (9,8)=1. 093 407 012.
Grid state before placing 8 at (4,1):
008 000 090
006 800 003
109 000 560
045 000 601
037 100 080
912 600 000
761 320 900
004 910 000
093 407 012 - Check (4,1) again. Row 4: 4,5,6,1. Col 1: 1,9,7. Box 4 (R4-6, C1-3): 4,5, 3,7, 9,1,2. Needs 6,8.
- Cell (4,1) is 0. Candidates: {1..9}. Remove 4,5,6,1 (row 4). Leaves {2,3,7,8,9}. Remove 1,9,7 (col 1). Leaves {2,3,8}. Remove 4,5,3,7,9,1,2 (box 4 neighbours). Leaves {8}. Yes, (4,1) = 8.
- Check (5,1) again. Row 5: 3,7,1,8. Col 1: 1,9,7,8 (now includes 8 at (4,1)). Box 4: 4,5,3,7,9,1,2,8 (now includes 8 at (4,1)). Needs 6.
- Cell (5,1) is 0. Candidates {1..9}. Remove 3,7,1,8 (row 5). Leaves {2,4,5,6,9}. Remove 1,9,7,8 (col 1). Leaves {2,4,5,6}. Remove 4,5,3,7,9,1,2,8 (box 4 neighbours). Cannot be 4,5,7,9,1,2,8. Leaves {6}. Yes, (5,1)=6.
My initial grid transcription in thought process seems ok. The placements seem ok.
Let's write the grid state again carefully.
845 000 601 (Row 4)
637 100 080 (Row 5)
912 600 000 (Row 6)
Col 1: 0, 0, 1, 8, 6, 9, 7, 0, 0. Missing 2,3,4,5.
Cells (1,1), (2,1), (8,1), (9,1) are empty.
(1,1) candidates {2,3,4,5}. Remove 8,9 (R1), 1,8,6,9,7(C1), 8,6,9,1 (B1). Candidates {2,3,4,5}. Remove 6 (B1), 8 (C1). Leaves {2,3,4,5}.
(2,1) candidates {1..9}. Remove 6,8,3 (R2), 1,8,6,9,7 (C1), 8,6,9,1 (B1). Candidates {2,4,5,7}. Remove 8,6,9,7 (C1). Leaves {2,4,5}.
(8,1) candidates {1..9}. Remove 4,9,1 (R8), 1,8,6,9,7 (C1), 7,6,1,4,3,9 (B7). Candidates {2,3,5,8}. Remove 8,6,7 (C1). Leaves {2,3,5}.
(9,1) candidates {1..9}. Remove 9,3,4,7,1,2 (R9), 1,8,6,9,7 (C1), 7,6,1,4,3,9 (B7). Candidates {5,8}. Remove 8,6,7 (C1). Leaves {5}.
So, (9,1) must be 5.
<step>Place 5 in (9,1).</step>
Grid:
008 000 090
006 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
004 910 000
593 407 012
- Cell (5,1) is 0. Candidates {1..9}. Remove 3,7,1,8 (row 5). Leaves {2,4,5,6,9}. Remove 1,9,7,8 (col 1). Leaves {2,4,5,6}. Remove 4,5,3,7,9,1,2,8 (box 4 neighbours). Cannot be 4,5,7,9,1,2,8. Leaves {6}. Yes, (5,1)=6.
- Now Col 1: 0,0,1,8,6,9,7,0,5. Missing 2,3,4.
- (1,1) Candidates {2,3,4,5}. Remove 5 (new C1). Leaves {2,3,4}.
- (2,1) Candidates {2,4,5}. Remove 5 (new C1). Leaves {2,4}.
- (8,1) Candidates {2,3,5}. Remove 5 (new C1). Leaves {2,3}.
- Row 9: 5,9,3,4,0,7,0,1,2. Missing 6,8.
- (9,5) Candidates {5,6,8}. Remove 5 (new R9). Leaves {6,8}.
- (9,7) Candidates {6,8}. Leaves {6,8}.
- Box 7 (R7-9, C1-3): 761, 004, 593. Needs 2,8.
- (8,1) Candidates {2,3}. Must be 2 or 8. Box needs 2,8. Row 8 has 4,9,1. Col 1 has 1,8,6,9,7,5. Needs 2,3,4. Cannot be 8 (C1). ERROR: Col 1 has 8 at (4,1). So (8,1) cannot be 8. Must be 2 or 3. But Box 7 needs 2 or 8. So (8,1) must be 2.
<step>Place 2 in (8,1).</step>
Grid:
008 000 090
006 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
204 910 000
593 407 012
- (8,1) Candidates {2,3}. Must be 2 or 8. Box needs 2,8. Row 8 has 4,9,1. Col 1 has 1,8,6,9,7,5. Needs 2,3,4. Cannot be 8 (C1). ERROR: Col 1 has 8 at (4,1). So (8,1) cannot be 8. Must be 2 or 3. But Box 7 needs 2 or 8. So (8,1) must be 2.
- Box 7 (R7-9, C1-3): Needs 8. Only empty cell is (8,2).
<step>Place 8 in (8,2).</step>
Grid:
008 000 090
006 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
284 910 000
593 407 012 - Col 1: 0,0,1,8,6,9,7,2,5. Missing 3,4.
- (1,1) Candidates {2,3,4}. Remove 2 (new C1). Leaves {3,4}.
- (2,1) Candidates {2,4}. Remove 2 (new C1). Leaves {4}.
<step>Place 4 in (2,1).</step>
Grid:
008 000 090
406 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
284 910 000
593 407 012
- Col 1: 0,4,1,8,6,9,7,2,5. Missing 3. Cell (1,1) must be 3.
<step>Place 3 in (1,1).</step>
Grid:
308 000 090
406 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
284 910 000
593 407 012 - Box 1 (R1-3, C1-3): 308, 406, 109. Needs 2,5,7.
- (1,2). Row 1: 3,8,9. Col 2: 4,3,1,6,8,9. Box 1: 3,8,4,6,1,9. Candidates {1..9}. Remove 3,8,9(R1). Remove 4,6,8,9(C2). Remove 4,6,1(B1). Leaves {2,5,7}. Still {2,5,7}.
- (2,2). Row 2: 4,6,8,3. Col 2: 4,3,1,6,8,9. Box 1: 3,8,4,6,1,9. Candidates {1..9}. Remove 4,6,8,3(R2). Remove 8,9(C2). Remove 1(B1). Leaves {2,5,7}. Still {2,5,7}.
- (3,2). Row 3: 1,9,5,6. Col 2: 4,3,1,6,8,9. Box 1: 3,8,4,6,1,9. Candidates {1..9}. Remove 1,9,5,6(R3). Remove 4,3,8(C2). Remove 8(B1). Leaves {2,7}. Still {2,7}.
- Row 8: 2,8,4,9,1,0,0,0,0. Missing 3,5,6,7.
- (8,6). Candidates {5,6,8}. Row 8 has 8. Col 6 has 7. Box 8 has 3,2,9,1,4,7. Needs 5,6,8. Candidates {5,6}. (Removed 8 from row).
- (8,7). Candidates {3,6,7,8}. Row 8 has 8. Col 7 has 8,6,9,5,1. Box 9 has 9,1,2,3(R9C3), 5(R9C1), 8(R8C2). Need to update Box 9. Box 9 (R7-9, C7-9): 900, 000, 012. Contains 9,1,2. Needs 3,4,5,6,7,8. (7,7)=9. (7,8)=0. (7,9)=0. (8,7)=0. (8,8)=0. (8,9)=0. (9,7)=0. (9,8)=1. (9,9)=2. Update numbers: (7,3)=1, (9,3)=3, (9,2)=9, (9,1)=5, (8,1)=2, (8,2)=8. Box 9 state: 900 / 080 / 012. Contains 9,8,1,2. Needs 3,4,5,6,7.
Let's re-evaluate candidates for (8,7). Row 8: 2,8,4,9,1. Needs 3,5,6,7. Col 7: 8,6,9,5,1,?. Box 9: 9,8,1,2. Needs 3,4,5,6,7. Candidates {3,5,6,7}. Remove 6,5 (from Col 7 list: 8,6,9,5,1). Leaves {3,7}. - (8,8). Candidates {3,5,7}. Row 8: 2,8,4,9,1. Col 8: 9,6,8,1. Box 9: 9,8,1,2. Needs 3,4,5,6,7. Candidates {3,5,7}. Remove 6 (Col 8). Leaves {3,5,7}.
- (8,9). Candidates {5,6,7,8}. Row 8 has 8. Col 9: 3,1,2. Box 9: 9,8,1,2. Needs 3,4,5,6,7. Candidates {5,6,7}. Remove 3 (Col 9). Leaves {5,6,7}.
- Row 8 needs 3,5,6,7.
- (8,6){5,6}
- (8,7){3,7}
- (8,8){3,5,7}
- (8,9){5,6,7}
- Where can 3 go in Row 8? Possible: (8,7), (8,8).
- Where can 5 go in Row 8? Possible: (8,6), (8,8), (8,9).
- Where can 6 go in Row 8? Possible: (8,6), (8,9).
- Where can 7 go in Row 8? Possible: (8,7), (8,8), (8,9).
- Look at Col 2. 0,0,0,4,3,1,6,8,9. Missing 2,5,7.
- (1,2){2,5,7}
- (2,2){2,5,7}
- (3,2){2,7}
- Look at Col 7. 0,0,5,6,0,0,9,0,0. Missing 1,2,3,4,7,8.
- (1,7) {1,2,4,7}. Row 1: 3,8,9. Box 3: 9,3,5,6. Candidates {1,2,4,7}. Remove 3,8,9(R1), 5,6(B3). Leaves {1,2,4,7}. OK.
- (2,7) {1,2,4,7,8,9}. Row 2: 4,6,8,3. Box 3: 9,3,5,6. Candidates {1,2,4,7,8,9}. Remove 4,6,8,3(R2), 5(C7), 9,5,6(B3). Leaves {1,2,7}.
- (3,7) is 5.
- (4,7) is 6.
- (5,7) {2,4}. Row 5: 6,3,7,1,8. Box 6: 6,1,8. Col 7: 5,6,9. Candidates {2,4}. Remove 6,3,7,1,8(R5), 5,6,9(C7), 6,1,8(B6). Leaves {2,4}. OK.
- (6,7) {3,4,7}. Row 6: 9,1,2,6. Box 6: 6,1,8. Col 7: 5,6,9. Candidates {3,4,7}. Remove 9,1,2,6(R6), 5(C7), 6,1,8(B6). Leaves {3,4,7}. OK.
- (7,7) is 9.
- (8,7) {3,7}. OK.
- (9,7) {6,8}. Row 9: 5,9,3,4,7,1,2. Box 9: 9,8,1,2. Col 7: 5,6,9. Candidates {6,8}. Remove 5,9,3,4,7,1,2(R9), 6(C7), 8(B9). Leaves { }. ERROR. Recheck (9,7). Row 9: 5,9,3,4,7,1,2. Needs 6,8. Col 7: 5,6,9. Needs 1,2,3,4,7,8. Box 9: 9,8,1,2. Needs 3,4,5,6,7. Candidates {6,8}. OK. Remove 7(R9). Leaves {6,8}. Remove 6(C7). Leaves {8}.
<step>Place 8 in (9,7).</step>
Grid:
308 000 090
406 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
284 910 000
593 407 812
- Row 9: 5,9,3,4,0,7,8,1,2. Missing 6. Cell (9,5) must be 6.
<step>Place 6 in (9,5).</step>
Grid:
308 000 090
406 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
284 910 000
593 467 812 - Box 8 (R7-9, C4-6): 320, 910, 467. Needs 5,8.
- (7,6). Candidates {5,8}. Row 7: 7,6,1,3,2,9. OK. Col 6: 7. OK. Box 8: 3,2,9,1,4,7,6. Needs 5,8. Candidates {5,8}.
- (8,6). Candidates {5,6}. Row 8: 2,8,4,9,1. Col 6: 7. Box 8: 3,2,9,1,4,7,6. Needs 5,8. Candidates {5}. (6 is placed in (9,5)).
<step>Place 5 in (8,6).</step>
Grid:
308 000 090
406 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 320 900
284 915 000
593 467 812
- Box 8 now needs 8. Cell (7,6) must be 8.
<step>Place 8 in (7,6).</step>
Grid:
308 000 090
406 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 328 900
284 915 000
593 467 812 - Row 8: 2,8,4,9,1,5,0,0,0. Missing 3,6,7.
- (8,7){3,7}. OK.
- (8,8){3,5,7}. Remove 5 (from 8,6). Leaves {3,7}.
- (8,9){5,6,7}. Remove 5 (from 8,6). Leaves {6,7}.
- Where can 6 go in Row 8? Only in (8,9).
<step>Place 6 in (8,9).</step>
Grid:
308 000 090
406 800 003
109 000 560
845 000 601
637 100 080
912 600 000
761 328 900
284 915 006
593 467 812 - Row 8: 2,8,4,9,1,5,0,0,6. Missing 3,7.
- (8,7){3,7}.
- (8,8){3,7}.
- Col 9: 0,3,0,1,0,0,0,6,2. Missing 4,5,7,8,9.
- (1,9) 0. Row 1: 3,8,9. Box 3: 9,3,5,6. Candidates {1,2,4,7}. Remove 3,8,9(R1), 3,1,2,6(C9), 5,6(B3). Leaves {2,4,7}. Update: C9 has 3,1,2,6. Needs 4,5,7,8,9. Cell (1,9) candidates {4,7}.
- (3,9) 0. Row 3: 1,9,5,6. Box 3: 9,3,5,6. Candidates {2,3,4,7,8}. Remove 1,9,5,6(R3), 3,1,2,6(C9). Leaves {4,7,8}. Remove 3(B3). Leaves {4,7,8}.
- (5,9) 0. Row 5: 6,3,7,1,8. Box 6: 6,1,8. Candidates {4,5,9}. Remove 6,3,7,1,8(R5), 3,1,2,6(C9), 8(B6). Leaves {4,5,9}. Recheck candidates for (5,9). Needs 2,4,5,9 (Row 5). Needs 4,5,7,8,9 (Col 9). Needs 2,3,4,5,7,9 (Box 6). Intersection: {4,5,9}. OK.
- (6,9) 0. Row 6: 9,1,2,6. Box 6: 6,1,8. Candidates {4,5,7}. Remove 9,1,2,6(R6), 3,1,2,6(C9), 8(B6). Leaves {4,5,7}. OK.
- (7,9) 0. Row 7: 7,6,1,3,2,8,9. Box 9: 9,8,1,2. Candidates {4,5}. Remove 7,6,1,3,2,8,9(R7), 3,1,2,6(C9), 8(B9). Leaves {4,5}. OK.
- Where can 4 go in Col 9? (1,9), (3,9), (5,9), (6,9), (7,9).
- Where can 5 go in Col 9? (5,9), (6,9), (7,9).
- Where can 7 go in Col 9? (1,9), (3,9), (6,9).
- Where can 8 go in Col 9? (3,9). -> Col 9 needs 4,5,7,8,9. Cell (3,9) has candidates {4,7,8}. Cell (1,9){4,7}. (5,9){4,5,9}. (6,9){4,5,7}. (7,9){4,5}. So 8 can only be in (3,9).
<step>Place 8 in (3,9).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 000 601
637 100 080
912 600 000
761 328 900
284 915 006
593 467 812 - Row 3: 1,0,9,0,0,0,5,6,8. Missing 2,3,4,7.
- (3,2){2,7}. OK.
- (3,4){2,7}. (Recheck: Row 3: 1,9,5,6,8. Col 4: 8,1,6,3,9,4. Box 2: 8. Candidates {2,3,4,7}. Remove 1,9,5,6,8(R3), 3,4(C4). Leaves {2,7}). OK.
- (3,5){4,7,8}. Remove 8 (R3). Leaves {4,7}. (Recheck: Row 3: 1,9,5,6,8. Col 5: 3,1,2,6. Box 2: 8. Candidates {2,3,4,7}. Remove 1,9,5,6,8(R3), 3,2,6(C5). Leaves {4,7}). OK.
- (3,6){2,3,4,8}. Remove 8 (R3). Leaves {2,3,4}. (Recheck: Row 3: 1,9,5,6,8. Col 6: 7,8,5. Box 2: 8. Candidates {2,3,4,7}. Remove 1,9,5,6,8(R3), 7,5(C6). Leaves {2,3,4}). OK.
- Col 9 needs 4,5,7,9.
- (1,9){4,7}. OK.
- (5,9){4,5,9}. OK.
- (6,9){4,5,7}. OK.
- (7,9){4,5}. OK.
- Where can 7 go in Col 9? (1,9), (6,9).
- Where can 4 go in Col 9? (1,9), (5,9), (6,9), (7,9).
- Where can 5 go in Col 9? (5,9), (6,9), (7,9).
- Where can 9 go in Col 9? (5,9).
<step>Place 9 in (5,9).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 000 601
637 100 089
912 600 000
761 328 900
284 915 006
593 467 812 - Row 5: 6,3,7,1,0,0,0,8,9. Missing 2,4,5.
- (5,5){2,4,5,9}. Remove 9 (R5). Leaves {2,4,5}. (Recheck: Row 5: 6,3,7,1,8,9. Col 5: 3,1,2,6. Box 5: 1,6. Needs 2,4,5. Candidates {2,4,5}). OK.
- (5,6){2,4,5,9}. Remove 9 (R5). Leaves {2,4,5}. (Recheck: Row 5: 6,3,7,1,8,9. Col 6: 7,8,5. Box 5: 1,6. Needs 2,4,5. Candidates {2,4}). OK.
- (5,7){2,4}. OK.
- Where can 5 go in Row 5? (5,5) or (5,6). Rechecked (5,6): Row 5 needs 2,4,5. Col 6 has 7,8,5. Box 5 has 1,6. Candidates {2,4}. So 5 cannot be in (5,6). Therefore 5 must be in (5,5).
<step>Place 5 in (5,5).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 000 601
637 150 089
912 600 000
761 328 900
284 915 006
593 467 812 - Row 5: 6,3,7,1,5,0,0,8,9. Missing 2,4.
- (5,6){2,4}. OK.
- (5,7){2,4}. OK.
- Col 5: 0,0,0,0,5,0,2,1,6. Missing 3,4,7,8,9.
- (1,5){4,5,6,7}. Remove 5,6 (C5). Leaves {4,7}. (Recheck: Row 1: 3,8,9. Box 2: 8. Col 5: 5,2,1,6. Candidates {1,2,4,5,6,7}. Remove 3,8,9(R1), 5,2,1,6(C5), 8(B2). Leaves {4,7}). OK.
- (2,5){4,5,7,9}. Remove 5 (C5). Leaves {4,7,9}. (Recheck: Row 2: 4,6,8,3. Box 2: 8. Col 5: 5,2,1,6. Candidates {1,2,4,5,7,9}. Remove 4,6,8,3(R2), 5,2,1,6(C5), 8(B2). Leaves {7,9}). OK.
- (3,5){4,7}. OK.
- (4,5){7,8,9}. Remove (none from C5). Leaves {7,8,9}. (Recheck: Row 4: 8,4,5,6,1. Box 5: 1,6,5. Col 5: 5,2,1,6. Candidates {2,3,7,8,9}. Remove 8,4,5,6,1(R4), 2(C5), (none B5). Leaves {3,7,9}. Error somewhere). Recheck (4,5). Row 4: 8,4,5,6,1. Col 5: 5,2,1,6. Box 5: 1,6,5. Needs 3,7,9. Candidates {3,7,9}. OK.
- (6,5){4,5,7,8}. Remove 5 (C5). Leaves {4,7,8}. (Recheck: Row 6: 9,1,2,6. Box 5: 1,6,5. Col 5: 5,2,1,6. Needs 3,4,7,8,9. Candidates {3,4,7,8}. OK.
- Where can 3 go in Col 5? (4,5), (6,5).
- Where can 4 go in Col 5? (1,5), (3,5), (6,5).
- Where can 7 go in Col 5? (1,5), (2,5), (3,5), (4,5), (6,5).
- Where can 8 go in Col 5? (6,5).
<step>Place 8 in (6,5).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 000 601
637 150 089
912 680 000
761 328 900
284 915 006
593 467 812 - Col 5: 0,0,0,0,5,8,2,1,6. Missing 3,4,7,9.
- (1,5){4,7}. OK.
- (2,5){7,9}. OK.
- (3,5){4,7}. OK.
- (4,5){3,7,9}. OK.
- Where can 3 go in Col 5? Only in (4,5).
<step>Place 3 in (4,5).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 030 601
637 150 089
912 680 000
761 328 900
284 915 006
593 467 812 - Col 5: 0,0,0,3,5,8,2,1,6. Missing 4,7,9.
- (1,5){4,7}. OK.
- (2,5){7,9}. OK.
- (3,5){4,7}. OK.
- Row 4: 8,4,5,0,3,0,6,0,1. Missing 2,7,9.
- (4,4){2,7,8}. Row 4 has 8. Col 4 has 8,1,6,3,9,4. Box 5 has 1,6,5,8,3. Candidates {2,7}. OK.
- (4,6){2,3,8,9}. Row 4 has 8,3. Col 6 has 7,8,5. Box 5 has 1,6,5,8,3. Candidates {2,9}. OK.
- (4,8){2,3,7}. Row 4 has 3. Col 8 has 9,6,8,1. Box 6 has 6,1,8,9. Candidates {2,7}. OK.
- Where can 9 go in Row 4? Only in (4,6).
<step>Place 9 in (4,6).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 039 601
637 150 089
912 680 000
761 328 900
284 915 006
593 467 812 - Row 4: 8,4,5,0,3,9,6,0,1. Missing 2,7.
- (4,4){2,7}.
- (4,8){2,7}.
- Col 6: 0,0,0,9,0,0,8,5,7. Missing 1,2,3,4,6.
- (1,6){1,2,3,4,5,6}. Remove 5 (C6). Leaves {1,2,3,4,6}. Row 1: 3,8,9. Box 2: 8. Candidates {1,2,4,6}.
- (2,6){1,2,4,5,9}. Remove 5,9 (C6). Leaves {1,2,4}. Row 2: 4,6,8,3. Box 2: 8. Candidates {1,2}.
- (3,6){2,3,4}. Row 3: 1,9,5,6,8. Box 2: 8. Candidates {2,3,4}. Remove none. OK.
- (5,6){2,4}. OK.
- (6,6) 0. Row 6: 9,1,2,6,8. Box 5: 1,6,5,8,3,9. Col 6: 9,8,5,7. Candidates {3,4,5,7,8}. Remove 9,1,2,6,8(R6), 5,7(C6), 3(B5). Leaves {4}.
<step>Place 4 in (6,6).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 039 601
637 150 089
912 684 000
761 328 900
284 915 006
593 467 812
- Col 6: 0,0,0,9,0,4,8,5,7. Missing 1,2,3,6.
- (1,6){1,2,4,6}. Remove 4 (C6). Leaves {1,2,6}.
- (2,6){1,2}. OK.
- (3,6){2,3,4}. Remove 4 (C6). Leaves {2,3}.
- (5,6){2,4}. Remove 4 (C6). Leaves {2}.
<step>Place 2 in (5,6).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 039 601
637 152 089
912 684 000
761 328 900
284 915 006
593 467 812
- Row 5: 6,3,7,1,5,2,0,8,9. Missing 4. Cell (5,7) must be 4.
<step>Place 4 in (5,7).</step>
Grid:
308 000 090
406 800 003
109 000 568
845 039 601
637 152 489
912 684 000
761 328 900
284 915 006
593 467 812 - Col 6: 0,0,0,9,2,4,8,5,7. Missing 1,3,6.
- (1,6){1,2,6}. Remove 2 (C6). Leaves {1,6}.
- (2,6){1,2}. Remove 2 (C6). Leaves {1}.
<step>Place 1 in (2,6).</step>
Grid:
308 001 090
406 801 003
109 000 568
845 039 601
637 152 489
912 684 000
761 328 900
284 915 006
593 467 812
- Col 6: 0,1,0,9,2,4,8,5,7. Missing 3,6.
- (1,6){1,6}. Remove 1 (C6). Leaves {6}.
<step>Place 6 in (1,6).</step>
Grid:
308 006 090
406 801 003
109 000 568
845 039 601
637 152 489
912 684 000
761 328 900
284 915 006
593 467 812
- (1,6){1,6}. Remove 1 (C6). Leaves {6}.
- Col 6: 6,1,0,9,2,4,8,5,7. Missing 3. Cell (3,6) must be 3.
<step>Place 3 in (3,6).</step>
Grid:
308 006 090
406 801 003
109 003 568
845 039 601
637 152 489
912 684 000
761 328 900
284 915 006
593 467 812 - Row 1: 3,0,8,0,0,6,0,9,0. Missing 1,2,4,5,7.
- (1,2){2,5,7}. OK.
- (1,4){2,5,7}. OK.
- (1,5){4,7}. OK.
- (1,7){1,2,4,7}. Row 1 has 6. Box 3 has 9,3,5,6,8. Col 7 has 5,4,9. Candidates {1,2,7}.
- (1,9){4,7}. OK.
- Row 3: 1,0,9,0,0,3,5,6,8. Missing 2,4,7.
- (3,2){2,7}. OK.
- (3,4){2,7}. OK.
- (3,5){4,7}. OK.
- Where can 4 go in Row 3? Only in (3,5).
<step>Place 4 in (3,5).</step>
Grid:
308 006 090
406 801 003
109 043 568
845 039 601
637 152 489
912 684 000
761 328 900
284 915 006
593 467 812 - Row 3: 1,0,9,0,4,3,5,6,8. Missing 2,7.
- (3,2){2,7}. OK.
- (3,4){2,7}. OK.
- Col 5: 0,0,4,3,5,8,2,1,6. Missing 7,9.
- (1,5){4,7}. Remove 4 (C5). Leaves {7}.
<step>Place 7 in (1,5).</step>
Grid:
308 076 090
406 801 003
109 043 568
845 039 601
637 152 489
912 684 000
761 328 900
284 915 006
593 467 812
- (1,5){4,7}. Remove 4 (C5). Leaves {7}.
- Col 5: 7,0,4,3,5,8,2,1,6. Missing 9. Cell (2,5) must be 9.
<step>Place 9 in (2,5).</step>
Grid:
308 076 090
406 891 003
109 043 568
845 039 601
637 152 489
912 684 000
761 328 900
284 915 006
593 467 812 - Row 1: 3,0,8,0,7,6,0,9,0. Missing 1,2,4,5.
- (1,2){2,5,7}. Remove 7 (R1). Leaves {2,5}.
- (1,4){2,5,7}. Remove 7 (R1). Leaves {2,5}.
- (1,7){1,2,7}. Remove 7 (R1). Leaves {1,2}.
- (1,9){4,7}. Remove 7 (R1). Leaves {4}.
<step>Place 4 in (1,9).</step>
Grid:
308 076 094
406 891 003
109 043 568
845 039 601
637 152 489
912 684 000
761 328 900
284 915 006
593 467 812
- Row 1: 3,0,8,0,7,6,0,9,4. Missing 1,2,5.
- (1,2){2,5}.
- (1,4){2,5}.
- (1,7){1,2}.
- Row 2: 4,0,6,8,9,1,0,0,3. Missing 2,5,7.
- (2,2){2,5,7}. OK.
- (2,7){1,2,7}. Row 2 has 1. Leaves {2,7}. OK.
- (2,8) 0. Row 2: 4,6,8,9,1,3. Col 8: 9,6,8,1,5. Box 3: 9,3,5,6,8,4(R1C9). Needs 1,2,7. Candidates {2,5,7}. Remove 5 (Col 8). Leaves {2,7}.
- Col 4: 0,8,0,0,1,6,3,9,4. Missing 2,5,7.
- (1,4){2,5}.
- (3,4){2,7}.
- (4,4){2,7}.
- Col 8: 9,0,6,0,8,0,0,0,1. Missing 2,3,4,5,7.
- (2,8){2,7}.
- (4,8){2,7}.
- (6,8) 0. Row 6: 9,1,2,6,8,4. Box 6: 6,1,8,9,4. Col 8: 9,6,8,1,5. Needs 2,3,4,7. Candidates {3,4,5,7}. Remove 4(R6), 5(C8). Leaves {3,7}.
- (7,8) 0. Row 7: 7,6,1,3,2,8,9. Box 9: 9,8,1,2,4(R5C7?), 6(R8C9), 5(R9C1). Needs 3,4,5,6,7. Col 8: 9,6,8,1,5. Needs 2,3,4,7. Candidates {4,5}. Remove 5(C8). Leaves {4}.
<step>Place 4 in (7,8).</step>
Grid:
308 076 094
406 891 003
109 043 568
845 039 601
637 152 489
912 684 000
761 328 940
284 915 006
593 467 812
- Col 8: 9,0,6,0,8,0,4,0,1. Missing 2,3,5,7.
- (2,8){2,7}.
- (4,8){2,7}.
- (6,8){3,7}.
- (8,8){3,7}. Recheck (8,8). Row 8: 2,8,4,9,1,5,6. Needs 3,7. Col 8: 9,6,8,1,5,4. Needs 2,3,7. Box 9: 9,8,1,2,4,6. Needs 3,5,7. Candidates {3,7}. OK.
- Where can 3 go in Col 8? (6,8) or (8,8).
- Where can 2 go in Col 8? (2,8) or (4,8).
- Where can 7 go in Col 8? (2,8), (4,8), (6,8), (8,8).
- Row 7: 7,6,1,3,2,8,9,4,0. Missing 5. Cell (7,9) must be 5.
<step>Place 5 in (7,9).</step>
Grid:
308 076 094
406 891 003
109 043 568
845 039 601
637 152 489
912 684 000
761 328 945
284 915 006
593 467 812 - Col 9: 4,3,8,1,9,0,5,6,2. Missing 7. Cell (6,9) must be 7.
<step>Place 7 in (6,9).</step>
Grid:
308 076 094
406 891 003
109 043 568
845 039 601
637 152 489
912 684 007
761 328 945
284 915 006
593 467 812 - Row 6: 9,1,2,6,8,4,0,0,7. Missing 3,5.
- (6,7) {3,4,7}. Row 6 has 4,7. Col 7 has 5,4,9. Box 6 has 6,1,8,9,4,7. Needs 2,3,5. Candidates {3}.
<step>Place 3 in (6,7).</step>
Grid:
308 076 094
406 891 003
109 043 568
845 039 601
637 152 489
912 684 307
761 328 945
284 915 006
593 467 812
- (6,7) {3,4,7}. Row 6 has 4,7. Col 7 has 5,4,9. Box 6 has 6,1,8,9,4,7. Needs 2,3,5. Candidates {3}.
- Row 6: 9,1,2,6,8,4,3,0,7. Missing 5. Cell (6,8) must be 5.
<step>Place 5 in (6,8).</step>
Grid:
308 076 094
406 891 003
109 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 006
593 467 812 - Col 8: 9,0,6,0,8,5,4,0,1. Missing 2,3,7.
- (2,8){2,7}.
- (4,8){2,7}.
- (8,8){3,7}.
- Where can 3 go in Col 8? Only in (8,8).
<step>Place 3 in (8,8).</step>
Grid:
308 076 094
406 891 003
109 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 036
593 467 812 - Col 8: 9,0,6,0,8,5,4,3,1. Missing 2,7.
- (2,8){2,7}.
- (4,8){2,7}.
- Row 8: 2,8,4,9,1,5,0,3,6. Missing 7. Cell (8,7) must be 7.
<step>Place 7 in (8,7).</step>
Grid:
308 076 094
406 891 003
109 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812 - Col 7: 0,0,5,6,4,3,9,7,8. Missing 1,2.
- (1,7){1,2}.
- (2,7){2,7}. Remove 7(C7). Leaves {2}.
<step>Place 2 in (2,7).</step>
Grid:
308 076 094
406 891 203
109 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812
- Col 7: 0,2,5,6,4,3,9,7,8. Missing 1. Cell (1,7) must be 1.
<step>Place 1 in (1,7).</step>
Grid:
308 076 194
406 891 203
109 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812 - Row 1: 3,0,8,0,7,6,1,9,4. Missing 2,5.
- (1,2){2,5}.
- (1,4){2,5}.
- Row 2: 4,0,6,8,9,1,2,0,3. Missing 5,7.
- (2,2){2,5,7}. Remove 2(R2). Leaves {5,7}.
- (2,8){2,7}. Remove 2(R2). Leaves {7}.
<step>Place 7 in (2,8).</step>
Grid:
308 076 194
406 891 273
109 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812
- Row 2: 4,0,6,8,9,1,2,7,3. Missing 5. Cell (2,2) must be 5.
<step>Place 5 in (2,2).</step>
Grid:
308 076 194
456 891 273
109 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812 - Col 2: 0,5,0,4,3,1,6,8,9. Missing 2,7.
- (1,2){2,5}. Remove 5(C2). Leaves {2}.
<step>Place 2 in (1,2).</step>
Grid:
328 076 194
456 891 273
109 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812
- (1,2){2,5}. Remove 5(C2). Leaves {2}.
- Col 2: 2,5,0,4,3,1,6,8,9. Missing 7. Cell (3,2) must be 7.
<step>Place 7 in (3,2).</step>
Grid:
328 076 194
456 891 273
179 043 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812 - Row 3: 1,7,9,0,4,3,5,6,8. Missing 2. Cell (3,4) must be 2.
<step>Place 2 in (3,4).</step>
Grid:
328 076 194
456 891 273
179 243 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812 - Col 4: 0,8,2,0,1,6,3,9,4. Missing 5,7.
- (1,4){2,5}. Remove 2(C4). Leaves {5}.
<step>Place 5 in (1,4).</step>
Grid:
328 576 194
456 891 273
179 243 568
845 039 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812
- (1,4){2,5}. Remove 2(C4). Leaves {5}.
- Col 4: 5,8,2,0,1,6,3,9,4. Missing 7. Cell (4,4) must be 7.
<step>Place 7 in (4,4).</step>
Grid:
328 576 194
456 891 273
179 243 568
845 739 601
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812 - Row 4: 8,4,5,7,3,9,6,0,1. Missing 2. Cell (4,8) must be 2.
<step>Place 2 in (4,8).</step>
Grid:
328 576 194
456 891 273
179 243 568
845 739 621
637 152 489
912 684 357
761 328 945
284 915 736
593 467 812 - Check grid. All cells filled. Verify rows, columns, boxes.
Row 1: 328576194 - OK
Row 2: 456891273 - OK
Row 3: 179243568 - OK
Row 4: 845739621 - OK
Row 5: 637152489 - OK
Row 6: 912684357 - OK
Row 7: 761328945 - OK
Row 8: 284915736 - OK
Row 9: 593467812 - OK
Col 1: 341869725 - OK
Col 2: 257431689 - OK
Col 3: 869572143 - OK
Col 4: 582716394 - OK
Col 5: 794358216 - OK
Col 6: 613924857 - OK
Col 7: 125643978 - OK
Col 8: 976285431 - OK
Col 9: 438197562 - OK
Box 1: 328 456 179 - OK
Box 2: 576 891 243 - OK
Box 3: 194 273 568 - OK
Box 4: 845 637 912 - OK
Box 5: 739 152 684 - OK
Box 6: 621 489 357 - OK
Box 7: 761 284 593 - OK
Box 8: 328 915 467 - OK
Box 9: 945 736 812 - OK
Solution seems correct.