Sudoku Solution No. 87

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 (✗ RlCcd)
1 Naked Single ✓ R5C4=2
Look at cell R5C4. Every other digit already appears in its row, column or box. Only one option remains: R5C4 = 2.
2 Naked Single ✓ R4C4=3
Look at cell R4C4. Every other digit already appears in its row, column or box. Only one option remains: R4C4 = 3.
3 Naked Single ✓ R6C5=9
Look at cell R6C5. Every other digit already appears in its row, column or box. Only one option remains: R6C5 = 9.
4 Naked Single ✓ R6C6=4
Look at cell R6C6. Every other digit already appears in its row, column or box. Only one option remains: R6C6 = 4.
5 Hidden Single ✓ R1C5=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R1C5 = 1.
6 Hidden Single ✓ R2C5=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R2C5 = 5.
7 Hidden Single ✓ R3C4=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R3C4 = 8.
8 Hidden Single ✓ R3C5=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R3C5 = 7.
9 Hidden Single ✓ R3C7=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R3C7 = 5.
10 Hidden Single ✓ R4C1=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R4C1 = 1.
11 Hidden Single ✓ R5C3=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R5C3 = 5.
12 Hidden Single ✓ R5C7=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R5C7 = 7.
13 Hidden Single ✓ R6C7=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R6C7 = 3.
14 Hidden Single ✓ R6C8=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R6C8 = 6.
15 Hidden Single ✓ R9C4=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R9C4 = 1.
16 Naked Single ✓ R2C4=6
Look at cell R2C4. Every other digit already appears in its row, column or box. Only one option remains: R2C4 = 6.
17 Hidden Single ✓ R1C1=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R1C1 = 6.
18 Hidden Single ✓ R1C3=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R1C3 = 8.
19 Hidden Single ✓ R3C1=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R3C1 = 9.
20 Hidden Single ✓ R3C9=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R3C9 = 6.
21 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.
22 Hidden Single ✓ R7C1=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R7C1 = 8.
23 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.
24 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.
25 Hidden Single ✓ R8C7=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R8C7 = 1.
26 Hidden Single ✓ R2C2=7
Scan the empty cells in this column where 7 could go. Across the whole column, 7 has only one possible spot left. So R2C2 = 7.
27 Naked Pair ✗ 5 eliminations
(1) Spot R1C6 and R3C6 on this column. (2) Spot R6C1 and R6C3 in this box. (3) Spot R7C5 and R8C5 in this box. (1) These two cells can only hold 2 and 3: they reserve those digits. (2) These two cells can only hold 2 and 7: they reserve those digits. (3) These two cells can only hold 2 and 3: they reserve those digits. (1) 2 and 3 are therefore removed from the other cells of the column. (2) 2 and 7 are therefore removed from the other cells of the box. (3) 2 and 3 are therefore removed from the other cells of the box.
28 Naked Pair ✗ 1 elimination
Spot R4C2 and R5C2 on this column. These two cells can only hold 4 and 9: they reserve those digits. 4 and 9 are therefore removed from the other cells of the column.
29 Naked Pair ✗ 4 eliminations
Spot R3C2 and R3C6 on this row. These two cells can only hold 2 and 3: they reserve those digits. 2 and 3 are therefore removed from the other cells of the row.
30 Box/Line ✗ 1 elimination
Look at where 9 can go on this column. All its spots lie within a single box (R4C9 and R5C9). 9 is therefore removed from the rest of the box.
31 Two-String Kite ✗ 1 elimination
Find 4 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 4. R8C8 is seen by both free ends: 4 is therefore eliminated there.
32 Naked Pair ✗ 5 eliminations
Spot R8C5 and R8C8 on this row. These two cells can only hold 2 and 3: they reserve those digits. 2 and 3 are therefore removed from the other cells of the row.
33 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. R2C3 is seen by both free ends: 3 is therefore eliminated there.
34 Hidden Single ✓ R1C6=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R1C6 = 3.
35 Hidden Single ✓ R3C2=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R3C2 = 3.
36 Hidden Single ✓ R7C3=3
Scan the empty cells in this column where 3 could go. Across the whole column, 3 has only one possible spot left. So R7C3 = 3.
37 Hidden Single ✓ R7C5=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R7C5 = 2.
38 Hidden Single ✓ R8C5=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R8C5 = 3.
39 Hidden Single ✓ R8C9=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R8C9 = 8.
40 Hidden Single ✓ R9C9=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R9C9 = 3.
41 Naked Single ✓ R3C6=2
Look at cell R3C6. Every other digit already appears in its row, column or box. Only one option remains: R3C6 = 2.
42 Naked Single ✓ R8C6=5
Look at cell R8C6. Every other digit already appears in its row, column or box. Only one option remains: R8C6 = 5.
43 Naked Single ✓ R8C8=2
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 2.
44 Naked Single ✓ R9C2=2
Look at cell R9C2. Every other digit already appears in its row, column or box. Only one option remains: R9C2 = 2.
45 Naked Single ✓ R9C6=8
Look at cell R9C6. Every other digit already appears in its row, column or box. Only one option remains: R9C6 = 8.
46 Naked Single ✓ R1C8=9
Look at cell R1C8. Every other digit already appears in its row, column or box. Only one option remains: R1C8 = 9.
47 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.
48 Naked Single ✓ R9C1=5
Look at cell R9C1. Every other digit already appears in its row, column or box. Only one option remains: R9C1 = 5.
49 Naked Single ✓ R1C7=2
Look at cell R1C7. Every other digit already appears in its row, column or box. Only one option remains: R1C7 = 2.
50 Naked Single ✓ R2C9=4
Look at cell R2C9. Every other digit already appears in its row, column or box. Only one option remains: R2C9 = 4.
51 Naked Single ✓ R3C8=1
Look at cell R3C8. Every other digit already appears in its row, column or box. Only one option remains: R3C8 = 1.
52 Naked Single ✓ R4C7=4
Look at cell R4C7. Every other digit already appears in its row, column or box. Only one option remains: R4C7 = 4.
53 Naked Single ✓ R5C9=9
Look at cell R5C9. Every other digit already appears in its row, column or box. Only one option remains: R5C9 = 9.
54 Naked Single ✓ R7C7=9
Look at cell R7C7. Every other digit already appears in its row, column or box. Only one option remains: R7C7 = 9.
55 Naked Single ✓ R2C1=2
Look at cell R2C1. Every other digit already appears in its row, column or box. Only one option remains: R2C1 = 2.
56 Naked Single ✓ R2C3=1
Look at cell R2C3. Every other digit already appears in its row, column or box. Only one option remains: R2C3 = 1.
57 Naked Single ✓ R2C8=3
Look at cell R2C8. Every other digit already appears in its row, column or box. Only one option remains: R2C8 = 3.
58 Naked Single ✓ R3C3=4
Look at cell R3C3. Every other digit already appears in its row, column or box. Only one option remains: R3C3 = 4.
59 Naked Single ✓ R4C2=9
Look at cell R4C2. Every other digit already appears in its row, column or box. Only one option remains: R4C2 = 9.
60 Naked Single ✓ R4C9=2
Look at cell R4C9. Every other digit already appears in its row, column or box. Only one option remains: R4C9 = 2.
61 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.
62 Naked Single ✓ R6C1=7
Look at cell R6C1. Every other digit already appears in its row, column or box. Only one option remains: R6C1 = 7.
63 Naked Single ✓ R6C3=2
Look at cell R6C3. Every other digit already appears in its row, column or box. Only one option remains: R6C3 = 2.
64 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.
65 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.