Sudoku Solution No. 127

Hard Score 72 / 100
Digits appear one by one.

Step-by-step solution

Steps 64 Estimated time 65 – 98 min Hardest technique Box/Line Clues 22
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCc≠d)
1 Hidden Single ✓ R1C6=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R1C6 = 7.
2 Hidden Single ✓ R2C4=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R2C4 = 8.
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 ✓ R3C2=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R3C2 = 7.
5 Hidden Single ✓ R4C4=3
Scan the empty cells in this column where 3 could go. Across the whole column, 3 has only one possible spot left. So R4C4 = 3.
6 Hidden Single ✓ R4C5=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R4C5 = 9.
7 Hidden Single ✓ R5C1=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R5C1 = 2.
8 Hidden Single ✓ R5C6=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R5C6 = 1.
9 Hidden Single ✓ R5C7=7
Scan the empty cells in this row where 7 could go. Across the whole row, 7 has only one possible spot left. So R5C7 = 7.
10 Hidden Single ✓ R6C5=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R6C5 = 2.
11 Hidden Single ✓ R7C6=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R7C6 = 8.
12 Hidden Single ✓ R8C5=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R8C5 = 7.
13 Hidden Single ✓ R8C6=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R8C6 = 4.
14 Naked Single ✓ R1C5=6
Look at cell R1C5. Every other digit already appears in its row, column or box. Only one option remains: R1C5 = 6.
15 Naked Single ✓ R3C5=5
Look at cell R3C5. Every other digit already appears in its row, column or box. Only one option remains: R3C5 = 5.
16 Naked Single ✓ R7C5=1
Look at cell R7C5. Every other digit already appears in its row, column or box. Only one option remains: R7C5 = 1.
17 Naked Single ✓ R3C4=9
Look at cell R3C4. Every other digit already appears in its row, column or box. Only one option remains: R3C4 = 9.
18 Hidden Single ✓ R2C9=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R2C9 = 5.
19 Hidden Single ✓ R3C1=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R3C1 = 1.
20 Hidden Single ✓ R5C2=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R5C2 = 5.
21 Hidden Single ✓ R8C8=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R8C8 = 1.
22 Hidden Single ✓ R9C2=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R9C2 = 1.
23 Naked Single ✓ R5C9=3
Look at cell R5C9. Every other digit already appears in its row, column or box. Only one option remains: R5C9 = 3.
24 Hidden Single ✓ R2C3=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R2C3 = 2.
25 Naked Pair ✗ 2 eliminations
Spot R2C1 and R2C2 in this box. These two cells can only hold 6 and 9: they reserve those digits. 6 and 9 are therefore removed from the other cells of the box.
26 Hidden Pair ✗ 2 eliminations
(1) Find where 2 and 9 can go on this row. (2) Find where 2 and 9 can go in this box. (1) These two digits only fit in R1C7 and R1C9 on the row. (2) These two digits only fit in R1C7 and R1C9 in the box. (1) The other candidates in R1C7 and R1C9 are therefore eliminated. (2) The other candidates in R1C7 and R1C9 are therefore eliminated.
27 Skyscraper ✗ 2 eliminations
Find 4 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 4. R1C2 and R6C3 is seen by both free ends: 4 is therefore eliminated there.
28 Pointing ✗ 1 elimination
Look at where 4 can go in this box. All its spots lie on a single column (R1C3 and R3C3). 4 is therefore removed from that column outside the box.
29 Hidden Single ✓ R9C1=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R9C1 = 4.
30 Skyscraper ✗ 2 eliminations
Find 8 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 8. R4C2 and R6C7 is seen by both free ends: 8 is therefore eliminated there.
31 Naked Single ✓ R4C2=4
Look at cell R4C2. Every other digit already appears in its row, column or box. Only one option remains: R4C2 = 4.
32 Hidden Single ✓ R1C2=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R1C2 = 8.
33 Hidden Single ✓ R1C3=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R1C3 = 4.
34 Hidden Single ✓ R3C7=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R3C7 = 6.
35 Hidden Single ✓ R3C9=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R3C9 = 4.
36 Hidden Single ✓ R4C7=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R4C7 = 8.
37 Hidden Single ✓ R4C9=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R4C9 = 6.
38 Hidden Single ✓ R6C8=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R6C8 = 4.
39 Hidden Single ✓ R8C9=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R8C9 = 8.
40 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.
41 Naked Single ✓ R3C3=3
Look at cell R3C3. Every other digit already appears in its row, column or box. Only one option remains: R3C3 = 3.
42 Naked Single ✓ R4C6=5
Look at cell R4C6. Every other digit already appears in its row, column or box. Only one option remains: R4C6 = 5.
43 Naked Single ✓ R6C6=6
Look at cell R6C6. Every other digit already appears in its row, column or box. Only one option remains: R6C6 = 6.
44 Naked Single ✓ R6C7=5
Look at cell R6C7. Every other digit already appears in its row, column or box. Only one option remains: R6C7 = 5.
45 Naked Single ✓ R9C7=2
Look at cell R9C7. Every other digit already appears in its row, column or box. Only one option remains: R9C7 = 2.
46 Naked Single ✓ R1C7=9
Look at cell R1C7. Every other digit already appears in its row, column or box. Only one option remains: R1C7 = 9.
47 Naked Single ✓ R1C9=2
Look at cell R1C9. Every other digit already appears in its row, column or box. Only one option remains: R1C9 = 2.
48 Naked Single ✓ R7C9=9
Look at cell R7C9. Every other digit already appears in its row, column or box. Only one option remains: R7C9 = 9.
49 Naked Single ✓ R8C7=3
Look at cell R8C7. Every other digit already appears in its row, column or box. Only one option remains: R8C7 = 3.
50 Hidden Single ✓ R6C1=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R6C1 = 8.
51 Hidden Single ✓ R6C2=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R6C2 = 3.
52 Hidden Single ✓ R6C3=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R6C3 = 9.
53 Hidden Single ✓ R7C1=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R7C1 = 3.
54 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.
55 Hidden Single ✓ R7C4=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R7C4 = 2.
56 Hidden Single ✓ R7C8=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R7C8 = 5.
57 Hidden Single ✓ R8C1=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R8C1 = 9.
58 Hidden Single ✓ R8C3=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R8C3 = 5.
59 Hidden Single ✓ R8C4=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R8C4 = 6.
60 Hidden Single ✓ R9C3=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R9C3 = 8.
61 Hidden Single ✓ R9C4=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R9C4 = 5.
62 Hidden Single ✓ R9C8=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R9C8 = 6.
63 Naked Single ✓ R2C1=6
Look at cell R2C1. Every other digit already appears in its row, column or box. Only one option remains: R2C1 = 6.
64 Naked Single ✓ R2C2=9
Look at cell R2C2. Every other digit already appears in its row, column or box. Only one option remains: R2C2 = 9.