Step-by-step solution
Steps 64
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 23
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 = 1.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R4C5 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R4C7 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R5C1 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R5C3 = 7.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R6C9 = 2.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R7C3 = 2.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C6 = 7.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R8C5 = 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.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 5.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 2.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 3.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C2 = 7.
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.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C4 = 7.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R4C2 = 2.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R6C3 = 1.
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 column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R7C9 = 6.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 4.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 3.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 6.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C3 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C9 = 8.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R2C3 = 3.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R2C4 = 1.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R4C1 = 3.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C6 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C8 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R6C6 = 3.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R9C5 = 6.
Spot R4C3 and R4C6 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.
Find 4 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 4.
R9C3 is seen by both free ends: 4 is therefore eliminated there.
Find where 4 appears on two rows: altogether, only two columns are involved (R6C2, R6C4, R9C2 and R9C4).
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 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.
R1C1 is seen by both free ends: 4 is therefore eliminated there.
Look at where 4 can go in this box.
All its spots lie on a single row (R3C1 and R3C3).
4 is therefore removed from that row outside the box.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R2C9 = 4.
Find 9 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 9.
R1C1, R3C1 and R9C2 is seen by both free ends: 9 is therefore eliminated there.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 1.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 4.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 9.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 4.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 8.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 9.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 9.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 5.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 4.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 9.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 5.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 9.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 9.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 6.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 4.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 4.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 9.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 5.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 9.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 8.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 1.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 6.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 5.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 4.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 5.