Sudoku Solution No. 18

Hard Score 71 / 100
Digits appear one by one.

Step-by-step solution

Steps 63 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 ✓ R3C8=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R3C8 = 4.
2 Hidden Single ✓ R4C2=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R4C2 = 4.
3 Hidden Single ✓ R4C4=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R4C4 = 8.
4 Hidden Single ✓ R6C2=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R6C2 = 6.
5 Hidden Single ✓ R7C9=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R7C9 = 8.
6 Hidden Single ✓ R9C1=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R9C1 = 8.
7 Naked Pair ✗ 4 eliminations
Spot R2C2 and R3C1 in this box. These two cells can only hold 3 and 5: they reserve those digits. 3 and 5 are therefore removed from the other cells of the box.
8 Naked Single ✓ R3C2=7
Look at cell R3C2. Every other digit already appears in its row, column or box. Only one option remains: R3C2 = 7.
9 Naked Single ✓ R1C2=1
Look at cell R1C2. Every other digit already appears in its row, column or box. Only one option remains: R1C2 = 1.
10 Hidden Single ✓ R1C3=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R1C3 = 8.
11 Hidden Single ✓ R1C6=7
Scan the empty cells in this row where 7 could go. Across the whole row, 7 has only one possible spot left. So R1C6 = 7.
12 Hidden Single ✓ R2C3=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R2C3 = 6.
13 Hidden Single ✓ R2C6=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R2C6 = 8.
14 Hidden Single ✓ R5C4=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R5C4 = 4.
15 Hidden Single ✓ R5C6=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R5C6 = 3.
16 Naked Single ✓ R2C4=2
Look at cell R2C4. Every other digit already appears in its row, column or box. Only one option remains: R2C4 = 2.
17 Naked Single ✓ R6C4=9
Look at cell R6C4. Every other digit already appears in its row, column or box. Only one option remains: R6C4 = 9.
18 Naked Single ✓ R3C4=6
Look at cell R3C4. Every other digit already appears in its row, column or box. Only one option remains: R3C4 = 6.
19 Hidden Single ✓ R9C5=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R9C5 = 6.
20 Naked Pair ✗ 2 eliminations
(1) Spot R1C5 and R3C5 on this column. (2) Spot R8C4 and R9C4 in this box. (1) These two cells can only hold 3 and 9: they reserve those digits. (2) These two cells can only hold 1 and 7: they reserve those digits. (1) 3 and 9 are therefore removed from the other cells of the column. (2) 1 and 7 are therefore removed from the other cells of the box.
21 Hidden Single ✓ R4C1=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R4C1 = 1.
22 Hidden Single ✓ R4C5=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R4C5 = 2.
23 Hidden Single ✓ R5C5=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R5C5 = 1.
24 Hidden Single ✓ R6C1=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R6C1 = 2.
25 Hidden Single ✓ R6C6=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R6C6 = 5.
26 Hidden Single ✓ R7C3=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R7C3 = 1.
27 Hidden Single ✓ R7C5=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R7C5 = 5.
28 Hidden Single ✓ R7C6=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R7C6 = 4.
29 Hidden Single ✓ R7C7=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R7C7 = 7.
30 Hidden Single ✓ R8C4=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R8C4 = 7.
31 Hidden Single ✓ R8C9=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R8C9 = 1.
32 Hidden Single ✓ R9C3=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R9C3 = 7.
33 Hidden Single ✓ R9C4=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R9C4 = 1.
34 Hidden Single ✓ R9C7=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R9C7 = 4.
35 Naked Single ✓ R7C8=9
Look at cell R7C8. Every other digit already appears in its row, column or box. Only one option remains: R7C8 = 9.
36 Naked Single ✓ R9C6=9
Look at cell R9C6. Every other digit already appears in its row, column or box. Only one option remains: R9C6 = 9.
37 Naked Single ✓ R7C2=2
Look at cell R7C2. Every other digit already appears in its row, column or box. Only one option remains: R7C2 = 2.
38 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.
39 Hidden Single ✓ R8C2=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R8C2 = 9.
40 Hidden Pair ✗ 4 eliminations
Find where 2 and 6 can go on this column. These two digits only fit in R1C9 and R5C9 on the column. The other candidates in R1C9 and R5C9 are therefore eliminated.
41 Skyscraper ✗ 2 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. R3C9 and R8C7 is seen by both free ends: 3 is therefore eliminated there.
42 Skyscraper ✗ 2 eliminations
Find 5 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 5. R3C9 and R8C7 is seen by both free ends: 5 is therefore eliminated there.
43 Naked Single ✓ R3C9=9
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 9.
44 Naked Single ✓ R8C7=6
Look at cell R8C7. Every other digit already appears in its row, column or box. Only one option remains: R8C7 = 6.
45 Naked Single ✓ R3C5=3
Look at cell R3C5. Every other digit already appears in its row, column or box. Only one option remains: R3C5 = 3.
46 Naked Single ✓ R1C5=9
Look at cell R1C5. Every other digit already appears in its row, column or box. Only one option remains: R1C5 = 9.
47 Naked Single ✓ R3C1=5
Look at cell R3C1. Every other digit already appears in its row, column or box. Only one option remains: R3C1 = 5.
48 Naked Single ✓ R8C1=3
Look at cell R8C1. Every other digit already appears in its row, column or box. Only one option remains: R8C1 = 3.
49 Naked Single ✓ R8C8=5
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 5.
50 Naked Single ✓ R9C2=5
Look at cell R9C2. Every other digit already appears in its row, column or box. Only one option remains: R9C2 = 5.
51 Naked Single ✓ R9C9=3
Look at cell R9C9. Every other digit already appears in its row, column or box. Only one option remains: R9C9 = 3.
52 Naked Single ✓ R2C2=3
Look at cell R2C2. Every other digit already appears in its row, column or box. Only one option remains: R2C2 = 3.
53 Naked Single ✓ R2C7=5
Look at cell R2C7. Every other digit already appears in its row, column or box. Only one option remains: R2C7 = 5.
54 Naked Single ✓ R4C9=5
Look at cell R4C9. Every other digit already appears in its row, column or box. Only one option remains: R4C9 = 5.
55 Naked Single ✓ R5C8=6
Look at cell R5C8. Every other digit already appears in its row, column or box. Only one option remains: R5C8 = 6.
56 Naked Single ✓ R5C9=2
Look at cell R5C9. Every other digit already appears in its row, column or box. Only one option remains: R5C9 = 2.
57 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.
58 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.
59 Naked Single ✓ R4C3=9
Look at cell R4C3. Every other digit already appears in its row, column or box. Only one option remains: R4C3 = 9.
60 Naked Single ✓ R4C7=3
Look at cell R4C7. Every other digit already appears in its row, column or box. Only one option remains: R4C7 = 3.
61 Naked Single ✓ R5C3=5
Look at cell R5C3. Every other digit already appears in its row, column or box. Only one option remains: R5C3 = 5.
62 Naked Single ✓ R5C7=9
Look at cell R5C7. Every other digit already appears in its row, column or box. Only one option remains: R5C7 = 9.
63 Naked Single ✓ R1C7=2
Look at cell R1C7. Every other digit already appears in its row, column or box. Only one option remains: R1C7 = 2.