Sudoku Solution No. 45

Hard Score 72 / 100
Digits appear one by one.

Step-by-step solution

Steps 64 Estimated time 104 – 156 min Hardest technique X-Wing Clues 23
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCc≠d)
1 Hidden Single ✓ R1C3=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R1C3 = 4.
2 Hidden Single ✓ R2C1=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R2C1 = 3.
3 Hidden Single ✓ R2C3=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R2C3 = 9.
4 Hidden Single ✓ R3C8=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R3C8 = 4.
5 Hidden Single ✓ R4C4=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R4C4 = 4.
6 Hidden Single ✓ R4C9=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R4C9 = 9.
7 Hidden Single ✓ R5C9=2
Scan the empty cells in this column where 2 could go. Across the whole column, 2 has only one possible spot left. So R5C9 = 2.
8 Hidden Single ✓ R6C5=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R6C5 = 3.
9 Hidden Single ✓ R6C6=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R6C6 = 2.
10 Hidden Single ✓ R7C2=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R7C2 = 4.
11 Hidden Single ✓ R9C7=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R9C7 = 4.
12 Hidden Single ✓ R4C2=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R4C2 = 6.
13 Hidden Single ✓ R5C5=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R5C5 = 9.
14 Hidden Single ✓ R5C7=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R5C7 = 6.
15 Hidden Single ✓ R6C1=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R6C1 = 9.
16 Hidden Single ✓ R7C6=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R7C6 = 9.
17 Hidden Single ✓ R8C2=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R8C2 = 3.
18 Hidden Single ✓ R8C3=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R8C3 = 2.
19 Hidden Single ✓ R8C6=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R8C6 = 6.
20 Hidden Single ✓ R9C2=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R9C2 = 9.
21 Naked Single ✓ R5C2=8
Look at cell R5C2. Every other digit already appears in its row, column or box. Only one option remains: R5C2 = 8.
22 Naked Single ✓ R3C2=2
Look at cell R3C2. Every other digit already appears in its row, column or box. Only one option remains: R3C2 = 2.
23 Hidden Single ✓ R1C1=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R1C1 = 8.
24 Hidden Single ✓ R3C3=7
Scan the empty cells in this column where 7 could go. Across the whole column, 7 has only one possible spot left. So R3C3 = 7.
25 Hidden Single ✓ R5C6=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R5C6 = 7.
26 Hidden Single ✓ R6C8=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R6C8 = 8.
27 Hidden Single ✓ R7C3=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R7C3 = 8.
28 Pointing ✗ 3 eliminations
Look at where 1 can go in this box. All its spots lie on a single column (R1C9 and R3C9). 1 is therefore removed from that column outside the box.
29 Box/Line ✗ 2 eliminations
Look at where 8 can go on this column. All its spots lie within a single box (R8C4 and R9C4). 8 is therefore removed from the rest of the box.
30 Hidden Pair ✗ 5 eliminations
Find where 3 and 8 can go on this row. These two digits only fit in R9C4 and R9C9 on the row. The other candidates in R9C4 and R9C9 are therefore eliminated.
31 Hidden Single ✓ R1C4=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R1C4 = 7.
32 Hidden Single ✓ R2C4=2
Scan the empty cells in this column where 2 could go. Across the whole column, 2 has only one possible spot left. So R2C4 = 2.
33 Hidden Single ✓ R9C5=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R9C5 = 2.
34 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. R8C4 is seen by both free ends: 1 is therefore eliminated there.
35 Two-String Kite ✗ 1 elimination
Find 5 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 5. R8C4 is seen by both free ends: 5 is therefore eliminated there.
36 Naked Single ✓ R8C4=8
Look at cell R8C4. Every other digit already appears in its row, column or box. Only one option remains: R8C4 = 8.
37 Naked Single ✓ R9C4=3
Look at cell R9C4. Every other digit already appears in its row, column or box. Only one option remains: R9C4 = 3.
38 Naked Single ✓ R9C9=8
Look at cell R9C9. Every other digit already appears in its row, column or box. Only one option remains: R9C9 = 8.
39 Hidden Single ✓ R7C8=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R7C8 = 6.
40 Hidden Single ✓ R7C9=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R7C9 = 3.
41 Skyscraper ✗ 1 elimination
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. R9C6 is seen by both free ends: 1 is therefore eliminated there.
42 Naked Single ✓ R9C6=5
Look at cell R9C6. Every other digit already appears in its row, column or box. Only one option remains: R9C6 = 5.
43 Naked Single ✓ R7C4=1
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 1.
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 ✓ R5C8=1
Look at cell R5C8. Every other digit already appears in its row, column or box. Only one option remains: R5C8 = 1.
46 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.
47 Naked Single ✓ R7C1=5
Look at cell R7C1. Every other digit already appears in its row, column or box. Only one option remains: R7C1 = 5.
48 Naked Single ✓ R8C7=1
Look at cell R8C7. Every other digit already appears in its row, column or box. Only one option remains: R8C7 = 1.
49 Naked Single ✓ R9C8=7
Look at cell R9C8. Every other digit already appears in its row, column or box. Only one option remains: R9C8 = 7.
50 Naked Single ✓ R2C8=5
Look at cell R2C8. Every other digit already appears in its row, column or box. Only one option remains: R2C8 = 5.
51 Naked Single ✓ R3C9=1
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 1.
52 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.
53 Naked Single ✓ R8C1=7
Look at cell R8C1. Every other digit already appears in its row, column or box. Only one option remains: R8C1 = 7.
54 Naked Single ✓ R8C9=5
Look at cell R8C9. Every other digit already appears in its row, column or box. Only one option remains: R8C9 = 5.
55 Naked Single ✓ R9C1=1
Look at cell R9C1. Every other digit already appears in its row, column or box. Only one option remains: R9C1 = 1.
56 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.
57 Naked Single ✓ R2C5=6
Look at cell R2C5. Every other digit already appears in its row, column or box. Only one option remains: R2C5 = 6.
58 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.
59 Naked Single ✓ R3C6=8
Look at cell R3C6. Every other digit already appears in its row, column or box. Only one option remains: R3C6 = 8.
60 Naked Single ✓ R4C3=5
Look at cell R4C3. Every other digit already appears in its row, column or box. Only one option remains: R4C3 = 5.
61 Naked Single ✓ R4C6=1
Look at cell R4C6. Every other digit already appears in its row, column or box. Only one option remains: R4C6 = 1.
62 Naked Single ✓ R1C5=1
Look at cell R1C5. Every other digit already appears in its row, column or box. Only one option remains: R1C5 = 1.
63 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.
64 Naked Single ✓ R4C5=8
Look at cell R4C5. Every other digit already appears in its row, column or box. Only one option remains: R4C5 = 8.