Sudoku Solution No. 53

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 24
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCcd)
1 Hidden Single ✓ R1C1=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R1C1 = 1.
2 Hidden Single ✓ R1C9=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R1C9 = 4.
3 Hidden Single ✓ R2C5=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R2C5 = 9.
4 Hidden Single ✓ R3C2=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R3C2 = 5.
5 Hidden Single ✓ R3C6=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R3C6 = 6.
6 Hidden Single ✓ R4C5=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R4C5 = 7.
7 Hidden Single ✓ R5C4=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R5C4 = 1.
8 Hidden Single ✓ R5C8=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R5C8 = 9.
9 Hidden Single ✓ R5C9=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R5C9 = 7.
10 Hidden Single ✓ R7C2=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R7C2 = 7.
11 Hidden Single ✓ R7C9=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R7C9 = 9.
12 Hidden Single ✓ R8C3=9
Scan the empty cells in this column where 9 could go. Across the whole column, 9 has only one possible spot left. So R8C3 = 9.
13 Hidden Single ✓ R9C6=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R9C6 = 9.
14 Hidden Single ✓ R9C7=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R9C7 = 7.
15 Hidden Single ✓ R7C6=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R7C6 = 5.
16 Hidden Single ✓ R9C8=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R9C8 = 5.
17 Hidden Single ✓ R9C4=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R9C4 = 4.
18 Hidden Pair ✗ 2 eliminations
Find where 5 and 6 can go in this box. These two digits only fit in R6C7 and R6C9 in the box. The other candidates in R6C7 and R6C9 are therefore eliminated.
19 Hidden Single ✓ R6C7=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R6C7 = 6.
20 Hidden Single ✓ R6C8=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R6C8 = 4.
21 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.
22 Hidden Single ✓ R8C7=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R8C7 = 4.
23 Hidden Single ✓ R8C9=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R8C9 = 6.
24 Hidden Single ✓ R2C7=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R2C7 = 5.
25 Hidden Single ✓ R5C3=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R5C3 = 6.
26 Naked Pair ✗ 3 eliminations
Spot R7C8 and R8C8 on this column. These two cells can only hold 1 and 8: they reserve those digits. 1 and 8 are therefore removed from the other cells of the column.
27 Hidden Pair ✗ 3 eliminations
Find where 4 and 8 can go on this row. These two digits only fit in R4C1 and R4C6 on the row. The other candidates in R4C1 and R4C6 are therefore eliminated.
28 Pointing ✗ 2 eliminations
Look at where 3 can go in this box. All its spots lie on a single row (R3C7 and R3C8). 3 is therefore removed from that row outside the box.
29 Box/Line ✗ 3 eliminations
(1) Look at where 8 can go on this column. (2) Look at where 3 can go on this column. (1) All its spots lie within a single box (R8C2 and R9C2). (2) All its spots lie within a single box (R1C3 and R2C3). (1) 8 is therefore removed from the rest of the box. (2) 3 is therefore removed from the rest of the box.
30 Naked Pair ✗ 4 eliminations
Spot R2C1 and R2C9 on this row. These two cells can only hold 2 and 8: they reserve those digits. 2 and 8 are therefore removed from the other cells of the row.
31 Skyscraper ✗ 1 elimination
Find 8 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 8. R1C3 is seen by both free ends: 8 is therefore eliminated there.
32 Box/Line ✗ 4 eliminations
Look at where 8 can go on this row. All its spots lie within a single box (R1C5 and R1C6). 8 is therefore removed from the rest of the box.
33 Hidden Single ✓ R9C2=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R9C2 = 8.
34 Skyscraper ✗ 1 elimination
Find 2 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 2. R5C1 is seen by both free ends: 2 is therefore eliminated there.
35 Two-String Kite ✗ 1 elimination
Find 2 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 2. R8C5 is seen by both free ends: 2 is therefore eliminated there.
36 Two-String Kite ✗ 1 elimination
Find 2 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 2. R1C3 is seen by both free ends: 2 is therefore eliminated there.
37 Naked Single ✓ R1C3=3
Look at cell R1C3. Every other digit already appears in its row, column or box. Only one option remains: R1C3 = 3.
38 Naked Single ✓ R2C3=7
Look at cell R2C3. Every other digit already appears in its row, column or box. Only one option remains: R2C3 = 7.
39 Naked Single ✓ R2C4=3
Look at cell R2C4. Every other digit already appears in its row, column or box. Only one option remains: R2C4 = 3.
40 Naked Single ✓ R7C4=8
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 8.
41 Naked Single ✓ R7C8=1
Look at cell R7C8. Every other digit already appears in its row, column or box. Only one option remains: R7C8 = 1.
42 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.
43 Naked Single ✓ R8C8=8
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 8.
44 Naked Single ✓ R9C5=6
Look at cell R9C5. Every other digit already appears in its row, column or box. Only one option remains: R9C5 = 6.
45 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.
46 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.
47 Naked Single ✓ R8C2=3
Look at cell R8C2. Every other digit already appears in its row, column or box. Only one option remains: R8C2 = 3.
48 Naked Single ✓ R8C5=1
Look at cell R8C5. Every other digit already appears in its row, column or box. Only one option remains: R8C5 = 1.
49 Naked Single ✓ R9C1=2
Look at cell R9C1. Every other digit already appears in its row, column or box. Only one option remains: R9C1 = 2.
50 Naked Single ✓ R2C1=8
Look at cell R2C1. Every other digit already appears in its row, column or box. Only one option remains: R2C1 = 8.
51 Naked Single ✓ R2C9=2
Look at cell R2C9. Every other digit already appears in its row, column or box. Only one option remains: R2C9 = 2.
52 Naked Single ✓ R3C3=2
Look at cell R3C3. Every other digit already appears in its row, column or box. Only one option remains: R3C3 = 2.
53 Naked Single ✓ R3C8=3
Look at cell R3C8. Every other digit already appears in its row, column or box. Only one option remains: R3C8 = 3.
54 Naked Single ✓ R4C1=4
Look at cell R4C1. Every other digit already appears in its row, column or box. Only one option remains: R4C1 = 4.
55 Naked Single ✓ R4C6=8
Look at cell R4C6. Every other digit already appears in its row, column or box. Only one option remains: R4C6 = 8.
56 Naked Single ✓ R4C8=2
Look at cell R4C8. Every other digit already appears in its row, column or box. Only one option remains: R4C8 = 2.
57 Naked Single ✓ R4C9=1
Look at cell R4C9. Every other digit already appears in its row, column or box. Only one option remains: R4C9 = 1.
58 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.
59 Naked Single ✓ R5C2=2
Look at cell R5C2. Every other digit already appears in its row, column or box. Only one option remains: R5C2 = 2.
60 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.
61 Naked Single ✓ R6C3=8
Look at cell R6C3. Every other digit already appears in its row, column or box. Only one option remains: R6C3 = 8.
62 Naked Single ✓ R6C5=2
Look at cell R6C5. Every other digit already appears in its row, column or box. Only one option remains: R6C5 = 2.
63 Naked Single ✓ R7C1=6
Look at cell R7C1. Every other digit already appears in its row, column or box. Only one option remains: R7C1 = 6.
64 Naked Single ✓ R1C5=8
Look at cell R1C5. Every other digit already appears in its row, column or box. Only one option remains: R1C5 = 8.
65 Naked Single ✓ R1C6=2
Look at cell R1C6. Every other digit already appears in its row, column or box. Only one option remains: R1C6 = 2.
66 Naked Single ✓ R3C7=1
Look at cell R3C7. Every other digit already appears in its row, column or box. Only one option remains: R3C7 = 1.
67 Naked Single ✓ R3C9=8
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 8.
68 Naked Single ✓ R4C7=3
Look at cell R4C7. Every other digit already appears in its row, column or box. Only one option remains: R4C7 = 3.