Sudoku Solution No. 51

Hard Score 72 / 100
Digits appear one by one.

Step-by-step solution

Steps 65 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 ✓ R2C2=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R2C2 = 1.
2 Hidden Single ✓ R4C2=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R4C2 = 2.
3 Hidden Single ✓ R4C4=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R4C4 = 6.
4 Hidden Single ✓ R5C5=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R5C5 = 1.
5 Hidden Single ✓ R6C5=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R6C5 = 4.
6 Hidden Single ✓ R6C8=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R6C8 = 1.
7 Hidden Single ✓ R6C9=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R6C9 = 5.
8 Hidden Single ✓ R8C3=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R8C3 = 3.
9 Hidden Single ✓ R8C8=7
Scan the empty cells in this row where 7 could go. Across the whole row, 7 has only one possible spot left. So R8C8 = 7.
10 Hidden Single ✓ R9C3=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R9C3 = 5.
11 Hidden Single ✓ R9C7=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R9C7 = 1.
12 Hidden Single ✓ R1C4=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R1C4 = 1.
13 Hidden Single ✓ R7C6=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R7C6 = 6.
14 Hidden Single ✓ R8C1=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R8C1 = 2.
15 Hidden Single ✓ R8C2=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R8C2 = 6.
16 Hidden Single ✓ R8C6=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R8C6 = 1.
17 Naked Single ✓ R8C9=4
Look at cell R8C9. Every other digit already appears in its row, column or box. Only one option remains: R8C9 = 4.
18 Hidden Single ✓ R1C3=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R1C3 = 4.
19 Hidden Single ✓ R1C8=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R1C8 = 5.
20 Hidden Single ✓ R2C1=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R2C1 = 6.
21 Hidden Single ✓ R2C8=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R2C8 = 4.
22 Hidden Single ✓ R3C7=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R3C7 = 6.
23 Hidden Single ✓ R5C9=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R5C9 = 6.
24 Hidden Single ✓ R6C3=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R6C3 = 6.
25 Hidden Single ✓ R1C9=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R1C9 = 2.
26 Hidden Single ✓ R7C8=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R7C8 = 2.
27 Pointing ✗ 1 elimination
Look at where 3 can go in this box. All its spots lie on a single column (R4C8 and R5C8). 3 is therefore removed from that column outside the box.
28 Pointing ✗ 3 eliminations
Look at where 3 can go in this box. All its spots lie on a single row (R2C7 and R2C9). 3 is therefore removed from that row outside the box.
29 Hidden Single ✓ R4C8=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R4C8 = 3.
30 Hidden Single ✓ R5C6=3
Scan the empty cells in this column where 3 could go. Across the whole column, 3 has only one possible spot left. So R5C6 = 3.
31 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.
32 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. R3C4 is seen by both free ends: 7 is therefore eliminated there.
33 Box/Line ✗ 1 elimination
Look at where 7 can go on this row. All its spots lie within a single box (R3C2 and R3C3). 7 is therefore removed from the rest of the box.
34 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. R3C2 is seen by both free ends: 8 is therefore eliminated there.
35 X-Wing ✗ 1 elimination
Find where 8 appears on two rows: altogether, only two columns are involved (R3C3, R3C8, R5C3 and R5C8). On each covered column, 8 must lie within one of these two rows. 8 is therefore removed from those two columns outside the two X-Wing rows.
36 Naked Single ✓ R2C3=2
Look at cell R2C3. Every other digit already appears in its row, column or box. Only one option remains: R2C3 = 2.
37 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.
38 Naked Single ✓ R7C5=3
Look at cell R7C5. Every other digit already appears in its row, column or box. Only one option remains: R7C5 = 3.
39 Naked Single ✓ R9C4=4
Look at cell R9C4. Every other digit already appears in its row, column or box. Only one option remains: R9C4 = 4.
40 Naked Single ✓ R3C5=2
Look at cell R3C5. Every other digit already appears in its row, column or box. Only one option remains: R3C5 = 2.
41 Naked Single ✓ R7C4=5
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 5.
42 Hidden Single ✓ R1C7=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R1C7 = 7.
43 Hidden Single ✓ R2C7=3
Scan the empty cells in this column where 3 could go. Across the whole column, 3 has only one possible spot left. So R2C7 = 3.
44 Hidden Single ✓ R3C4=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R3C4 = 3.
45 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.
46 Hidden Single ✓ R9C9=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R9C9 = 3.
47 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. R2C9 is seen by both free ends: 9 is therefore eliminated there.
48 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.
49 Naked Single ✓ R3C8=9
Look at cell R3C8. Every other digit already appears in its row, column or box. Only one option remains: R3C8 = 9.
50 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.
51 Naked Single ✓ R6C7=9
Look at cell R6C7. Every other digit already appears in its row, column or box. Only one option remains: R6C7 = 9.
52 Naked Single ✓ R7C7=8
Look at cell R7C7. Every other digit already appears in its row, column or box. Only one option remains: R7C7 = 8.
53 Naked Single ✓ R7C9=9
Look at cell R7C9. Every other digit already appears in its row, column or box. Only one option remains: R7C9 = 9.
54 Naked Single ✓ R3C2=7
Look at cell R3C2. Every other digit already appears in its row, column or box. Only one option remains: R3C2 = 7.
55 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.
56 Naked Single ✓ R5C3=7
Look at cell R5C3. Every other digit already appears in its row, column or box. Only one option remains: R5C3 = 7.
57 Naked Single ✓ R5C4=9
Look at cell R5C4. Every other digit already appears in its row, column or box. Only one option remains: R5C4 = 9.
58 Naked Single ✓ R6C2=8
Look at cell R6C2. Every other digit already appears in its row, column or box. Only one option remains: R6C2 = 8.
59 Naked Single ✓ R6C6=7
Look at cell R6C6. Every other digit already appears in its row, column or box. Only one option remains: R6C6 = 7.
60 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.
61 Naked Single ✓ R1C1=9
Look at cell R1C1. Every other digit already appears in its row, column or box. Only one option remains: R1C1 = 9.
62 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.
63 Naked Single ✓ R2C4=7
Look at cell R2C4. Every other digit already appears in its row, column or box. Only one option remains: R2C4 = 7.
64 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.
65 Naked Single ✓ R9C1=8
Look at cell R9C1. Every other digit already appears in its row, column or box. Only one option remains: R9C1 = 8.