Step-by-step solution
Steps 68
Estimated time 112 – 168 min
Hardest technique X-Wing
Clues 23
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R1C2 = 6.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R1C5 = 3.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R2C1 = 1.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R2C4 = 9.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R3C7 = 9.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R4C2 = 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 row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R5C7 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R6C1 = 3.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R6C3 = 5.
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 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C1 = 9.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R8C2 = 1.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R9C9 = 9.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 7.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R3C5 = 5.
Spot R5C6 and R9C6 on this column.
These two cells can only hold 5 and 8: they reserve those digits.
5 and 8 are therefore removed from the other cells of the column.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 2.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 8.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 8.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 7.
Spot R8C6 and R8C7 on this row.
These two cells can only hold 4 and 6: they reserve those digits.
4 and 6 are therefore removed from the other cells of the row.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 2.
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 R5C2 = 7.
(1) Spot R7C5 and R7C9 on this row. (2) Spot R8C3 and R9C3 on this column. (3) Spot R8C3 and R9C3 in this box. (4) Spot R7C9 and R8C7 in this box.
(1) These two cells can only hold 4 and 6: they reserve those digits. (2) These two cells can only hold 3 and 8: they reserve those digits. (3) These two cells can only hold 3 and 8: they reserve those digits. (4) These two cells can only hold 4 and 6: they reserve those digits.
(1) 4 and 6 are therefore removed from the other cells of the row. (2) 3 and 8 are therefore removed from the other cells of the column. (3) 3 and 8 are therefore removed from the other cells of the box. (4) 4 and 6 are therefore removed from the other cells of the box.
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.
R6C9 is seen by both free ends: 4 is therefore eliminated there.
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.
R4C7 is seen by both free ends: 4 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.
R6C9 is seen by both free ends: 6 is therefore eliminated there.
Spot R6C2 and R6C9 on this row.
These two cells can only hold 2 and 8: they reserve those digits.
2 and 8 are therefore removed from the other cells of the row.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 7.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R4C8 = 7.
Look at where 2 can go in this box.
All its spots lie on a single column (R4C9 and R6C9).
2 is therefore removed from that column outside the box.
Find where 4 appears on two rows: altogether, only two columns are involved (R4C5, R4C9, R7C5 and R7C9).
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 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.
R4C7 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 5.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 8.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 2.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 8.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 5.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 8.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 3.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 8.
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 = 4.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 2.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 6.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 7.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 2.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 1.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 3.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 8.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 3.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 5.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 1.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 4.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 6.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 2.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 5.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 8.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 7.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 4.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 4.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 6.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 6.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 4.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 6.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 4.