Step-by-step solution
Steps 67
Estimated time 108 – 162 min
Hardest technique X-Wing
Clues 23
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 4.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 5.
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 1 could go.
Across the whole box, 1 has only one possible spot left.
So R1C1 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R1C4 = 6.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R2C4 = 7.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R2C7 = 5.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C1 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C2 = 9.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R3C5 = 5.
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.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R4C7 = 6.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R5C1 = 3.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R5C3 = 6.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R5C4 = 1.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C9 = 5.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R6C2 = 5.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R6C9 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R8C5 = 3.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R9C1 = 5.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 7.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R1C7 = 7.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R2C2 = 3.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R7C1 = 7.
Spot R7C7 and R7C9 on this row.
These two cells can only hold 3 and 9: they reserve those digits.
3 and 9 are therefore removed from the other cells of the row.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R9C4 = 9.
Spot R9C5 and R9C6 in this box.
These two cells can only hold 4 and 7: they reserve those digits.
4 and 7 are therefore removed from the other cells of the box.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C9 = 4.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R3C4 = 4.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R1C6 = 3.
Find 2 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 2.
R5C6 is seen by both free ends: 2 is therefore eliminated there.
Find 2 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 2.
R4C2 is seen by both free ends: 2 is therefore eliminated there.
Find 8 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 8.
R5C6 is seen by both free ends: 8 is therefore eliminated there.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 4.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 7.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 4.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R4C5 = 7.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R6C7 = 4.
Look at where 2 can go in this box.
All its spots lie on a single row (R5C7 and R5C8).
2 is therefore removed from that row outside the box.
Find where 8 appears on two columns: altogether, only two rows are involved (R3C6, R4C6, R3C9 and R4C9).
On each covered row, 8 must lie within one of these two columns.
8 is therefore removed from those two rows outside the two X-Wing columns.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 4.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R2C1 = 4.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R7C3 = 4.
Look at where 8 can go in this box.
All its spots lie on a single row (R6C1 and R6C3).
8 is therefore removed from that row outside the box.
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.
R1C2 is seen by both free ends: 2 is therefore eliminated there.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 8.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 2.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 2.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 8.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 8.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 3.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 2.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 2.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 8.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 9.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 2.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 8.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 9.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 8.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 2.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 2.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 9.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 8.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 8.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 9.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 2.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 3.