Step-by-step solution
Steps 65
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 R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 4.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 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 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 box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R3C1 = 5.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R3C5 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C6 = 7.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R4C2 = 5.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R4C8 = 7.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R5C2 = 4.
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.
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.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R7C2 = 7.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 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 R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 4.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R1C1 = 1.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C4 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C8 = 8.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R3C4 = 1.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R4C5 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C4 = 3.
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.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C5 = 6.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R6C8 = 3.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R7C4 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C7 = 8.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R7C8 = 4.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R9C5 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C7 = 5.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 2.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R2C7 = 1.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R7C9 = 1.
Spot R1C2 and R1C3 in this box.
These two cells can only hold 8 and 9: they reserve those digits.
8 and 9 are therefore removed from the other cells of the box.
Look at where 6 can go on this row.
All its spots lie within a single box (R8C7 and R8C8).
6 is therefore removed from the rest of the box.
Spot R2C9 and R9C9 on this column.
These two cells can only hold 2 and 3: they reserve those digits.
2 and 3 are therefore removed from the other cells of the column.
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.
R8C3 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.
R9C2 is seen by both free ends: 2 is therefore eliminated there.
Find where 2 appears on two columns: altogether, only two rows are involved (R3C2, R8C2, R3C8 and R8C8).
On each covered row, 2 must lie within one of these two columns.
2 is therefore removed from those two rows outside the two X-Wing columns.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 5.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 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 = 3.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 6.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 5.
Find 3 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 3.
R3C2 and R8C3 is seen by both free ends: 3 is therefore eliminated there.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 2.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 6.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 9.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 6.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 9.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 2.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 3.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 8.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 3.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 2.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 3.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 2.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 9.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 3.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 6.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 8.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 9.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 8.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 2.