Sudoku Solution No. 106

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 24
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCcd)
1 Hidden Single ✓ R1C3=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R1C3 = 3.
2 Hidden Single ✓ R1C7=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R1C7 = 9.
3 Hidden Single ✓ R1C8=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R1C8 = 4.
4 Hidden Single ✓ R2C5=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R2C5 = 4.
5 Hidden Single ✓ R2C9=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R2C9 = 8.
6 Hidden Single ✓ R3C4=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R3C4 = 8.
7 Hidden Single ✓ R3C5=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R3C5 = 3.
8 Hidden Single ✓ R4C1=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R4C1 = 8.
9 Hidden Single ✓ R5C1=9
Scan the empty cells in this column where 9 could go. Across the whole column, 9 has only one possible spot left. So R5C1 = 9.
10 Hidden Single ✓ R5C7=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R5C7 = 3.
11 Hidden Single ✓ R5C8=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R5C8 = 6.
12 Hidden Single ✓ R8C1=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R8C1 = 3.
13 Hidden Single ✓ R9C6=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R9C6 = 3.
14 Hidden Single ✓ R1C1=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R1C1 = 6.
15 Hidden Single ✓ R2C2=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R2C2 = 2.
16 Hidden Single ✓ R2C7=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R2C7 = 6.
17 Hidden Single ✓ R3C8=2
Scan the empty cells in this column where 2 could go. Across the whole column, 2 has only one possible spot left. So R3C8 = 2.
18 Hidden Single ✓ R7C1=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R7C1 = 2.
19 Hidden Single ✓ R9C1=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R9C1 = 7.
20 Hidden Pair ✗ 8 eliminations
(1) Find where 6 and 9 can go on this column. (2) Find where 5 and 8 can go on this column. (3) Find where 5 and 8 can go in this box. (1) These two digits only fit in R6C4 and R9C4 on the column. (2) These two digits only fit in R7C7 and R9C7 on the column. (3) These two digits only fit in R7C7 and R9C7 in the box. (1) The other candidates in R6C4 and R9C4 are therefore eliminated. (2) The other candidates in R7C7 and R9C7 are therefore eliminated. (3) The other candidates in R7C7 and R9C7 are therefore eliminated.
21 Hidden Single ✓ R1C4=2
Scan the empty cells in this column where 2 could go. Across the whole column, 2 has only one possible spot left. So R1C4 = 2.
22 Box/Line ✗ 3 eliminations
Look at where 5 can go on this row. All its spots lie within a single box (R8C4 and R8C5). 5 is therefore removed from the rest of the box.
23 Hidden Triple ✗ 4 eliminations
Find where 2, 6 and 9 can go in this box. These three digits only fit in R4C5, R6C5 and R6C4. The other candidates in R4C5, R6C5 and R6C4 are therefore eliminated.
24 Two-String Kite ✗ 1 elimination
Find 1 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 1. R1C6 is seen by both free ends: 1 is therefore eliminated there.
25 Naked Pair ✗ 4 eliminations
Spot R1C6 and R6C6 on this column. These two cells can only hold 5 and 7: they reserve those digits. 5 and 7 are therefore removed from the other cells of the column.
26 Hidden Pair ✗ 4 eliminations
Find where 7 and 9 can go on this row. These two digits only fit in R7C5 and R7C8 on the row. The other candidates in R7C5 and R7C8 are therefore eliminated.
27 Pointing ✗ 2 eliminations
Look at where 6 can go in this box. All its spots lie on a single row (R9C4 and R9C5). 6 is therefore removed from that row outside the box.
28 Skyscraper ✗ 3 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. R5C4, R5C5 and R6C7 is seen by both free ends: 7 is therefore eliminated there.
29 Naked Single ✓ R6C7=2
Look at cell R6C7. Every other digit already appears in its row, column or box. Only one option remains: R6C7 = 2.
30 Hidden Single ✓ R4C5=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R4C5 = 2.
31 Hidden Single ✓ R6C6=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R6C6 = 7.
32 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.
33 Hidden Single ✓ R6C3=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R6C3 = 5.
34 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. R1C9 and R4C7 is seen by both free ends: 7 is therefore eliminated there.
35 Naked Single ✓ R1C9=1
Look at cell R1C9. Every other digit already appears in its row, column or box. Only one option remains: R1C9 = 1.
36 Naked Single ✓ R3C7=7
Look at cell R3C7. Every other digit already appears in its row, column or box. Only one option remains: R3C7 = 7.
37 Naked Single ✓ R4C7=1
Look at cell R4C7. Every other digit already appears in its row, column or box. Only one option remains: R4C7 = 1.
38 Naked Single ✓ R5C9=7
Look at cell R5C9. Every other digit already appears in its row, column or box. Only one option remains: R5C9 = 7.
39 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.
40 Naked Single ✓ R2C4=1
Look at cell R2C4. Every other digit already appears in its row, column or box. Only one option remains: R2C4 = 1.
41 Naked Single ✓ R3C2=1
Look at cell R3C2. Every other digit already appears in its row, column or box. Only one option remains: R3C2 = 1.
42 Naked Single ✓ R4C6=4
Look at cell R4C6. Every other digit already appears in its row, column or box. Only one option remains: R4C6 = 4.
43 Naked Single ✓ R5C2=4
Look at cell R5C2. Every other digit already appears in its row, column or box. Only one option remains: R5C2 = 4.
44 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.
45 Naked Single ✓ R7C5=9
Look at cell R7C5. Every other digit already appears in its row, column or box. Only one option remains: R7C5 = 9.
46 Naked Single ✓ R7C8=7
Look at cell R7C8. Every other digit already appears in its row, column or box. Only one option remains: R7C8 = 7.
47 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.
48 Naked Single ✓ R8C8=1
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 1.
49 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.
50 Naked Single ✓ R9C4=6
Look at cell R9C4. Every other digit already appears in its row, column or box. Only one option remains: R9C4 = 6.
51 Naked Single ✓ R9C7=8
Look at cell R9C7. Every other digit already appears in its row, column or box. Only one option remains: R9C7 = 8.
52 Naked Single ✓ R9C8=9
Look at cell R9C8. Every other digit already appears in its row, column or box. Only one option remains: R9C8 = 9.
53 Naked Single ✓ R2C3=7
Look at cell R2C3. Every other digit already appears in its row, column or box. Only one option remains: R2C3 = 7.
54 Naked Single ✓ R4C3=6
Look at cell R4C3. Every other digit already appears in its row, column or box. Only one option remains: R4C3 = 6.
55 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.
56 Naked Single ✓ R6C5=6
Look at cell R6C5. Every other digit already appears in its row, column or box. Only one option remains: R6C5 = 6.
57 Naked Single ✓ R7C2=6
Look at cell R7C2. Every other digit already appears in its row, column or box. Only one option remains: R7C2 = 6.
58 Naked Single ✓ R7C3=1
Look at cell R7C3. Every other digit already appears in its row, column or box. Only one option remains: R7C3 = 1.
59 Naked Single ✓ R7C6=8
Look at cell R7C6. Every other digit already appears in its row, column or box. Only one option remains: R7C6 = 8.
60 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.
61 Naked Single ✓ R8C5=5
Look at cell R8C5. Every other digit already appears in its row, column or box. Only one option remains: R8C5 = 5.
62 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.
63 Naked Single ✓ R9C5=1
Look at cell R9C5. Every other digit already appears in its row, column or box. Only one option remains: R9C5 = 1.
64 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.
65 Naked Single ✓ R5C5=8
Look at cell R5C5. Every other digit already appears in its row, column or box. Only one option remains: R5C5 = 8.
66 Naked Single ✓ R5C6=1
Look at cell R5C6. Every other digit already appears in its row, column or box. Only one option remains: R5C6 = 1.