Step-by-step solution
Steps 66
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 R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 9.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R1C2 = 4.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R1C8 = 7.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R2C8 = 3.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R3C7 = 9.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R3C9 = 2.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R5C4 = 4.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R6C8 = 4.
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 box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R8C3 = 3.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R9C7 = 7.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R9C9 = 5.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R4C7 = 2.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R5C3 = 2.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R7C1 = 2.
(1) Spot R8C7 and R8C8 on this row. (2) Spot R2C9 and R5C9 on this column.
(1) These two cells can only hold 1 and 6: they reserve those digits. (2) These two cells can only hold 1 and 6: they reserve those digits.
(1) 1 and 6 are therefore removed from the other cells of the row. (2) 1 and 6 are therefore removed from the other cells of the column.
Look at where 8 can go in this box.
All its spots lie on a single row (R2C1 and R2C3).
8 is therefore removed from that row outside the box.
Find where 5 appears on two rows: altogether, only two columns are involved (R5C2, R5C5, R7C2 and R7C5).
On each covered column, 5 must lie within one of these two rows.
5 is therefore removed from those two columns outside the two X-Wing rows.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 8.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R5C7 = 8.
(1) Spot R3C2 and R3C8 on this row. (2) Spot R1C1 and R3C2 in this box.
(1) These two cells can only hold 1 and 6: they reserve those digits. (2) These two cells can only hold 1 and 6: they reserve those digits.
(1) 1 and 6 are therefore removed from the other cells of the row. (2) 1 and 6 are therefore removed from the other cells of the box.
Find 1 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 1.
R5C2 is seen by both free ends: 1 is therefore eliminated there.
Find 6 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 6.
R5C2 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 5.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 8.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 9.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 5.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 2.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 4.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 4.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 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 R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 8.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R1C6 = 2.
Spot R1C4, R2C4 and R9C4 on this column.
These three cells share only 1, 3 and 9.
1, 3 and 9 are therefore removed from the rest of the column.
Find 6 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 6.
R1C5, R4C6 and R6C6 is seen by both free ends: 6 is therefore eliminated there.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C1 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C4 = 9.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R2C6 = 6.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R2C9 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R3C2 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C8 = 6.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R4C1 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R4C5 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R4C6 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C5 = 1.
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 R6C1 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R6C7 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C7 = 6.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R8C8 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R9C5 = 9.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 3.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 3.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 7.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 6.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 5.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 3.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 1.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 1.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 8.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 8.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 7.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 3.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 5.