Sudoku Solution No. 21

Hard Score 71 / 100
Digits appear one by one.

Step-by-step solution

Steps 65 Estimated time 65 – 98 min Hardest technique Box/Line Clues 23
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCc≠d)
1 Naked Single ✓ R6C1=5
Look at cell R6C1. Every other digit already appears in its row, column or box. Only one option remains: R6C1 = 5.
2 Hidden Single ✓ R1C8=3
Scan the empty cells in this column where 3 could go. Across the whole column, 3 has only one possible spot left. So R1C8 = 3.
3 Hidden Single ✓ R2C8=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R2C8 = 7.
4 Hidden Single ✓ R4C9=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R4C9 = 8.
5 Hidden Single ✓ R6C4=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R6C4 = 8.
6 Hidden Single ✓ R7C7=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R7C7 = 2.
7 Hidden Single ✓ R9C4=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R9C4 = 1.
8 Hidden Single ✓ R9C7=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R9C7 = 8.
9 Hidden Single ✓ R4C1=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R4C1 = 4.
10 Naked Pair ✗ 9 eliminations
(1) Spot R8C2 and R8C8 on this row. (2) Spot R6C2 and R6C3 in this box. (1) These two cells can only hold 5 and 9: they reserve those digits. (2) These two cells can only hold 3 and 6: they reserve those digits. (1) 5 and 9 are therefore removed from the other cells of the row. (2) 3 and 6 are therefore removed from the other cells of the box.
11 Naked Single ✓ R8C3=8
Look at cell R8C3. Every other digit already appears in its row, column or box. Only one option remains: R8C3 = 8.
12 Naked Single ✓ R8C6=2
Look at cell R8C6. Every other digit already appears in its row, column or box. Only one option remains: R8C6 = 2.
13 Pointing ✗ 3 eliminations
(1) Look at where 1 can go in this box. (2) Look at where 5 can go in this box. (1) All its spots lie on a single column (R1C9, R2C9 and R3C9). (2) All its spots lie on a single column (R7C2 and R8C2). (1) 1 is therefore removed from that column outside the box. (2) 5 is therefore removed from that column outside the box.
14 Naked Triple ✗ 5 eliminations
Spot R5C6, R5C7 and R5C9 on this row. These three cells share only 4, 5 and 6. 4, 5 and 6 are therefore removed from the rest of the row.
15 Naked Single ✓ R5C8=1
Look at cell R5C8. Every other digit already appears in its row, column or box. Only one option remains: R5C8 = 1.
16 Hidden Triple ✗ 7 eliminations
Find where 4, 7 and 9 can go in this box. These three digits only fit in R1C4, R1C5 and R3C5. The other candidates in R1C4, R1C5 and R3C5 are therefore eliminated.
17 Pointing ✗ 2 eliminations
Look at where 2 can go in this box. All its spots lie on a single row (R2C4 and R2C5). 2 is therefore removed from that row outside the box.
18 Skyscraper ✗ 2 eliminations
Find 6 on two rows, each with exactly two candidate positions. A shared column connects one end of each pair. Whichever way the logic falls, one of the two free ends must hold 6. R5C9 and R7C8 is seen by both free ends: 6 is therefore eliminated there.
19 Hidden Single ✓ R4C8=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R4C8 = 6.
20 Hidden Single ✓ R5C6=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R5C6 = 6.
21 Hidden Single ✓ R9C9=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R9C9 = 6.
22 Naked Single ✓ R9C5=5
Look at cell R9C5. Every other digit already appears in its row, column or box. Only one option remains: R9C5 = 5.
23 Naked Single ✓ R7C4=7
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 7.
24 Naked Single ✓ R7C6=8
Look at cell R7C6. Every other digit already appears in its row, column or box. Only one option remains: R7C6 = 8.
25 Naked Single ✓ R7C5=6
Look at cell R7C5. Every other digit already appears in its row, column or box. Only one option remains: R7C5 = 6.
26 Hidden Single ✓ R1C1=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R1C1 = 8.
27 Hidden Single ✓ R1C7=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R1C7 = 6.
28 Hidden Single ✓ R2C3=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R2C3 = 6.
29 Hidden Single ✓ R2C4=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R2C4 = 2.
30 Hidden Single ✓ R2C5=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R2C5 = 8.
31 Hidden Single ✓ R3C2=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R3C2 = 3.
32 Hidden Single ✓ R4C4=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R4C4 = 5.
33 Hidden Single ✓ R6C2=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R6C2 = 6.
34 Hidden Single ✓ R6C3=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R6C3 = 3.
35 Naked Single ✓ R2C1=1
Look at cell R2C1. Every other digit already appears in its row, column or box. Only one option remains: R2C1 = 1.
36 Naked Single ✓ R2C9=5
Look at cell R2C9. Every other digit already appears in its row, column or box. Only one option remains: R2C9 = 5.
37 Naked Single ✓ R3C7=4
Look at cell R3C7. Every other digit already appears in its row, column or box. Only one option remains: R3C7 = 4.
38 Naked Single ✓ R5C7=5
Look at cell R5C7. Every other digit already appears in its row, column or box. Only one option remains: R5C7 = 5.
39 Naked Single ✓ R5C9=4
Look at cell R5C9. Every other digit already appears in its row, column or box. Only one option remains: R5C9 = 4.
40 Naked Single ✓ R7C1=9
Look at cell R7C1. Every other digit already appears in its row, column or box. Only one option remains: R7C1 = 9.
41 Naked Single ✓ R7C8=5
Look at cell R7C8. Every other digit already appears in its row, column or box. Only one option remains: R7C8 = 5.
42 Naked Single ✓ R8C2=5
Look at cell R8C2. Every other digit already appears in its row, column or box. Only one option remains: R8C2 = 5.
43 Naked Single ✓ R8C8=9
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 9.
44 Naked Single ✓ R7C2=1
Look at cell R7C2. Every other digit already appears in its row, column or box. Only one option remains: R7C2 = 1.
45 Hidden Single ✓ R4C3=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R4C3 = 1.
46 Skyscraper ✗ 2 eliminations
Find 9 on two rows, each with exactly two candidate positions. A shared column connects one end of each pair. Whichever way the logic falls, one of the two free ends must hold 9. R1C2 and R5C3 is seen by both free ends: 9 is therefore eliminated there.
47 Naked Single ✓ R1C2=2
Look at cell R1C2. Every other digit already appears in its row, column or box. Only one option remains: R1C2 = 2.
48 Naked Single ✓ R1C9=1
Look at cell R1C9. Every other digit already appears in its row, column or box. Only one option remains: R1C9 = 1.
49 Naked Single ✓ R3C1=7
Look at cell R3C1. Every other digit already appears in its row, column or box. Only one option remains: R3C1 = 7.
50 Naked Single ✓ R3C5=9
Look at cell R3C5. Every other digit already appears in its row, column or box. Only one option remains: R3C5 = 9.
51 Naked Single ✓ R3C9=2
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 2.
52 Naked Single ✓ R4C2=9
Look at cell R4C2. Every other digit already appears in its row, column or box. Only one option remains: R4C2 = 9.
53 Naked Single ✓ R4C5=2
Look at cell R4C5. Every other digit already appears in its row, column or box. Only one option remains: R4C5 = 2.
54 Naked Single ✓ R5C1=2
Look at cell R5C1. Every other digit already appears in its row, column or box. Only one option remains: R5C1 = 2.
55 Naked Single ✓ R5C3=7
Look at cell R5C3. Every other digit already appears in its row, column or box. Only one option remains: R5C3 = 7.
56 Naked Single ✓ R5C5=3
Look at cell R5C5. Every other digit already appears in its row, column or box. Only one option remains: R5C5 = 3.
57 Naked Single ✓ R8C5=4
Look at cell R8C5. Every other digit already appears in its row, column or box. Only one option remains: R8C5 = 4.
58 Naked Single ✓ R1C4=4
Look at cell R1C4. Every other digit already appears in its row, column or box. Only one option remains: R1C4 = 4.
59 Naked Single ✓ R1C5=7
Look at cell R1C5. Every other digit already appears in its row, column or box. Only one option remains: R1C5 = 7.
60 Naked Single ✓ R1C6=5
Look at cell R1C6. Every other digit already appears in its row, column or box. Only one option remains: R1C6 = 5.
61 Naked Single ✓ R3C3=5
Look at cell R3C3. Every other digit already appears in its row, column or box. Only one option remains: R3C3 = 5.
62 Naked Single ✓ R3C6=1
Look at cell R3C6. Every other digit already appears in its row, column or box. Only one option remains: R3C6 = 1.
63 Naked Single ✓ R5C4=9
Look at cell R5C4. Every other digit already appears in its row, column or box. Only one option remains: R5C4 = 9.
64 Naked Single ✓ R8C4=3
Look at cell R8C4. Every other digit already appears in its row, column or box. Only one option remains: R8C4 = 3.
65 Naked Single ✓ R1C3=9
Look at cell R1C3. Every other digit already appears in its row, column or box. Only one option remains: R1C3 = 9.