Sudoku Solution No. 81

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 24
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCcd)
1 Naked Single ✓ R9C1=6
Look at cell R9C1. Every other digit already appears in its row, column or box. Only one option remains: R9C1 = 6.
2 Naked Single ✓ R9C2=5
Look at cell R9C2. Every other digit already appears in its row, column or box. Only one option remains: R9C2 = 5.
3 Hidden Single ✓ R2C2=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R2C2 = 8.
4 Hidden Single ✓ R3C3=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R3C3 = 5.
5 Hidden Single ✓ R4C9=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R4C9 = 5.
6 Hidden Single ✓ R5C2=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R5C2 = 2.
7 Hidden Single ✓ R5C5=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R5C5 = 8.
8 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.
9 Hidden Single ✓ R5C9=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R5C9 = 9.
10 Hidden Single ✓ R6C7=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R6C7 = 8.
11 Hidden Single ✓ R7C7=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R7C7 = 5.
12 Hidden Single ✓ R7C9=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R7C9 = 6.
13 Hidden Single ✓ R8C2=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R8C2 = 4.
14 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.
15 Hidden Single ✓ R8C5=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R8C5 = 5.
16 Hidden Single ✓ R8C9=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R8C9 = 7.
17 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.
18 Hidden Single ✓ R6C3=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R6C3 = 4.
19 Pointing ✗ 3 eliminations
(1) Look at where 4 can go in this box. (2) Look at where 2 can go in this box. (1) All its spots lie on a single column (R4C8 and R5C8). (2) All its spots lie on a single column (R8C6 and R9C6). (1) 4 is therefore removed from that column outside the box. (2) 2 is therefore removed from that column outside the box.
20 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. R1C3 is seen by both free ends: 1 is therefore eliminated there.
21 X-Wing ✗ 2 eliminations
Find where 1 appears on two columns: altogether, only two rows are involved (R2C3, R5C3, R2C8 and R5C8). On each covered row, 1 must lie within one of these two columns. 1 is therefore removed from those two rows outside the two X-Wing columns.
22 Hidden Pair ✗ 6 eliminations
(1) Find where 1 and 2 can go on this column. (2) Find where 1 and 2 can go in this box. (1) These two digits only fit in R1C4 and R3C4 on the column. (2) These two digits only fit in R1C4 and R3C4 in the box. (1) The other candidates in R1C4 and R3C4 are therefore eliminated. (2) The other candidates in R1C4 and R3C4 are therefore eliminated.
23 Hidden Single ✓ R1C6=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R1C6 = 8.
24 Hidden Single ✓ R7C4=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R7C4 = 8.
25 Hidden Single ✓ R8C6=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R8C6 = 2.
26 Hidden Single ✓ R8C8=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R8C8 = 8.
27 Hidden Single ✓ R9C8=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R9C8 = 2.
28 Naked Pair ✗ 3 eliminations
Spot R7C6 and R9C6 on this column. These two cells can only hold 3 and 9: they reserve those digits. 3 and 9 are therefore removed from the other cells of the column.
29 Skyscraper ✗ 2 eliminations
Find 6 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 6. R5C3 and R4C5 is seen by both free ends: 6 is therefore eliminated there.
30 Hidden Single ✓ R3C6=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R3C6 = 4.
31 Hidden Single ✓ R5C6=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R5C6 = 6.
32 Naked Pair ✗ 5 eliminations
(1) Spot R3C1 and R3C4 on this row. (2) Spot R5C3 and R6C2 in this box. (1) These two cells can only hold 1 and 2: they reserve those digits. (2) These two cells can only hold 1 and 3: they reserve those digits. (1) 1 and 2 are therefore removed from the other cells of the row. (2) 1 and 3 are therefore removed from the other cells of the box.
33 Skyscraper ✗ 2 eliminations
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. R1C3 and R3C7 is seen by both free ends: 3 is therefore eliminated there.
34 Naked Single ✓ R1C3=6
Look at cell R1C3. Every other digit already appears in its row, column or box. Only one option remains: R1C3 = 6.
35 Naked Single ✓ R3C2=3
Look at cell R3C2. Every other digit already appears in its row, column or box. Only one option remains: R3C2 = 3.
36 Naked Single ✓ R4C3=7
Look at cell R4C3. Every other digit already appears in its row, column or box. Only one option remains: R4C3 = 7.
37 Naked Single ✓ R6C2=1
Look at cell R6C2. Every other digit already appears in its row, column or box. Only one option remains: R6C2 = 1.
38 Naked Single ✓ R6C9=3
Look at cell R6C9. Every other digit already appears in its row, column or box. Only one option remains: R6C9 = 3.
39 Naked Single ✓ R7C2=7
Look at cell R7C2. Every other digit already appears in its row, column or box. Only one option remains: R7C2 = 7.
40 Naked Single ✓ R1C9=1
Look at cell R1C9. Every other digit already appears in its row, column or box. Only one option remains: R1C9 = 1.
41 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.
42 Naked Single ✓ R3C1=2
Look at cell R3C1. Every other digit already appears in its row, column or box. Only one option remains: R3C1 = 2.
43 Naked Single ✓ R3C4=1
Look at cell R3C4. Every other digit already appears in its row, column or box. Only one option remains: R3C4 = 1.
44 Naked Single ✓ R4C2=6
Look at cell R4C2. Every other digit already appears in its row, column or box. Only one option remains: R4C2 = 6.
45 Naked Single ✓ R4C8=4
Look at cell R4C8. Every other digit already appears in its row, column or box. Only one option remains: R4C8 = 4.
46 Naked Single ✓ R5C3=3
Look at cell R5C3. Every other digit already appears in its row, column or box. Only one option remains: R5C3 = 3.
47 Naked Single ✓ R5C4=4
Look at cell R5C4. Every other digit already appears in its row, column or box. Only one option remains: R5C4 = 4.
48 Naked Single ✓ R5C8=1
Look at cell R5C8. Every other digit already appears in its row, column or box. Only one option remains: R5C8 = 1.
49 Naked Single ✓ R7C1=1
Look at cell R7C1. Every other digit already appears in its row, column or box. Only one option remains: R7C1 = 1.
50 Naked Single ✓ R1C1=4
Look at cell R1C1. Every other digit already appears in its row, column or box. Only one option remains: R1C1 = 4.
51 Naked Single ✓ R1C4=2
Look at cell R1C4. Every other digit already appears in its row, column or box. Only one option remains: R1C4 = 2.
52 Naked Single ✓ R1C7=3
Look at cell R1C7. Every other digit already appears in its row, column or box. Only one option remains: R1C7 = 3.
53 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.
54 Naked Single ✓ R2C8=9
Look at cell R2C8. Every other digit already appears in its row, column or box. Only one option remains: R2C8 = 9.
55 Naked Single ✓ R3C7=6
Look at cell R3C7. Every other digit already appears in its row, column or box. Only one option remains: R3C7 = 6.
56 Naked Single ✓ R7C8=3
Look at cell R7C8. Every other digit already appears in its row, column or box. Only one option remains: R7C8 = 3.
57 Naked Single ✓ R9C7=9
Look at cell R9C7. Every other digit already appears in its row, column or box. Only one option remains: R9C7 = 9.
58 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.
59 Naked Single ✓ R2C5=6
Look at cell R2C5. Every other digit already appears in its row, column or box. Only one option remains: R2C5 = 6.
60 Naked Single ✓ R2C7=4
Look at cell R2C7. Every other digit already appears in its row, column or box. Only one option remains: R2C7 = 4.
61 Naked Single ✓ R3C5=9
Look at cell R3C5. Every other digit already appears in its row, column or box. Only one option remains: R3C5 = 9.
62 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.
63 Naked Single ✓ R4C5=3
Look at cell R4C5. Every other digit already appears in its row, column or box. Only one option remains: R4C5 = 3.
64 Naked Single ✓ R7C6=9
Look at cell R7C6. Every other digit already appears in its row, column or box. Only one option remains: R7C6 = 9.
65 Naked Single ✓ R9C6=3
Look at cell R9C6. Every other digit already appears in its row, column or box. Only one option remains: R9C6 = 3.