Step-by-step solution
Steps 66
Estimated time 68 – 102 min
Hardest technique Box/Line
Clues 22
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 8.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 5.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 9.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C1 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R2C4 = 1.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R2C8 = 7.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R3C3 = 7.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R3C5 = 9.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R3C9 = 1.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R4C1 = 1.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R4C6 = 7.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R4C9 = 6.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R5C6 = 9.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R6C2 = 7.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R7C8 = 9.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C9 = 5.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C2 = 9.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R8C3 = 1.
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.
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.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R5C2 = 5.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R5C4 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R6C1 = 8.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R6C8 = 5.
(1) Spot R8C1 and R8C4 on this row. (2) Spot R9C8 and R9C9 on this row.
(1) These two cells can only hold 3 and 6: they reserve those digits. (2) These two cells can only hold 3 and 8: they reserve those digits.
(1) 3 and 6 are therefore removed from the other cells of the row. (2) 3 and 8 are therefore removed from the other cells of the row.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R7C2 = 8.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R8C5 = 8.
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.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R2C5 = 5.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R3C1 = 5.
Look at where 6 can go in this box.
All its spots lie on a single column (R7C1 and R8C1).
6 is therefore removed from that column outside the box.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 2.
Spot R7C1 and R8C1 in this box.
These two cells can only hold 3 and 6: they reserve those digits.
3 and 6 are therefore removed from the other cells of the box.
Find where 4 appears on two rows: altogether, only two columns are involved (R2C2, R2C6, R9C2 and R9C6).
On each covered column, 4 must lie within one of these two rows.
4 is therefore removed from those two columns outside the two X-Wing rows.
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.
R7C5 is seen by both free ends: 2 is therefore eliminated there.
Look at where 2 can go in this box.
All its spots lie on a single column (R7C6 and R9C6).
2 is therefore removed from that column outside the box.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R1C4 = 2.
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.
R6C4 is seen by both free ends: 4 is therefore eliminated there.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 3.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 6.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 4.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 8.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 3.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 3.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 8.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 4.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 6.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 3.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 4.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 2.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 6.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 2.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 4.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 3.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 8.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 4.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 6.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 2.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 2.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 3.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 4.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 4.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 3.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 2.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 3.