Sudoku Solution No. 123

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 Hidden Single ✓ R2C4=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R2C4 = 9.
2 Hidden Single ✓ R3C1=6
Scan the empty cells in this column where 6 could go. Across the whole column, 6 has only one possible spot left. So R3C1 = 6.
3 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.
4 Hidden Single ✓ R9C2=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R9C2 = 4.
5 Hidden Single ✓ R9C9=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R9C9 = 2.
6 Naked Single ✓ R9C4=3
Look at cell R9C4. Every other digit already appears in its row, column or box. Only one option remains: R9C4 = 3.
7 Naked Single ✓ R7C4=4
Look at cell R7C4. Every other digit already appears in its row, column or box. Only one option remains: R7C4 = 4.
8 Naked Single ✓ R7C7=6
Look at cell R7C7. Every other digit already appears in its row, column or box. Only one option remains: R7C7 = 6.
9 Hidden Single ✓ R4C5=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R4C5 = 5.
10 Hidden Single ✓ R6C6=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R6C6 = 4.
11 Hidden Single ✓ R7C3=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R7C3 = 3.
12 Hidden Single ✓ R7C5=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R7C5 = 9.
13 Hidden Single ✓ R8C5=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R8C5 = 1.
14 Hidden Single ✓ R8C6=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R8C6 = 5.
15 Naked Single ✓ R5C5=8
Look at cell R5C5. Every other digit already appears in its row, column or box. Only one option remains: R5C5 = 8.
16 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.
17 Hidden Single ✓ R1C2=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R1C2 = 9.
18 Hidden Single ✓ R1C3=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R1C3 = 2.
19 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.
20 Hidden Single ✓ R6C1=9
Scan the empty cells in this column where 9 could go. Across the whole column, 9 has only one possible spot left. So R6C1 = 9.
21 Hidden Single ✓ R9C8=9
Scan the empty cells in this row where 9 could go. Across the whole row, 9 has only one possible spot left. So R9C8 = 9.
22 Hidden Single ✓ R5C2=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R5C2 = 3.
23 Hidden Single ✓ R1C9=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R1C9 = 6.
24 Hidden Single ✓ R5C4=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R5C4 = 2.
25 Hidden Single ✓ R5C8=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R5C8 = 6.
26 Hidden Single ✓ R6C4=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R6C4 = 6.
27 Naked Pair ✗ 4 eliminations
(1) Spot R1C6 and R5C6 on this column. (2) Spot R1C6 and R3C4 in this box. (1) These two cells can only hold 1 and 7: they reserve those digits. (2) These two cells can only hold 1 and 7: they reserve those digits. (1) 1 and 7 are therefore removed from the other cells of the column. (2) 1 and 7 are therefore removed from the other cells of the box.
28 Skyscraper ✗ 1 elimination
Find 7 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 7. R3C3 is seen by both free ends: 7 is therefore eliminated there.
29 Hidden Single ✓ R2C1=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R2C1 = 7.
30 Naked Single ✓ R2C7=3
Look at cell R2C7. Every other digit already appears in its row, column or box. Only one option remains: R2C7 = 3.
31 Naked Single ✓ R4C1=8
Look at cell R4C1. Every other digit already appears in its row, column or box. Only one option remains: R4C1 = 8.
32 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.
33 Naked Single ✓ R9C3=8
Look at cell R9C3. Every other digit already appears in its row, column or box. Only one option remains: R9C3 = 8.
34 Naked Single ✓ R2C6=8
Look at cell R2C6. Every other digit already appears in its row, column or box. Only one option remains: R2C6 = 8.
35 Naked Single ✓ R3C6=3
Look at cell R3C6. Every other digit already appears in its row, column or box. Only one option remains: R3C6 = 3.
36 Hidden Single ✓ R3C2=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R3C2 = 8.
37 Hidden Single ✓ R4C9=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R4C9 = 3.
38 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. R4C8 is seen by both free ends: 1 is therefore eliminated there.
39 Hidden Pair ✗ 2 eliminations
Find where 1 and 8 can go in this box. These two digits only fit in R6C8 and R6C9 in the box. The other candidates in R6C8 and R6C9 are therefore eliminated.
40 Naked Pair ✗ 2 eliminations
Spot R6C8 and R6C9 on this row. These two cells can only hold 1 and 8: they reserve those digits. 1 and 8 are therefore removed from the other cells of the row.
41 Hidden Pair ✗ 2 eliminations
Find where 4 and 7 can go on this column. These two digits only fit in R3C9 and R8C9 on the column. The other candidates in R3C9 and R8C9 are therefore eliminated.
42 Skyscraper ✗ 1 elimination
Find 1 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 1. R3C3 is seen by both free ends: 1 is therefore eliminated there.
43 Naked Single ✓ R3C3=5
Look at cell R3C3. Every other digit already appears in its row, column or box. Only one option remains: R3C3 = 5.
44 Naked Single ✓ R6C3=7
Look at cell R6C3. Every other digit already appears in its row, column or box. Only one option remains: R6C3 = 7.
45 Naked Single ✓ R6C7=2
Look at cell R6C7. Every other digit already appears in its row, column or box. Only one option remains: R6C7 = 2.
46 Naked Single ✓ R2C2=1
Look at cell R2C2. Every other digit already appears in its row, column or box. Only one option remains: R2C2 = 1.
47 Naked Single ✓ R2C9=5
Look at cell R2C9. Every other digit already appears in its row, column or box. Only one option remains: R2C9 = 5.
48 Naked Single ✓ R4C2=2
Look at cell R4C2. Every other digit already appears in its row, column or box. Only one option remains: R4C2 = 2.
49 Naked Single ✓ R5C3=1
Look at cell R5C3. Every other digit already appears in its row, column or box. Only one option remains: R5C3 = 1.
50 Naked Single ✓ R5C6=7
Look at cell R5C6. Every other digit already appears in its row, column or box. Only one option remains: R5C6 = 7.
51 Naked Single ✓ R6C2=5
Look at cell R6C2. Every other digit already appears in its row, column or box. Only one option remains: R6C2 = 5.
52 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.
53 Naked Single ✓ R1C6=1
Look at cell R1C6. Every other digit already appears in its row, column or box. Only one option remains: R1C6 = 1.
54 Naked Single ✓ R1C8=7
Look at cell R1C8. Every other digit already appears in its row, column or box. Only one option remains: R1C8 = 7.
55 Naked Single ✓ R3C4=7
Look at cell R3C4. Every other digit already appears in its row, column or box. Only one option remains: R3C4 = 7.
56 Naked Single ✓ R3C9=4
Look at cell R3C9. Every other digit already appears in its row, column or box. Only one option remains: R3C9 = 4.
57 Naked Single ✓ R4C4=1
Look at cell R4C4. Every other digit already appears in its row, column or box. Only one option remains: R4C4 = 1.
58 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.
59 Naked Single ✓ R6C9=1
Look at cell R6C9. Every other digit already appears in its row, column or box. Only one option remains: R6C9 = 1.
60 Naked Single ✓ R7C8=5
Look at cell R7C8. Every other digit already appears in its row, column or box. Only one option remains: R7C8 = 5.
61 Naked Single ✓ R8C9=7
Look at cell R8C9. Every other digit already appears in its row, column or box. Only one option remains: R8C9 = 7.
62 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.
63 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.
64 Naked Single ✓ R6C8=8
Look at cell R6C8. Every other digit already appears in its row, column or box. Only one option remains: R6C8 = 8.
65 Naked Single ✓ R8C7=4
Look at cell R8C7. Every other digit already appears in its row, column or box. Only one option remains: R8C7 = 4.