Sudoku Solution No. 43

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 (✗ RlCc≠d)
1 Naked Single ✓ R6C3=6
Look at cell R6C3. Every other digit already appears in its row, column or box. Only one option remains: R6C3 = 6.
2 Naked Single ✓ R6C1=9
Look at cell R6C1. Every other digit already appears in its row, column or box. Only one option remains: R6C1 = 9.
3 Hidden Single ✓ R1C2=9
Scan the empty cells in this column where 9 could go. Across the whole column, 9 has only one possible spot left. So R1C2 = 9.
4 Hidden Single ✓ R1C4=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R1C4 = 4.
5 Hidden Single ✓ R1C5=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R1C5 = 8.
6 Hidden Single ✓ R2C4=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R2C4 = 6.
7 Hidden Single ✓ R4C2=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R4C2 = 7.
8 Hidden Single ✓ R5C2=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R5C2 = 4.
9 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.
10 Hidden Single ✓ R5C9=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R5C9 = 6.
11 Hidden Single ✓ R6C6=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R6C6 = 8.
12 Hidden Single ✓ R7C1=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R7C1 = 4.
13 Hidden Single ✓ R8C1=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R8C1 = 6.
14 Hidden Single ✓ R8C2=8
Scan the empty cells in this column where 8 could go. Across the whole column, 8 has only one possible spot left. So R8C2 = 8.
15 Hidden Single ✓ R9C6=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R9C6 = 6.
16 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.
17 Naked Single ✓ R6C4=7
Look at cell R6C4. Every other digit already appears in its row, column or box. Only one option remains: R6C4 = 7.
18 Hidden Single ✓ R4C4=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R4C4 = 3.
19 Hidden Single ✓ R5C8=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R5C8 = 2.
20 Hidden Single ✓ R7C3=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R7C3 = 1.
21 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.
22 Hidden Single ✓ R5C5=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R5C5 = 1.
23 Naked Pair ✗ 4 eliminations
Spot R3C5 and R7C5 on this column. These two cells can only hold 3 and 7: they reserve those digits. 3 and 7 are therefore removed from the other cells of the column.
24 Naked Single ✓ R8C4=9
Look at cell R8C4. Every other digit already appears in its row, column or box. Only one option remains: R8C4 = 9.
25 Naked Single ✓ R8C8=4
Look at cell R8C8. Every other digit already appears in its row, column or box. Only one option remains: R8C8 = 4.
26 Naked Single ✓ R9C8=1
Look at cell R9C8. Every other digit already appears in its row, column or box. Only one option remains: R9C8 = 1.
27 Naked Single ✓ R2C8=8
Look at cell R2C8. Every other digit already appears in its row, column or box. Only one option remains: R2C8 = 8.
28 Naked Single ✓ R4C8=9
Look at cell R4C8. Every other digit already appears in its row, column or box. Only one option remains: R4C8 = 9.
29 Naked Single ✓ R5C4=5
Look at cell R5C4. Every other digit already appears in its row, column or box. Only one option remains: R5C4 = 5.
30 Naked Single ✓ R5C6=9
Look at cell R5C6. Every other digit already appears in its row, column or box. Only one option remains: R5C6 = 9.
31 Naked Single ✓ R8C5=5
Look at cell R8C5. Every other digit already appears in its row, column or box. Only one option remains: R8C5 = 5.
32 Naked Single ✓ R9C5=4
Look at cell R9C5. Every other digit already appears in its row, column or box. Only one option remains: R9C5 = 4.
33 Hidden Single ✓ R2C9=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R2C9 = 4.
34 Hidden Single ✓ R8C9=7
Scan the empty cells in this row where 7 could go. Across the whole row, 7 has only one possible spot left. So R8C9 = 7.
35 Hidden Single ✓ R9C7=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R9C7 = 5.
36 Naked Pair ✗ 2 eliminations
(1) Spot R7C5 and R7C6 on this row. (2) Spot R8C7 and R9C9 in this box. (1) These two cells can only hold 3 and 7: they reserve those digits. (2) These two cells can only hold 2 and 3: they reserve those digits. (1) 3 and 7 are therefore removed from the other cells of the row. (2) 2 and 3 are therefore removed from the other cells of the box.
37 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. R2C7 is seen by both free ends: 2 is therefore eliminated there.
38 Two-String Kite ✗ 1 elimination
Find 3 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 3. R2C7 is seen by both free ends: 3 is therefore eliminated there.
39 Naked Single ✓ R2C7=1
Look at cell R2C7. Every other digit already appears in its row, column or box. Only one option remains: R2C7 = 1.
40 Naked Single ✓ R4C7=8
Look at cell R4C7. Every other digit already appears in its row, column or box. Only one option remains: R4C7 = 8.
41 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.
42 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.
43 Naked Single ✓ R7C9=8
Look at cell R7C9. Every other digit already appears in its row, column or box. Only one option remains: R7C9 = 8.
44 Hidden Single ✓ R1C1=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R1C1 = 1.
45 Hidden Single ✓ R3C9=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R3C9 = 9.
46 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. R1C3 is seen by both free ends: 2 is therefore eliminated there.
47 Pointing ✗ 1 elimination
Look at where 2 can go in this box. All its spots lie on a single row (R2C1 and R2C2). 2 is therefore removed from that row outside the box.
48 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. R1C3 is seen by both free ends: 3 is therefore eliminated there.
49 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.
50 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.
51 Naked Single ✓ R2C2=3
Look at cell R2C2. Every other digit already appears in its row, column or box. Only one option remains: R2C2 = 3.
52 Naked Single ✓ R2C6=5
Look at cell R2C6. Every other digit already appears in its row, column or box. Only one option remains: R2C6 = 5.
53 Naked Single ✓ R4C1=5
Look at cell R4C1. Every other digit already appears in its row, column or box. Only one option remains: R4C1 = 5.
54 Naked Single ✓ R4C3=2
Look at cell R4C3. Every other digit already appears in its row, column or box. Only one option remains: R4C3 = 2.
55 Naked Single ✓ R8C3=3
Look at cell R8C3. Every other digit already appears in its row, column or box. Only one option remains: R8C3 = 3.
56 Naked Single ✓ R8C7=2
Look at cell R8C7. Every other digit already appears in its row, column or box. Only one option remains: R8C7 = 2.
57 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.
58 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.
59 Naked Single ✓ R1C9=2
Look at cell R1C9. Every other digit already appears in its row, column or box. Only one option remains: R1C9 = 2.
60 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.
61 Naked Single ✓ R1C6=3
Look at cell R1C6. Every other digit already appears in its row, column or box. Only one option remains: R1C6 = 3.
62 Naked Single ✓ R3C5=7
Look at cell R3C5. Every other digit already appears in its row, column or box. Only one option remains: R3C5 = 7.
63 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.
64 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.
65 Naked Single ✓ R7C6=7
Look at cell R7C6. Every other digit already appears in its row, column or box. Only one option remains: R7C6 = 7.