Sudoku Solution No. 13

Hard Score 71 / 100
Digits appear one by one.

Step-by-step solution

Steps 66 Estimated time 68 – 102 min Hardest technique Box/Line Clues 23
Given digit (clue) Solved digit Placement (✓ RlCc=d) Elimination (✗ RlCc≠d)
1 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.
2 Hidden Single ✓ R3C5=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R3C5 = 6.
3 Hidden Single ✓ R3C6=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R3C6 = 5.
4 Hidden Single ✓ R4C5=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R4C5 = 2.
5 Hidden Single ✓ R6C3=3
Scan the empty cells in this row where 3 could go. Across the whole row, 3 has only one possible spot left. So R6C3 = 3.
6 Hidden Single ✓ R7C9=5
Scan the empty cells in this row where 5 could go. Across the whole row, 5 has only one possible spot left. So R7C9 = 5.
7 Hidden Single ✓ R8C7=2
Scan the empty cells in this row where 2 could go. Across the whole row, 2 has only one possible spot left. So R8C7 = 2.
8 Hidden Single ✓ R5C2=6
Scan the empty cells in this row where 6 could go. Across the whole row, 6 has only one possible spot left. So R5C2 = 6.
9 Hidden Single ✓ R5C5=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R5C5 = 7.
10 Hidden Single ✓ R7C3=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R7C3 = 6.
11 Naked Pair ✗ 9 eliminations
(1) Spot R4C4 and R6C4 on this column. (2) Spot R4C4 and R6C4 in this box. (1) These two cells can only hold 4 and 9: they reserve those digits. (2) These two cells can only hold 4 and 9: they reserve those digits. (1) 4 and 9 are therefore removed from the other cells of the column. (2) 4 and 9 are therefore removed from the other cells of the box.
12 Naked Pair ✗ 2 eliminations
Spot R4C6 and R6C6 on this column. These two cells can only hold 1 and 6: they reserve those digits. 1 and 6 are therefore removed from the other cells of the column.
13 Hidden Pair ✗ 5 eliminations
(1) Find where 5 and 6 can go on this column. (2) Find where 5 and 6 can go in this box. (1) These two digits only fit in R4C8 and R6C8 on the column. (2) These two digits only fit in R4C8 and R6C8 in the box. (1) The other candidates in R4C8 and R6C8 are therefore eliminated. (2) The other candidates in R4C8 and R6C8 are therefore eliminated.
14 Hidden Single ✓ R5C7=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R5C7 = 8.
15 Hidden Single ✓ R1C1=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R1C1 = 3.
16 Hidden Single ✓ R1C2=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R1C2 = 5.
17 Hidden Single ✓ R2C6=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R2C6 = 7.
18 Hidden Single ✓ R2C8=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R2C8 = 3.
19 Hidden Single ✓ R3C4=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R3C4 = 3.
20 Hidden Single ✓ R4C1=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R4C1 = 5.
21 Hidden Single ✓ R4C3=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R4C3 = 8.
22 Hidden Single ✓ R4C8=6
Scan the empty cells in this box where 6 could go. Across the whole box, 6 has only one possible spot left. So R4C8 = 6.
23 Hidden Single ✓ R6C8=5
Scan the empty cells in this box where 5 could go. Across the whole box, 5 has only one possible spot left. So R6C8 = 5.
24 Hidden Single ✓ R7C4=8
Scan the empty cells in this row where 8 could go. Across the whole row, 8 has only one possible spot left. So R7C4 = 8.
25 Hidden Single ✓ R7C5=3
Scan the empty cells in this box where 3 could go. Across the whole box, 3 has only one possible spot left. So R7C5 = 3.
26 Hidden Single ✓ R8C4=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R8C4 = 7.
27 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.
28 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.
29 Naked Single ✓ R4C6=1
Look at cell R4C6. Every other digit already appears in its row, column or box. Only one option remains: R4C6 = 1.
30 Naked Single ✓ R6C6=6
Look at cell R6C6. Every other digit already appears in its row, column or box. Only one option remains: R6C6 = 6.
31 Hidden Single ✓ R4C2=7
Scan the empty cells in this row where 7 could go. Across the whole row, 7 has only one possible spot left. So R4C2 = 7.
32 Hidden Single ✓ R9C2=2
Scan the empty cells in this column where 2 could go. Across the whole column, 2 has only one possible spot left. So R9C2 = 2.
33 Naked Pair ✗ 3 eliminations
Spot R2C3 and R9C3 on this column. These two cells can only hold 1 and 4: they reserve those digits. 1 and 4 are therefore removed from the other cells of the column.
34 Pointing ✗ 1 elimination
Look at where 1 can go in this box. All its spots lie on a single row (R3C7, R3C8 and R3C9). 1 is therefore removed from that row outside the box.
35 X-Wing ✗ 3 eliminations
Find where 1 appears on two rows: altogether, only two columns are involved (R6C2, R6C7, R7C2 and R7C7). On each covered column, 1 must lie within one of these two rows. 1 is therefore removed from those two columns outside the two X-Wing rows.
36 Hidden Single ✓ R2C3=1
Scan the empty cells in this row where 1 could go. Across the whole row, 1 has only one possible spot left. So R2C3 = 1.
37 Hidden Single ✓ R8C6=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R8C6 = 4.
38 Hidden Single ✓ R9C3=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R9C3 = 4.
39 Hidden Single ✓ R9C6=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R9C6 = 9.
40 Naked Single ✓ R9C7=7
Look at cell R9C7. Every other digit already appears in its row, column or box. Only one option remains: R9C7 = 7.
41 Naked Pair ✗ 3 eliminations
Spot R3C1 and R3C7 on this row. 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 row.
42 Skyscraper ✗ 2 eliminations
Find 4 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 4. R1C9 and R6C7 is seen by both free ends: 4 is therefore eliminated there.
43 Hidden Single ✓ R1C5=4
Scan the empty cells in this row where 4 could go. Across the whole row, 4 has only one possible spot left. So R1C5 = 4.
44 Hidden Single ✓ R1C8=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R1C8 = 7.
45 Hidden Single ✓ R1C9=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R1C9 = 9.
46 Hidden Single ✓ R2C2=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R2C2 = 4.
47 Hidden Single ✓ R2C5=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R2C5 = 9.
48 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.
49 Hidden Single ✓ R3C3=7
Scan the empty cells in this box where 7 could go. Across the whole box, 7 has only one possible spot left. So R3C3 = 7.
50 Hidden Single ✓ R3C7=4
Scan the empty cells in this column where 4 could go. Across the whole column, 4 has only one possible spot left. So R3C7 = 4.
51 Hidden Single ✓ R3C8=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R3C8 = 1.
52 Hidden Single ✓ R3C9=2
Scan the empty cells in this box where 2 could go. Across the whole box, 2 has only one possible spot left. So R3C9 = 2.
53 Hidden Single ✓ R4C4=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R4C4 = 9.
54 Hidden Single ✓ R4C9=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R4C9 = 4.
55 Hidden Single ✓ R5C1=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R5C1 = 4.
56 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.
57 Hidden Single ✓ R6C2=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R6C2 = 1.
58 Hidden Single ✓ R6C4=4
Scan the empty cells in this box where 4 could go. Across the whole box, 4 has only one possible spot left. So R6C4 = 4.
59 Hidden Single ✓ R6C7=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R6C7 = 9.
60 Hidden Single ✓ R7C2=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R7C2 = 9.
61 Hidden Single ✓ R7C7=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R7C7 = 1.
62 Hidden Single ✓ R8C1=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R8C1 = 8.
63 Hidden Single ✓ R8C8=9
Scan the empty cells in this box where 9 could go. Across the whole box, 9 has only one possible spot left. So R8C8 = 9.
64 Hidden Single ✓ R9C1=1
Scan the empty cells in this box where 1 could go. Across the whole box, 1 has only one possible spot left. So R9C1 = 1.
65 Hidden Single ✓ R9C8=8
Scan the empty cells in this box where 8 could go. Across the whole box, 8 has only one possible spot left. So R9C8 = 8.
66 Naked Single ✓ R1C3=2
Look at cell R1C3. Every other digit already appears in its row, column or box. Only one option remains: R1C3 = 2.