Sudoku Solution No. 116

Hard Score 72 / 100
Digits appear one by one.

Step-by-step solution

Steps 66 Estimated time 68 – 102 min Hardest technique Box/Line Clues 22
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCcd)
1 Naked Single ✓ R5C8=5
Look at cell R5C8. Every other digit already appears in its row, column or box. Only one option remains: R5C8 = 5.
2 Naked Single ✓ R6C4=8
Look at cell R6C4. Every other digit already appears in its row, column or box. Only one option remains: R6C4 = 8.
3 Naked Single ✓ R4C4=3
Look at cell R4C4. Every other digit already appears in its row, column or box. Only one option remains: R4C4 = 3.
4 Naked Single ✓ R5C5=7
Look at cell R5C5. Every other digit already appears in its row, column or box. Only one option remains: R5C5 = 7.
5 Naked Single ✓ R2C4=6
Look at cell R2C4. Every other digit already appears in its row, column or box. Only one option remains: R2C4 = 6.
6 Naked Single ✓ R5C3=6
Look at cell R5C3. Every other digit already appears in its row, column or box. Only one option remains: R5C3 = 6.
7 Naked Single ✓ R7C4=4
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 4.
8 Naked Single ✓ R5C1=3
Look at cell R5C1. Every other digit already appears in its row, column or box. Only one option remains: R5C1 = 3.
9 Hidden Single ✓ R1C3=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R1C3 = 1.
10 Hidden Single ✓ R1C5=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R1C5 = 4.
11 Hidden Single ✓ R2C1=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R2C1 = 7.
12 Hidden Single ✓ R2C3=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R2C3 = 9.
13 Hidden Single ✓ R2C5=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R2C5 = 5.
14 Hidden Single ✓ R3C6=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R3C6 = 1.
15 Hidden Single ✓ R4C5=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R4C5 = 1.
16 Hidden Single ✓ R4C6=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R4C6 = 9.
17 Hidden Single ✓ R6C8=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R6C8 = 1.
18 Hidden Single ✓ R7C9=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R7C9 = 1.
19 Naked Single ✓ R6C6=5
Look at cell R6C6. Every other digit already appears in its row, column or box. Only one option remains: R6C6 = 5.
20 Hidden Single ✓ R4C3=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R4C3 = 8.
21 Naked Pair ✗ 8 eliminations
(1) Spot R7C5 and R7C8 on this row. (2) Spot R1C6 and R2C6 on this column. (1) These two cells can only hold 3 and 9: they reserve those digits. (2) These two cells can only hold 3 and 8: they reserve those digits. (1) 3 and 9 are therefore removed from the other cells of the row. (2) 3 and 8 are therefore removed from the other cells of the column.
22 Hidden Single ✓ R1C7=9
Scan the empty cells in this column where 9 could go. Across the whole column, 9 has only one possible spot left. So R1C7 = 9.
23 Hidden Single ✓ R7C2=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R7C2 = 6.
24 Hidden Single ✓ R7C5=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R7C5 = 3.
25 Hidden Single ✓ R7C8=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R7C8 = 9.
26 Hidden Single ✓ R8C7=3
Scan the empty cells in this column where 3 could go. Across the whole column, 3 has only one possible spot left. So R8C7 = 3.
27 Hidden Single ✓ R9C2=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R9C2 = 3.
28 Hidden Single ✓ R9C5=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R9C5 = 9.
29 Hidden Single ✓ R9C6=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R9C6 = 6.
30 Naked Single ✓ R8C5=8
Look at cell R8C5. Every other digit already appears in its row, column or box. Only one option remains: R8C5 = 8.
31 Pointing ✗ 5 eliminations
(1) Look at where 2 can go in this box. (2) Look at where 2 can go in this box. (3) Look at where 4 can go in this box. (1) All its spots lie on a single row (R1C1 and R1C2). (2) All its spots lie on a single row (R4C8 and R4C9). (3) All its spots lie on a single column (R8C3 and R9C3). (1) 2 is therefore removed from that row outside the box. (2) 2 is therefore removed from that row outside the box. (3) 4 is therefore removed from that column outside the box.
32 Naked Pair ✗ 2 eliminations
Spot R1C6 and R1C8 on this row. These two cells can only hold 3 and 8: they reserve those digits. 3 and 8 are therefore removed from the other cells of the row.
33 Hidden Single ✓ R3C2=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R3C2 = 8.
34 Box/Line ✗ 1 elimination
Look at where 5 can go on this column. All its spots lie within a single box (R7C3 and R8C3). 5 is therefore removed from the rest of the box.
35 Naked Pair ✗ 3 eliminations
Spot R8C2 and R8C6 on this row. These two cells can only hold 2 and 7: they reserve those digits. 2 and 7 are therefore removed from the other cells of the row.
36 Naked Triple ✗ 5 eliminations
Spot R1C9, R3C9 and R8C9 on this column. These three cells share only 4, 5 and 6. 4, 5 and 6 are therefore removed from the rest of the column.
37 Naked Single ✓ R4C7=6
Look at cell R4C7. Every other digit already appears in its row, column or box. Only one option remains: R4C7 = 6.
38 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. R6C3 and R8C2 is seen by both free ends: 7 is therefore eliminated there.
39 Naked Single ✓ R6C3=2
Look at cell R6C3. Every other digit already appears in its row, column or box. Only one option remains: R6C3 = 2.
40 Naked Single ✓ R8C2=2
Look at cell R8C2. Every other digit already appears in its row, column or box. Only one option remains: R8C2 = 2.
41 Naked Single ✓ R8C6=7
Look at cell R8C6. Every other digit already appears in its row, column or box. Only one option remains: R8C6 = 7.
42 Naked Single ✓ R1C2=5
Look at cell R1C2. Every other digit already appears in its row, column or box. Only one option remains: R1C2 = 5.
43 Naked Single ✓ R1C9=6
Look at cell R1C9. Every other digit already appears in its row, column or box. Only one option remains: R1C9 = 6.
44 Naked Single ✓ R3C1=6
Look at cell R3C1. Every other digit already appears in its row, column or box. Only one option remains: R3C1 = 6.
45 Naked Single ✓ R4C2=7
Look at cell R4C2. Every other digit already appears in its row, column or box. Only one option remains: R4C2 = 7.
46 Naked Single ✓ R4C9=2
Look at cell R4C9. Every other digit already appears in its row, column or box. Only one option remains: R4C9 = 2.
47 Naked Single ✓ R6C1=4
Look at cell R6C1. Every other digit already appears in its row, column or box. Only one option remains: R6C1 = 4.
48 Naked Single ✓ R6C7=7
Look at cell R6C7. Every other digit already appears in its row, column or box. Only one option remains: R6C7 = 7.
49 Naked Single ✓ R7C6=2
Look at cell R7C6. Every other digit already appears in its row, column or box. Only one option remains: R7C6 = 2.
50 Naked Single ✓ R7C7=5
Look at cell R7C7. Every other digit already appears in its row, column or box. Only one option remains: R7C7 = 5.
51 Naked Single ✓ R8C9=4
Look at cell R8C9. Every other digit already appears in its row, column or box. Only one option remains: R8C9 = 4.
52 Naked Single ✓ R9C8=8
Look at cell R9C8. Every other digit already appears in its row, column or box. Only one option remains: R9C8 = 8.
53 Naked Single ✓ R9C9=7
Look at cell R9C9. Every other digit already appears in its row, column or box. Only one option remains: R9C9 = 7.
54 Naked Single ✓ R1C1=2
Look at cell R1C1. Every other digit already appears in its row, column or box. Only one option remains: R1C1 = 2.
55 Naked Single ✓ R1C8=3
Look at cell R1C8. Every other digit already appears in its row, column or box. Only one option remains: R1C8 = 3.
56 Naked Single ✓ R2C8=2
Look at cell R2C8. Every other digit already appears in its row, column or box. Only one option remains: R2C8 = 2.
57 Naked Single ✓ R2C9=8
Look at cell R2C9. Every other digit already appears in its row, column or box. Only one option remains: R2C9 = 8.
58 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.
59 Naked Single ✓ R3C9=5
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 5.
60 Naked Single ✓ R4C1=5
Look at cell R4C1. Every other digit already appears in its row, column or box. Only one option remains: R4C1 = 5.
61 Naked Single ✓ R4C8=4
Look at cell R4C8. Every other digit already appears in its row, column or box. Only one option remains: R4C8 = 4.
62 Naked Single ✓ R7C3=7
Look at cell R7C3. Every other digit already appears in its row, column or box. Only one option remains: R7C3 = 7.
63 Naked Single ✓ R8C3=5
Look at cell R8C3. Every other digit already appears in its row, column or box. Only one option remains: R8C3 = 5.
64 Naked Single ✓ R9C3=4
Look at cell R9C3. Every other digit already appears in its row, column or box. Only one option remains: R9C3 = 4.
65 Naked Single ✓ R1C6=8
Look at cell R1C6. Every other digit already appears in its row, column or box. Only one option remains: R1C6 = 8.
66 Naked Single ✓ R2C6=3
Look at cell R2C6. Every other digit already appears in its row, column or box. Only one option remains: R2C6 = 3.