Sudoku Solution No. 15

Hard Score 71 / 100
Digits appear one by one.

Step-by-step solution

Steps 65 Estimated time 104 – 156 min Hardest technique X-Wing Clues 24
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCcd)
1 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.
2 Naked Single ✓ R1C1=6
Look at cell R1C1. Every other digit already appears in its row, column or box. Only one option remains: R1C1 = 6.
3 Naked Single ✓ R1C3=5
Look at cell R1C3. Every other digit already appears in its row, column or box. Only one option remains: R1C3 = 5.
4 Naked Single ✓ R2C2=8
Look at cell R2C2. Every other digit already appears in its row, column or box. Only one option remains: R2C2 = 8.
5 Naked Single ✓ R3C3=9
Look at cell R3C3. Every other digit already appears in its row, column or box. Only one option remains: R3C3 = 9.
6 Hidden Single ✓ R1C4=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R1C4 = 1.
7 Hidden Single ✓ R1C8=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R1C8 = 2.
8 Hidden Single ✓ R2C6=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R2C6 = 2.
9 Hidden Single ✓ R4C6=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R4C6 = 1.
10 Hidden Single ✓ R5C6=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R5C6 = 8.
11 Hidden Single ✓ R5C9=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R5C9 = 2.
12 Hidden Single ✓ R6C6=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R6C6 = 5.
13 Hidden Single ✓ R6C8=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R6C8 = 8.
14 Hidden Single ✓ R6C9=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R6C9 = 1.
15 Hidden Single ✓ R7C1=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R7C1 = 2.
16 Hidden Single ✓ R7C2=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R7C2 = 5.
17 Hidden Single ✓ R7C4=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R7C4 = 8.
18 Hidden Single ✓ R7C5=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R7C5 = 1.
19 Hidden Single ✓ R8C4=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R8C4 = 2.
20 Hidden Single ✓ R8C5=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R8C5 = 9.
21 Hidden Single ✓ R3C9=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R3C9 = 8.
22 Hidden Single ✓ R5C3=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R5C3 = 1.
23 Hidden Single ✓ R9C5=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R9C5 = 7.
24 Hidden Single ✓ R4C2=7
Scan the empty cells in this column where 7 could go. Across the whole column, 7 has only one possible spot left. So R4C2 = 7.
25 Hidden Single ✓ R6C4=7
Scan the empty cells in this row where 7 could go. Across the whole row, 7 has only one possible spot left. So R6C4 = 7.
26 Naked Pair ✗ 7 eliminations
(1) Spot R8C1 and R8C6 on this row. (2) Spot R1C7 and R1C9 in this box. (1) These two cells can only hold 3 and 4: they reserve those digits. (2) These two cells can only hold 4 and 7: they reserve those digits. (1) 3 and 4 are therefore removed from the other cells of the row. (2) 4 and 7 are therefore removed from the other cells of the box.
27 Box/Line ✗ 1 elimination
Look at where 4 can go on this row. All its spots lie within a single box (R7C7, R7C8 and R7C9). 4 is therefore removed from the rest of the box.
28 Two-String Kite ✗ 1 elimination
Find 6 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 6. R4C9 is seen by both free ends: 6 is therefore eliminated there.
29 Box/Line ✗ 1 elimination
Look at where 6 can go on this column. All its spots lie within a single box (R8C9 and R9C9). 6 is therefore removed from the rest of the box.
30 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.
31 Hidden Single ✓ R2C8=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R2C8 = 9.
32 Hidden Single ✓ R2C9=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R2C9 = 5.
33 Hidden Single ✓ R3C4=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R3C4 = 4.
34 Hidden Single ✓ R3C5=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R3C5 = 5.
35 Naked Single ✓ R2C5=3
Look at cell R2C5. Every other digit already appears in its row, column or box. Only one option remains: R2C5 = 3.
36 Naked Pair ✗ 2 eliminations
Spot R5C2 and R5C5 on this row. These two cells can only hold 4 and 6: they reserve those digits. 4 and 6 are therefore removed from the other cells of the row.
37 Box/Line ✗ 1 elimination
Look at where 4 can go on this row. All its spots lie within a single box (R4C8 and R4C9). 4 is therefore removed from the rest of the box.
38 Naked Pair ✗ 2 eliminations
Spot R3C7 and R6C7 on this column. These two cells can only hold 3 and 6: they reserve those digits. 3 and 6 are therefore removed from the other cells of the column.
39 Naked Single ✓ R5C7=9
Look at cell R5C7. Every other digit already appears in its row, column or box. Only one option remains: R5C7 = 9.
40 Naked Single ✓ R5C4=3
Look at cell R5C4. Every other digit already appears in its row, column or box. Only one option remains: R5C4 = 3.
41 Naked Single ✓ R4C4=9
Look at cell R4C4. Every other digit already appears in its row, column or box. Only one option remains: R4C4 = 9.
42 Hidden Single ✓ R7C9=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R7C9 = 9.
43 Skyscraper ✗ 1 elimination
Find 3 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 3. R7C8 is seen by both free ends: 3 is therefore eliminated there.
44 Naked Single ✓ R7C8=4
Look at cell R7C8. Every other digit already appears in its row, column or box. Only one option remains: R7C8 = 4.
45 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.
46 Naked Single ✓ R8C9=6
Look at cell R8C9. Every other digit already appears in its row, column or box. Only one option remains: R8C9 = 6.
47 Naked Single ✓ R9C9=3
Look at cell R9C9. Every other digit already appears in its row, column or box. Only one option remains: R9C9 = 3.
48 Naked Single ✓ R1C7=4
Look at cell R1C7. Every other digit already appears in its row, column or box. Only one option remains: R1C7 = 4.
49 Naked Single ✓ R1C9=7
Look at cell R1C9. Every other digit already appears in its row, column or box. Only one option remains: R1C9 = 7.
50 Naked Single ✓ R4C9=4
Look at cell R4C9. Every other digit already appears in its row, column or box. Only one option remains: R4C9 = 4.
51 Naked Single ✓ R7C3=3
Look at cell R7C3. Every other digit already appears in its row, column or box. Only one option remains: R7C3 = 3.
52 Naked Single ✓ R8C1=4
Look at cell R8C1. Every other digit already appears in its row, column or box. Only one option remains: R8C1 = 4.
53 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.
54 Naked Single ✓ R8C6=3
Look at cell R8C6. Every other digit already appears in its row, column or box. Only one option remains: R8C6 = 3.
55 Naked Single ✓ R9C2=6
Look at cell R9C2. Every other digit already appears in its row, column or box. Only one option remains: R9C2 = 6.
56 Naked Single ✓ R9C6=4
Look at cell R9C6. Every other digit already appears in its row, column or box. Only one option remains: R9C6 = 4.
57 Naked Single ✓ R4C3=6
Look at cell R4C3. Every other digit already appears in its row, column or box. Only one option remains: R4C3 = 6.
58 Naked Single ✓ R4C8=3
Look at cell R4C8. Every other digit already appears in its row, column or box. Only one option remains: R4C8 = 3.
59 Naked Single ✓ R5C2=4
Look at cell R5C2. Every other digit already appears in its row, column or box. Only one option remains: R5C2 = 4.
60 Naked Single ✓ R5C5=6
Look at cell R5C5. Every other digit already appears in its row, column or box. Only one option remains: R5C5 = 6.
61 Naked Single ✓ R6C1=3
Look at cell R6C1. Every other digit already appears in its row, column or box. Only one option remains: R6C1 = 3.
62 Naked Single ✓ R6C5=4
Look at cell R6C5. Every other digit already appears in its row, column or box. Only one option remains: R6C5 = 4.
63 Naked Single ✓ R6C7=6
Look at cell R6C7. Every other digit already appears in its row, column or box. Only one option remains: R6C7 = 6.
64 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.
65 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.