Sudoku Solution No. 20

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 Hidden Single ✓ R4C4=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R4C4 = 4.
2 Hidden Single ✓ R4C6=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R4C6 = 8.
3 Hidden Single ✓ R6C4=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R6C4 = 1.
4 Hidden Single ✓ R7C7=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R7C7 = 8.
5 Hidden Single ✓ R7C8=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R7C8 = 4.
6 Hidden Single ✓ R8C2=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R8C2 = 1.
7 Hidden Single ✓ R8C5=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R8C5 = 8.
8 Hidden Single ✓ R9C4=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R9C4 = 5.
9 Hidden Single ✓ R9C5=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R9C5 = 2.
10 Naked Single ✓ R7C6=9
Look at cell R7C6. Every other digit already appears in its row, column or box. Only one option remains: R7C6 = 9.
11 Naked Single ✓ R3C6=5
Look at cell R3C6. Every other digit already appears in its row, column or box. Only one option remains: R3C6 = 5.
12 Naked Single ✓ R1C6=2
Look at cell R1C6. Every other digit already appears in its row, column or box. Only one option remains: R1C6 = 2.
13 Hidden Single ✓ R1C4=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R1C4 = 9.
14 Hidden Single ✓ R1C9=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R1C9 = 4.
15 Hidden Single ✓ R2C2=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R2C2 = 2.
16 Hidden Single ✓ R2C3=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R2C3 = 4.
17 Hidden Single ✓ R2C9=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R2C9 = 8.
18 Hidden Single ✓ R5C4=2
Scan the empty cells in this column where 2 could go. Across the whole column, 2 has only one possible spot left. So R5C4 = 2.
19 Hidden Single ✓ R6C1=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R6C1 = 8.
20 Hidden Single ✓ R6C2=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R6C2 = 4.
21 Hidden Single ✓ R7C4=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R7C4 = 6.
22 Naked Single ✓ R5C1=7
Look at cell R5C1. Every other digit already appears in its row, column or box. Only one option remains: R5C1 = 7.
23 Hidden Single ✓ R1C2=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R1C2 = 8.
24 Hidden Single ✓ R1C3=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R1C3 = 5.
25 Hidden Single ✓ R2C8=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R2C8 = 5.
26 Hidden Single ✓ R4C1=2
Scan the empty cells in this column where 2 could go. Across the whole column, 2 has only one possible spot left. So R4C1 = 2.
27 Hidden Single ✓ R6C8=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R6C8 = 2.
28 Hidden Single ✓ R2C5=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R2C5 = 1.
29 Naked Pair ✗ 2 eliminations
Spot R1C1 and R3C1 in this box. These two cells can only hold 1 and 3: they reserve those digits. 1 and 3 are therefore removed from the other cells of the box.
30 Naked Pair ✗ 6 eliminations
Spot R3C2 and R3C3 on this row. These two cells can only hold 6 and 7: they reserve those digits. 6 and 7 are therefore removed from the other cells of the row.
31 Naked Single ✓ R5C9=5
Look at cell R5C9. Every other digit already appears in its row, column or box. Only one option remains: R5C9 = 5.
32 Naked Single ✓ R4C9=7
Look at cell R4C9. Every other digit already appears in its row, column or box. Only one option remains: R4C9 = 7.
33 Hidden Single ✓ R4C2=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R4C2 = 5.
34 Pointing ✗ 1 elimination
Look at where 3 can go in this box. All its spots lie on a single column (R4C3 and R6C3). 3 is therefore removed from that column outside the box.
35 Skyscraper ✗ 3 eliminations
Find 3 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 3. R1C8, R3C8 and R9C7 is seen by both free ends: 3 is therefore eliminated there.
36 Pointing ✗ 1 elimination
Look at where 3 can go in this box. All its spots lie on a single column (R8C8 and R9C8). 3 is therefore removed from that column outside the box.
37 Hidden Single ✓ R4C3=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R4C3 = 3.
38 Skyscraper ✗ 1 elimination
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. R6C3 is seen by both free ends: 9 is therefore eliminated there.
39 Naked Single ✓ R6C3=6
Look at cell R6C3. Every other digit already appears in its row, column or box. Only one option remains: R6C3 = 6.
40 Naked Single ✓ R3C3=7
Look at cell R3C3. Every other digit already appears in its row, column or box. Only one option remains: R3C3 = 7.
41 Naked Single ✓ R5C2=9
Look at cell R5C2. Every other digit already appears in its row, column or box. Only one option remains: R5C2 = 9.
42 Naked Single ✓ R5C5=6
Look at cell R5C5. Every other digit already appears in its row, column or box. Only one option remains: R5C5 = 6.
43 Naked Single ✓ R8C3=9
Look at cell R8C3. Every other digit already appears in its row, column or box. Only one option remains: R8C3 = 9.
44 Naked Single ✓ R3C2=6
Look at cell R3C2. Every other digit already appears in its row, column or box. Only one option remains: R3C2 = 6.
45 Naked Single ✓ R4C5=9
Look at cell R4C5. Every other digit already appears in its row, column or box. Only one option remains: R4C5 = 9.
46 Naked Single ✓ R4C8=6
Look at cell R4C8. Every other digit already appears in its row, column or box. Only one option remains: R4C8 = 6.
47 Hidden Single ✓ R1C7=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R1C7 = 6.
48 Skyscraper ✗ 2 eliminations
Find 7 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 7. R2C4 and R7C5 is seen by both free ends: 7 is therefore eliminated there.
49 Naked Single ✓ R2C4=3
Look at cell R2C4. Every other digit already appears in its row, column or box. Only one option remains: R2C4 = 3.
50 Naked Single ✓ R2C7=7
Look at cell R2C7. Every other digit already appears in its row, column or box. Only one option remains: R2C7 = 7.
51 Naked Single ✓ R7C5=3
Look at cell R7C5. Every other digit already appears in its row, column or box. Only one option remains: R7C5 = 3.
52 Naked Single ✓ R8C4=7
Look at cell R8C4. Every other digit already appears in its row, column or box. Only one option remains: R8C4 = 7.
53 Naked Single ✓ R8C8=3
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 3.
54 Naked Single ✓ R9C7=9
Look at cell R9C7. Every other digit already appears in its row, column or box. Only one option remains: R9C7 = 9.
55 Naked Single ✓ R9C8=7
Look at cell R9C8. Every other digit already appears in its row, column or box. Only one option remains: R9C8 = 7.
56 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.
57 Naked Single ✓ R1C8=1
Look at cell R1C8. Every other digit already appears in its row, column or box. Only one option remains: R1C8 = 1.
58 Naked Single ✓ R3C8=9
Look at cell R3C8. Every other digit already appears in its row, column or box. Only one option remains: R3C8 = 9.
59 Naked Single ✓ R3C9=3
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 3.
60 Naked Single ✓ R6C7=3
Look at cell R6C7. Every other digit already appears in its row, column or box. Only one option remains: R6C7 = 3.
61 Naked Single ✓ R6C9=9
Look at cell R6C9. Every other digit already appears in its row, column or box. Only one option remains: R6C9 = 9.
62 Naked Single ✓ R7C2=7
Look at cell R7C2. Every other digit already appears in its row, column or box. Only one option remains: R7C2 = 7.
63 Naked Single ✓ R9C2=3
Look at cell R9C2. Every other digit already appears in its row, column or box. Only one option remains: R9C2 = 3.
64 Naked Single ✓ R1C1=3
Look at cell R1C1. Every other digit already appears in its row, column or box. Only one option remains: R1C1 = 3.
65 Naked Single ✓ R3C1=1
Look at cell R3C1. Every other digit already appears in its row, column or box. Only one option remains: R3C1 = 1.