Sudoku Solution No. 91

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 (✗ RlCc≠d)
1 Hidden Single ✓ R3C4=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R3C4 = 6.
2 Hidden Single ✓ R5C1=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R5C1 = 6.
3 Hidden Single ✓ R5C3=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R5C3 = 1.
4 Hidden Single ✓ R6C7=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R6C7 = 6.
5 Hidden Single ✓ R7C5=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R7C5 = 6.
6 Hidden Single ✓ R8C2=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R8C2 = 7.
7 Hidden Single ✓ R8C3=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R8C3 = 6.
8 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.
9 Hidden Single ✓ R9C4=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R9C4 = 1.
10 Hidden Pair ✗ 5 eliminations
Find where 2 and 4 can go on this column. These two digits only fit in R4C7 and R7C7 on the column. The other candidates in R4C7 and R7C7 are therefore eliminated.
11 Pointing ✗ 5 eliminations
(1) Look at where 2 can go in this box. (2) Look at where 5 can go in this box. (3) Look at where 8 can go in this box. (1) All its spots lie on a single column (R1C6 and R3C6). (2) All its spots lie on a single row (R3C8 and R3C9). (3) All its spots lie on a single column (R4C9 and R5C9). (1) 2 is therefore removed from that column outside the box. (2) 5 is therefore removed from that row outside the box. (3) 8 is therefore removed from that column outside the box.
12 Hidden Single ✓ R7C8=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R7C8 = 8.
13 Hidden Single ✓ R4C7=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R4C7 = 2.
14 Hidden Single ✓ R6C4=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R6C4 = 2.
15 Hidden Single ✓ R6C8=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R6C8 = 4.
16 Hidden Single ✓ R7C7=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R7C7 = 4.
17 Hidden Single ✓ R4C2=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R4C2 = 4.
18 Hidden Single ✓ R5C2=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R5C2 = 2.
19 Pointing ✗ 5 eliminations
(1) Look at where 3 can go in this box. (2) Look at where 7 can go in this box. (1) All its spots lie on a single column (R4C9 and R6C9). (2) All its spots lie on a single column (R4C9, R5C9 and R6C9). (1) 3 is therefore removed from that column outside the box. (2) 7 is therefore removed from that column outside the box.
20 Hidden Single ✓ R4C5=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R4C5 = 8.
21 Hidden Single ✓ R4C9=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R4C9 = 3.
22 Hidden Single ✓ R5C9=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R5C9 = 8.
23 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.
24 Hidden Single ✓ R6C9=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R6C9 = 7.
25 Hidden Single ✓ R7C1=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R7C1 = 3.
26 Naked Single ✓ R5C6=4
Look at cell R5C6. Every other digit already appears in its row, column or box. Only one option remains: R5C6 = 4.
27 Naked Single ✓ R5C5=7
Look at cell R5C5. Every other digit already appears in its row, column or box. Only one option remains: R5C5 = 7.
28 Hidden Single ✓ R1C5=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R1C5 = 3.
29 Hidden Single ✓ R2C4=7
Scan the empty cells in this column where 7 could go. Across the whole column, 7 has only one possible spot left. So R2C4 = 7.
30 Hidden Single ✓ R9C5=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R9C5 = 4.
31 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.
32 Naked Single ✓ R1C8=7
Look at cell R1C8. Every other digit already appears in its row, column or box. Only one option remains: R1C8 = 7.
33 Hidden Single ✓ R3C1=7
Scan the empty cells in this row where 7 could go. Across the whole row, 7 has only one possible spot left. So R3C1 = 7.
34 Hidden Single ✓ R4C3=7
Scan the empty cells in this column where 7 could go. Across the whole column, 7 has only one possible spot left. So R4C3 = 7.
35 Hidden Single ✓ R3C6=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R3C6 = 2.
36 Skyscraper ✗ 1 elimination
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. R7C3 is seen by both free ends: 5 is therefore eliminated there.
37 Pointing ✗ 1 elimination
Look at where 5 can go in this box. All its spots lie on a single row (R9C1 and R9C3). 5 is therefore removed from that row outside the box.
38 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. R2C1 is seen by both free ends: 9 is therefore eliminated there.
39 Naked Single ✓ R2C1=1
Look at cell R2C1. Every other digit already appears in its row, column or box. Only one option remains: R2C1 = 1.
40 Hidden Single ✓ R1C7=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R1C7 = 1.
41 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. R7C3 is seen by both free ends: 9 is therefore eliminated there.
42 Naked Single ✓ R7C3=2
Look at cell R7C3. Every other digit already appears in its row, column or box. Only one option remains: R7C3 = 2.
43 Hidden Single ✓ R1C1=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R1C1 = 2.
44 Hidden Single ✓ R9C9=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R9C9 = 2.
45 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. R2C5 is seen by both free ends: 9 is therefore eliminated there.
46 Naked Single ✓ R2C5=5
Look at cell R2C5. Every other digit already appears in its row, column or box. Only one option remains: R2C5 = 5.
47 Naked Single ✓ R6C5=9
Look at cell R6C5. Every other digit already appears in its row, column or box. Only one option remains: R6C5 = 9.
48 Naked Single ✓ R4C4=5
Look at cell R4C4. Every other digit already appears in its row, column or box. Only one option remains: R4C4 = 5.
49 Naked Single ✓ R6C3=5
Look at cell R6C3. Every other digit already appears in its row, column or box. Only one option remains: R6C3 = 5.
50 Naked Single ✓ R7C4=9
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 9.
51 Naked Single ✓ R7C9=5
Look at cell R7C9. Every other digit already appears in its row, column or box. Only one option remains: R7C9 = 5.
52 Naked Single ✓ R8C6=5
Look at cell R8C6. Every other digit already appears in its row, column or box. Only one option remains: R8C6 = 5.
53 Naked Single ✓ R8C8=3
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 3.
54 Naked Single ✓ R3C8=5
Look at cell R3C8. Every other digit already appears in its row, column or box. Only one option remains: R3C8 = 5.
55 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.
56 Naked Single ✓ R4C1=9
Look at cell R4C1. Every other digit already appears in its row, column or box. Only one option remains: R4C1 = 9.
57 Naked Single ✓ R8C7=9
Look at cell R8C7. Every other digit already appears in its row, column or box. Only one option remains: R8C7 = 9.
58 Naked Single ✓ R9C1=5
Look at cell R9C1. Every other digit already appears in its row, column or box. Only one option remains: R9C1 = 5.
59 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.
60 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.
61 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.
62 Naked Single ✓ R9C2=9
Look at cell R9C2. Every other digit already appears in its row, column or box. Only one option remains: R9C2 = 9.
63 Naked Single ✓ R9C3=8
Look at cell R9C3. Every other digit already appears in its row, column or box. Only one option remains: R9C3 = 8.
64 Naked Single ✓ R1C3=9
Look at cell R1C3. Every other digit already appears in its row, column or box. Only one option remains: R1C3 = 9.
65 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.
66 Naked Single ✓ R2C6=9
Look at cell R2C6. Every other digit already appears in its row, column or box. Only one option remains: R2C6 = 9.