Sudoku Solution No. 56

Hard Score 72 / 100
Digits appear one by one.

Step-by-step solution

Steps 68 Estimated time 112 – 168 min Hardest technique X-Wing Clues 23
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCcd)
1 Naked Single ✓ R9C3=9
Look at cell R9C3. Every other digit already appears in its row, column or box. Only one option remains: R9C3 = 9.
2 Hidden Single ✓ R2C4=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R2C4 = 6.
3 Hidden Single ✓ R3C1=9
Scan the empty cells in this column where 9 could go. Across the whole column, 9 has only one possible spot left. So R3C1 = 9.
4 Hidden Single ✓ R6C1=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R6C1 = 2.
5 Hidden Single ✓ R6C5=7
Scan the empty cells in this column where 7 could go. Across the whole column, 7 has only one possible spot left. So R6C5 = 7.
6 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.
7 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.
8 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.
9 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.
10 Hidden Single ✓ R8C6=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R8C6 = 4.
11 Hidden Single ✓ R9C1=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R9C1 = 8.
12 Hidden Single ✓ R1C4=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R1C4 = 8.
13 Hidden Single ✓ R1C6=2
Scan the empty cells in this column where 2 could go. Across the whole column, 2 has only one possible spot left. So R1C6 = 2.
14 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.
15 Hidden Single ✓ R6C6=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R6C6 = 3.
16 Hidden Single ✓ R9C7=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R9C7 = 4.
17 Hidden Single ✓ R9C9=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R9C9 = 6.
18 Hidden Single ✓ R1C2=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R1C2 = 3.
19 Hidden Single ✓ R2C2=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R2C2 = 5.
20 Hidden Single ✓ R2C5=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R2C5 = 3.
21 Hidden Single ✓ R2C7=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R2C7 = 2.
22 Hidden Single ✓ R2C9=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R2C9 = 4.
23 Hidden Single ✓ R3C2=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R3C2 = 4.
24 Hidden Single ✓ R3C5=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R3C5 = 5.
25 Hidden Single ✓ R4C1=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R4C1 = 4.
26 Hidden Single ✓ R4C3=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R4C3 = 5.
27 Hidden Single ✓ R4C6=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R4C6 = 8.
28 Hidden Single ✓ R5C6=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R5C6 = 5.
29 Hidden Single ✓ R5C7=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R5C7 = 8.
30 Hidden Single ✓ R6C2=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R6C2 = 8.
31 Hidden Single ✓ R6C7=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R6C7 = 5.
32 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.
33 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. R4C8 is seen by both free ends: 1 is therefore eliminated there.
34 Skyscraper ✗ 1 elimination
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. R4C8 is seen by both free ends: 7 is therefore eliminated there.
35 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. R8C8 is seen by both free ends: 1 is therefore eliminated there.
36 Box/Line ✗ 1 elimination
Look at where 1 can go on this column. All its spots lie within a single box (R1C8 and R2C8). 1 is therefore removed from the rest of the box.
37 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. R7C9 is seen by both free ends: 1 is therefore eliminated there.
38 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. R8C8 is seen by both free ends: 7 is therefore eliminated there.
39 Hidden Pair ✗ 1 elimination
Find where 1 and 7 can go on this column. These two digits only fit in R1C8 and R2C8 on the column. The other candidates in R1C8 and R2C8 are therefore eliminated.
40 Hidden Single ✓ R1C7=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R1C7 = 9.
41 Naked Pair ✗ 2 eliminations
Spot R8C3 and R8C7 on this row. These two cells can only hold 1 and 7: they reserve those digits. 1 and 7 are therefore removed from the other cells of the row.
42 Pointing ✗ 1 elimination
Look at where 1 can go in this box. All its spots lie on a single column (R7C7 and R8C7). 1 is therefore removed from that column outside the box.
43 Skyscraper ✗ 1 elimination
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. R7C2 is seen by both free ends: 7 is therefore eliminated there.
44 Naked Single ✓ R7C2=1
Look at cell R7C2. Every other digit already appears in its row, column or box. Only one option remains: R7C2 = 1.
45 Naked Single ✓ R8C3=7
Look at cell R8C3. Every other digit already appears in its row, column or box. Only one option remains: R8C3 = 7.
46 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.
47 Naked Single ✓ R1C3=1
Look at cell R1C3. Every other digit already appears in its row, column or box. Only one option remains: R1C3 = 1.
48 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.
49 Naked Single ✓ R2C1=7
Look at cell R2C1. Every other digit already appears in its row, column or box. Only one option remains: R2C1 = 7.
50 Naked Single ✓ R2C8=1
Look at cell R2C8. Every other digit already appears in its row, column or box. Only one option remains: R2C8 = 1.
51 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.
52 Naked Single ✓ R4C7=6
Look at cell R4C7. Every other digit already appears in its row, column or box. Only one option remains: R4C7 = 6.
53 Naked Single ✓ R4C8=9
Look at cell R4C8. Every other digit already appears in its row, column or box. Only one option remains: R4C8 = 9.
54 Naked Single ✓ R5C1=1
Look at cell R5C1. Every other digit already appears in its row, column or box. Only one option remains: R5C1 = 1.
55 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.
56 Naked Single ✓ R6C9=1
Look at cell R6C9. Every other digit already appears in its row, column or box. Only one option remains: R6C9 = 1.
57 Naked Single ✓ R7C9=2
Look at cell R7C9. Every other digit already appears in its row, column or box. Only one option remains: R7C9 = 2.
58 Naked Single ✓ R8C8=5
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 5.
59 Naked Single ✓ R8C9=9
Look at cell R8C9. Every other digit already appears in its row, column or box. Only one option remains: R8C9 = 9.
60 Naked Single ✓ R9C8=3
Look at cell R9C8. Every other digit already appears in its row, column or box. Only one option remains: R9C8 = 3.
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 ✓ R3C8=6
Look at cell R3C8. Every other digit already appears in its row, column or box. Only one option remains: R3C8 = 6.
63 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.
64 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.
65 Naked Single ✓ R7C4=3
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 3.
66 Naked Single ✓ R7C7=7
Look at cell R7C7. Every other digit already appears in its row, column or box. Only one option remains: R7C7 = 7.
67 Naked Single ✓ R8C4=2
Look at cell R8C4. Every other digit already appears in its row, column or box. Only one option remains: R8C4 = 2.
68 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.