Sudoku Solution No. 128

Hard Score 72 / 100
Digits appear one by one.

Step-by-step solution

Steps 66 Estimated time 108 – 162 min Hardest technique X-Wing Clues 23
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCcd)
1 Naked Single ✓ R6C1=2
Look at cell R6C1. Every other digit already appears in its row, column or box. Only one option remains: R6C1 = 2.
2 Naked Single ✓ R6C2=5
Look at cell R6C2. Every other digit already appears in its row, column or box. Only one option remains: R6C2 = 5.
3 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.
4 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.
5 Naked Single ✓ R9C1=6
Look at cell R9C1. Every other digit already appears in its row, column or box. Only one option remains: R9C1 = 6.
6 Naked Single ✓ R1C1=1
Look at cell R1C1. Every other digit already appears in its row, column or box. Only one option remains: R1C1 = 1.
7 Naked Single ✓ R3C1=4
Look at cell R3C1. Every other digit already appears in its row, column or box. Only one option remains: R3C1 = 4.
8 Naked Single ✓ R6C6=8
Look at cell R6C6. Every other digit already appears in its row, column or box. Only one option remains: R6C6 = 8.
9 Naked Single ✓ R6C8=6
Look at cell R6C8. Every other digit already appears in its row, column or box. Only one option remains: R6C8 = 6.
10 Hidden Single ✓ R1C3=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R1C3 = 2.
11 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.
12 Hidden Single ✓ R2C5=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R2C5 = 2.
13 Hidden Single ✓ R2C6=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R2C6 = 4.
14 Hidden Single ✓ R4C2=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R4C2 = 1.
15 Hidden Single ✓ R4C5=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R4C5 = 6.
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 ✓ R4C8=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R4C8 = 5.
18 Hidden Single ✓ R4C9=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R4C9 = 4.
19 Hidden Single ✓ R5C7=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R5C7 = 2.
20 Hidden Single ✓ R5C9=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R5C9 = 1.
21 Hidden Single ✓ R7C2=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R7C2 = 4.
22 Hidden Single ✓ R7C6=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R7C6 = 2.
23 Hidden Single ✓ R7C7=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R7C7 = 6.
24 Hidden Single ✓ R8C2=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R8C2 = 2.
25 Hidden Single ✓ R8C8=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R8C8 = 7.
26 Hidden Single ✓ R8C9=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R8C9 = 5.
27 Naked Single ✓ R4C3=7
Look at cell R4C3. Every other digit already appears in its row, column or box. Only one option remains: R4C3 = 7.
28 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.
29 Naked Single ✓ R5C3=4
Look at cell R5C3. Every other digit already appears in its row, column or box. Only one option remains: R5C3 = 4.
30 Naked Pair ✗ 6 eliminations
Spot R9C2 and R9C3 on this row. These two cells can only hold 8 and 9: they reserve those digits. 8 and 9 are therefore removed from the other cells of the row.
31 Naked Single ✓ R9C7=1
Look at cell R9C7. Every other digit already appears in its row, column or box. Only one option remains: R9C7 = 1.
32 Hidden Single ✓ R2C8=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R2C8 = 1.
33 Hidden Single ✓ R3C6=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R3C6 = 1.
34 Hidden Single ✓ R7C5=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R7C5 = 1.
35 Hidden Pair ✗ 1 elimination
Find where 8 and 9 can go in this box. These two digits only fit in R7C4 and R8C5 in the box. The other candidates in R7C4 and R8C5 are therefore eliminated.
36 Two-String Kite ✗ 1 elimination
Find 8 on one row and one column, each with two candidate positions, sharing a box. The two strands meet in the shared box. One of the two free ends must hold 8. R2C4 is seen by both free ends: 8 is therefore eliminated there.
37 Two-String Kite ✗ 1 elimination
Find 9 on one row and one column, each with two candidate positions, sharing a box. The two strands meet in the shared box. One of the two free ends must hold 9. R2C4 is seen by both free ends: 9 is therefore eliminated there.
38 Hidden Pair ✗ 2 eliminations
Find where 8 and 9 can go on this column. These two digits only fit in R3C4 and R7C4 on the column. The other candidates in R3C4 and R7C4 are therefore eliminated.
39 Hidden Single ✓ R3C2=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R3C2 = 3.
40 Hidden Single ✓ R3C5=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R3C5 = 7.
41 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.
42 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.
43 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.
44 Naked Single ✓ R5C6=7
Look at cell R5C6. Every other digit already appears in its row, column or box. Only one option remains: R5C6 = 7.
45 Naked Single ✓ R9C4=7
Look at cell R9C4. Every other digit already appears in its row, column or box. Only one option remains: R9C4 = 7.
46 Naked Single ✓ R9C6=3
Look at cell R9C6. Every other digit already appears in its row, column or box. Only one option remains: R9C6 = 3.
47 Naked Single ✓ R5C4=5
Look at cell R5C4. Every other digit already appears in its row, column or box. Only one option remains: R5C4 = 5.
48 Skyscraper ✗ 1 elimination
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. R1C9 is seen by both free ends: 8 is therefore eliminated there.
49 Pointing ✗ 1 elimination
Look at where 8 can go in this box. All its spots lie on a single row (R2C7 and R2C9). 8 is therefore removed from that row outside the box.
50 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. R1C5 is seen by both free ends: 9 is therefore eliminated there.
51 Naked Single ✓ R1C5=8
Look at cell R1C5. Every other digit already appears in its row, column or box. Only one option remains: R1C5 = 8.
52 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.
53 Naked Single ✓ R7C4=8
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 8.
54 Naked Single ✓ R7C9=3
Look at cell R7C9. Every other digit already appears in its row, column or box. Only one option remains: R7C9 = 3.
55 Naked Single ✓ R8C5=9
Look at cell R8C5. Every other digit already appears in its row, column or box. Only one option remains: R8C5 = 9.
56 Naked Single ✓ R8C7=8
Look at cell R8C7. Every other digit already appears in its row, column or box. Only one option remains: R8C7 = 8.
57 Naked Single ✓ R1C9=7
Look at cell R1C9. Every other digit already appears in its row, column or box. Only one option remains: R1C9 = 7.
58 Naked Single ✓ R2C7=9
Look at cell R2C7. Every other digit already appears in its row, column or box. Only one option remains: R2C7 = 9.
59 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.
60 Naked Single ✓ R3C3=8
Look at cell R3C3. Every other digit already appears in its row, column or box. Only one option remains: R3C3 = 8.
61 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.
62 Naked Single ✓ R9C3=9
Look at cell R9C3. Every other digit already appears in its row, column or box. Only one option remains: R9C3 = 9.
63 Naked Single ✓ R1C2=9
Look at cell R1C2. Every other digit already appears in its row, column or box. Only one option remains: R1C2 = 9.
64 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.
65 Naked Single ✓ R2C2=7
Look at cell R2C2. Every other digit already appears in its row, column or box. Only one option remains: R2C2 = 7.
66 Naked Single ✓ R9C2=8
Look at cell R9C2. Every other digit already appears in its row, column or box. Only one option remains: R9C2 = 8.