Step-by-step solution
Steps 65
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 22
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 5.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 4.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 8.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 6.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R1C4 = 2.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R1C6 = 6.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R3C4 = 4.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R4C1 = 4.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R5C5 = 9.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R7C4 = 6.
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.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R8C2 = 1.
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.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R1C3 = 4.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C5 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C3 = 8.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C4 = 5.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R2C5 = 1.
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.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R3C3 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R3C5 = 3.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R4C6 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R5C6 = 2.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R5C9 = 6.
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.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R6C9 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C8 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C4 = 8.
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.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R4C8 = 2.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R6C2 = 6.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R6C3 = 2.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R7C1 = 2.
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.
Find where 3 appears on two rows: altogether, only two columns are involved (R2C1, R2C9, R8C1 and R8C9).
On each covered column, 3 must lie within one of these two rows.
3 is therefore removed from those two columns outside the two X-Wing rows.
Find 5 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 5.
R1C9 and R5C8 is seen by both free ends: 5 is therefore eliminated there.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R4C9 = 5.
Look at where 5 can go on this column.
All its spots lie within a single box (R1C2 and R3C2).
5 is therefore removed from the rest of the box.
Spot R1C1 and R1C9 on this row.
These two cells can only hold 7 and 9: they reserve those digits.
7 and 9 are therefore removed from the other cells of the row.
Find 7 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 7.
R5C8 is seen by both free ends: 7 is therefore eliminated there.
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.
R4C7 is seen by both free ends: 7 is therefore eliminated there.
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 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C9 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C9 = 9.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C2 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R5C1 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R6C8 = 7.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R7C7 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C5 = 7.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R8C9 = 3.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 3.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 5.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 3.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 1.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 5.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 3.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 3.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 3.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 5.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 5.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 5.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 3.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 1.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 7.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 1.