Sudoku Solution No. 71

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 ✓ R6C4=9
Look at cell R6C4. Every other digit already appears in its row, column or box. Only one option remains: R6C4 = 9.
2 Naked Single ✓ R1C4=6
Look at cell R1C4. Every other digit already appears in its row, column or box. Only one option remains: R1C4 = 6.
3 Naked Single ✓ R6C1=1
Look at cell R6C1. Every other digit already appears in its row, column or box. Only one option remains: R6C1 = 1.
4 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.
5 Hidden Single ✓ R1C2=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R1C2 = 1.
6 Hidden Single ✓ R1C8=5
Scan the empty cells in this column where 5 could go. Across the whole column, 5 has only one possible spot left. So R1C8 = 5.
7 Hidden Single ✓ R3C3=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R3C3 = 8.
8 Hidden Single ✓ R4C6=1
Scan the empty cells in this column where 1 could go. Across the whole column, 1 has only one possible spot left. So R4C6 = 1.
9 Hidden Single ✓ R5C2=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R5C2 = 8.
10 Hidden Single ✓ R5C9=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R5C9 = 1.
11 Hidden Single ✓ R6C7=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R6C7 = 8.
12 Hidden Single ✓ R7C2=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R7C2 = 5.
13 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.
14 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.
15 Hidden Single ✓ R9C2=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R9C2 = 7.
16 Hidden Single ✓ R9C5=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R9C5 = 1.
17 Hidden Single ✓ R9C8=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R9C8 = 8.
18 Naked Single ✓ R6C8=3
Look at cell R6C8. Every other digit already appears in its row, column or box. Only one option remains: R6C8 = 3.
19 Hidden Single ✓ R1C7=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R1C7 = 4.
20 Hidden Single ✓ R4C8=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R4C8 = 4.
21 Hidden Single ✓ R7C9=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R7C9 = 4.
22 Hidden Single ✓ R8C9=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R8C9 = 3.
23 Box/Line ✗ 1 elimination
Look at where 2 can go on this row. All its spots lie within a single box (R9C1 and R9C3). 2 is therefore removed from the rest of the box.
24 Naked Triple ✗ 9 eliminations
(1) Spot R3C2, R3C7 and R3C9 on this row. (2) Spot R1C3, R2C2 and R3C2 in this box. (1) These three cells share only 3, 6 and 7. (2) These three cells share only 3, 6 and 9. (1) 3, 6 and 7 are therefore removed from the rest of the row. (2) 3, 6 and 9 are therefore removed from the rest of the box.
25 Pointing ✗ 2 eliminations
(1) Look at where 6 can go in this box. (2) Look at where 7 can go in this box. (1) All its spots lie on a single column (R2C2 and R3C2). (2) All its spots lie on a single row (R2C4, R2C5 and R2C6). (1) 6 is therefore removed from that column outside the box. (2) 7 is therefore removed from that row outside the box.
26 Two-String Kite ✗ 1 elimination
Find 9 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 9. R9C1 is seen by both free ends: 9 is therefore eliminated there.
27 Pointing ✗ 2 eliminations
Look at where 9 can go in this box. All its spots lie on a single column (R8C3 and R9C3). 9 is therefore removed from that column outside the box.
28 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.
29 Naked Single ✓ R1C5=9
Look at cell R1C5. Every other digit already appears in its row, column or box. Only one option remains: R1C5 = 9.
30 Naked Single ✓ R3C2=6
Look at cell R3C2. Every other digit already appears in its row, column or box. Only one option remains: R3C2 = 6.
31 Naked Single ✓ R3C9=7
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 7.
32 Naked Single ✓ R2C2=9
Look at cell R2C2. Every other digit already appears in its row, column or box. Only one option remains: R2C2 = 9.
33 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.
34 Naked Single ✓ R4C2=3
Look at cell R4C2. Every other digit already appears in its row, column or box. Only one option remains: R4C2 = 3.
35 Naked Single ✓ R2C7=6
Look at cell R2C7. Every other digit already appears in its row, column or box. Only one option remains: R2C7 = 6.
36 Hidden Single ✓ R2C5=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R2C5 = 3.
37 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.
38 Hidden Single ✓ R7C5=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R7C5 = 6.
39 Hidden Pair ✗ 1 elimination
Find where 2 and 7 can go on this row. These two digits only fit in R4C4 and R4C7 on the row. The other candidates in R4C4 and R4C7 are therefore eliminated.
40 X-Wing ✗ 2 eliminations
Find where 2 appears on two columns: altogether, only two rows are involved (R5C5, R8C5, R5C8 and R8C8). On each covered row, 2 must lie within one of these two columns. 2 is therefore removed from those two rows outside the two X-Wing columns.
41 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. R4C3 and R9C1 is seen by both free ends: 6 is therefore eliminated there.
42 Naked Single ✓ R4C3=5
Look at cell R4C3. Every other digit already appears in its row, column or box. Only one option remains: R4C3 = 5.
43 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.
44 Naked Single ✓ R2C3=2
Look at cell R2C3. Every other digit already appears in its row, column or box. Only one option remains: R2C3 = 2.
45 Naked Single ✓ R2C4=7
Look at cell R2C4. Every other digit already appears in its row, column or box. Only one option remains: R2C4 = 7.
46 Naked Single ✓ R2C6=4
Look at cell R2C6. Every other digit already appears in its row, column or box. Only one option remains: R2C6 = 4.
47 Naked Single ✓ R3C1=4
Look at cell R3C1. Every other digit already appears in its row, column or box. Only one option remains: R3C1 = 4.
48 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.
49 Naked Single ✓ R4C4=2
Look at cell R4C4. Every other digit already appears in its row, column or box. Only one option remains: R4C4 = 2.
50 Naked Single ✓ R4C7=7
Look at cell R4C7. Every other digit already appears in its row, column or box. Only one option remains: R4C7 = 7.
51 Naked Single ✓ R5C5=7
Look at cell R5C5. Every other digit already appears in its row, column or box. Only one option remains: R5C5 = 7.
52 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.
53 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.
54 Naked Single ✓ R7C7=2
Look at cell R7C7. Every other digit already appears in its row, column or box. Only one option remains: R7C7 = 2.
55 Naked Single ✓ R8C5=2
Look at cell R8C5. Every other digit already appears in its row, column or box. Only one option remains: R8C5 = 2.
56 Naked Single ✓ R8C6=7
Look at cell R8C6. Every other digit already appears in its row, column or box. Only one option remains: R8C6 = 7.
57 Naked Single ✓ R8C8=6
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 6.
58 Naked Single ✓ R9C9=9
Look at cell R9C9. Every other digit already appears in its row, column or box. Only one option remains: R9C9 = 9.
59 Naked Single ✓ R2C1=5
Look at cell R2C1. Every other digit already appears in its row, column or box. Only one option remains: R2C1 = 5.
60 Naked Single ✓ R4C9=6
Look at cell R4C9. Every other digit already appears in its row, column or box. Only one option remains: R4C9 = 6.
61 Naked Single ✓ R5C1=6
Look at cell R5C1. Every other digit already appears in its row, column or box. Only one option remains: R5C1 = 6.
62 Naked Single ✓ R5C8=2
Look at cell R5C8. Every other digit already appears in its row, column or box. Only one option remains: R5C8 = 2.
63 Naked Single ✓ R8C3=9
Look at cell R8C3. Every other digit already appears in its row, column or box. Only one option remains: R8C3 = 9.
64 Naked Single ✓ R9C3=6
Look at cell R9C3. Every other digit already appears in its row, column or box. Only one option remains: R9C3 = 6.
65 Naked Single ✓ R4C1=9
Look at cell R4C1. Every other digit already appears in its row, column or box. Only one option remains: R4C1 = 9.