Sudoku Solution No. 111

Hard Score 72 / 100
Digits appear one by one.

Step-by-step solution

Steps 63 Estimated time 104 – 156 min Hardest technique X-Wing Clues 23
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCcd)
1 Hidden Single ✓ R1C1=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R1C1 = 9.
2 Hidden Single ✓ R1C8=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R1C8 = 5.
3 Hidden Single ✓ R2C2=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R2C2 = 1.
4 Hidden Single ✓ R4C7=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R4C7 = 6.
5 Hidden Single ✓ R5C2=9
Scan the empty cells in this column where 9 could go. Across the whole column, 9 has only one possible spot left. So R5C2 = 9.
6 Hidden Single ✓ R5C3=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R5C3 = 5.
7 Hidden Single ✓ R6C9=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R6C9 = 9.
8 Hidden Single ✓ R7C5=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R7C5 = 9.
9 Hidden Single ✓ R8C2=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R8C2 = 5.
10 Hidden Single ✓ R8C5=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R8C5 = 8.
11 Hidden Single ✓ R9C7=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R9C7 = 9.
12 Naked Single ✓ R1C4=2
Look at cell R1C4. Every other digit already appears in its row, column or box. Only one option remains: R1C4 = 2.
13 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.
14 Naked Single ✓ R1C7=1
Look at cell R1C7. Every other digit already appears in its row, column or box. Only one option remains: R1C7 = 1.
15 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.
16 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.
17 Naked Single ✓ R3C2=8
Look at cell R3C2. Every other digit already appears in its row, column or box. Only one option remains: R3C2 = 8.
18 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.
19 Hidden Single ✓ R3C1=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R3C1 = 6.
20 Hidden Single ✓ R3C3=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R3C3 = 2.
21 Hidden Single ✓ R4C3=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R4C3 = 8.
22 Hidden Single ✓ R5C5=7
Scan the empty cells in this column where 7 could go. Across the whole column, 7 has only one possible spot left. So R5C5 = 7.
23 Hidden Single ✓ R5C9=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R5C9 = 1.
24 Hidden Single ✓ R6C1=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R6C1 = 7.
25 Hidden Single ✓ R8C1=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R8C1 = 4.
26 Hidden Single ✓ R8C6=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R8C6 = 6.
27 Hidden Single ✓ R2C8=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R2C8 = 2.
28 Hidden Single ✓ R8C9=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R8C9 = 2.
29 Skyscraper ✗ 2 eliminations
Find 1 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 1. R9C3 and R7C6 is seen by both free ends: 1 is therefore eliminated there.
30 Naked Pair ✗ 7 eliminations
(1) Spot R2C6 and R7C6 on this column. (2) Spot R7C6 and R8C4 in this box. (1) These two cells can only hold 3 and 7: they reserve those digits. (2) These two cells can only hold 3 and 7: they reserve those digits. (1) 3 and 7 are therefore removed from the other cells of the column. (2) 3 and 7 are therefore removed from the other cells of the box.
31 Naked Single ✓ R3C6=5
Look at cell R3C6. Every other digit already appears in its row, column or box. Only one option remains: R3C6 = 5.
32 Naked Single ✓ R9C5=2
Look at cell R9C5. Every other digit already appears in its row, column or box. Only one option remains: R9C5 = 2.
33 Naked Single ✓ R9C6=1
Look at cell R9C6. Every other digit already appears in its row, column or box. Only one option remains: R9C6 = 1.
34 Naked Single ✓ R4C5=3
Look at cell R4C5. Every other digit already appears in its row, column or box. Only one option remains: R4C5 = 3.
35 Naked Single ✓ R6C6=4
Look at cell R6C6. Every other digit already appears in its row, column or box. Only one option remains: R6C6 = 4.
36 Naked Single ✓ R6C8=3
Look at cell R6C8. Every other digit already appears in its row, column or box. Only one option remains: R6C8 = 3.
37 Naked Single ✓ R9C4=5
Look at cell R9C4. Every other digit already appears in its row, column or box. Only one option remains: R9C4 = 5.
38 Naked Single ✓ R4C4=1
Look at cell R4C4. Every other digit already appears in its row, column or box. Only one option remains: R4C4 = 1.
39 Naked Single ✓ R5C6=2
Look at cell R5C6. Every other digit already appears in its row, column or box. Only one option remains: R5C6 = 2.
40 Naked Single ✓ R6C3=1
Look at cell R6C3. Every other digit already appears in its row, column or box. Only one option remains: R6C3 = 1.
41 Naked Single ✓ R4C1=2
Look at cell R4C1. Every other digit already appears in its row, column or box. Only one option remains: R4C1 = 2.
42 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.
43 Naked Single ✓ R7C1=1
Look at cell R7C1. Every other digit already appears in its row, column or box. Only one option remains: R7C1 = 1.
44 Two-String Kite ✗ 1 elimination
Find 3 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 3. R2C7 is seen by both free ends: 3 is therefore eliminated there.
45 X-Wing ✗ 1 elimination
Find where 3 appears on two columns: altogether, only two rows are involved (R3C4, R8C4, R3C7 and R8C7). On each covered row, 3 must lie within one of these two columns. 3 is therefore removed from those two rows outside the two X-Wing columns.
46 Two-String Kite ✗ 1 elimination
Find 7 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 7. R3C9 is seen by both free ends: 7 is therefore eliminated there.
47 Naked Single ✓ R3C9=4
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 4.
48 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.
49 Naked Single ✓ R8C7=7
Look at cell R8C7. Every other digit already appears in its row, column or box. Only one option remains: R8C7 = 7.
50 Naked Single ✓ R9C3=6
Look at cell R9C3. Every other digit already appears in its row, column or box. Only one option remains: R9C3 = 6.
51 Naked Single ✓ R9C8=4
Look at cell R9C8. Every other digit already appears in its row, column or box. Only one option remains: R9C8 = 4.
52 Naked Single ✓ R2C7=8
Look at cell R2C7. Every other digit already appears in its row, column or box. Only one option remains: R2C7 = 8.
53 Naked Single ✓ R2C9=7
Look at cell R2C9. Every other digit already appears in its row, column or box. Only one option remains: R2C9 = 7.
54 Naked Single ✓ R3C7=3
Look at cell R3C7. Every other digit already appears in its row, column or box. Only one option remains: R3C7 = 3.
55 Naked Single ✓ R5C7=4
Look at cell R5C7. Every other digit already appears in its row, column or box. Only one option remains: R5C7 = 4.
56 Naked Single ✓ R5C8=8
Look at cell R5C8. Every other digit already appears in its row, column or box. Only one option remains: R5C8 = 8.
57 Naked Single ✓ R7C3=3
Look at cell R7C3. Every other digit already appears in its row, column or box. Only one option remains: R7C3 = 3.
58 Naked Single ✓ R7C6=7
Look at cell R7C6. Every other digit already appears in its row, column or box. Only one option remains: R7C6 = 7.
59 Naked Single ✓ R7C8=6
Look at cell R7C8. Every other digit already appears in its row, column or box. Only one option remains: R7C8 = 6.
60 Naked Single ✓ R7C9=8
Look at cell R7C9. Every other digit already appears in its row, column or box. Only one option remains: R7C9 = 8.
61 Naked Single ✓ R8C4=3
Look at cell R8C4. Every other digit already appears in its row, column or box. Only one option remains: R8C4 = 3.
62 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.
63 Naked Single ✓ R3C4=7
Look at cell R3C4. Every other digit already appears in its row, column or box. Only one option remains: R3C4 = 7.