Step-by-step solution
Steps 64
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 25
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R1C5 = 5.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R2C4 = 8.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R4C5 = 2.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R8C1 = 7.
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 column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R9C3 = 1.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 5.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 6.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 4.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 7.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 9.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 5.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R1C3 = 4.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R1C9 = 9.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R2C7 = 1.
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 box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R3C5 = 4.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R3C6 = 9.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R4C1 = 9.
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 column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R5C9 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C2 = 5.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R6C7 = 9.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R7C1 = 5.
Spot R2C9 and R7C9 on this column.
These two cells can only hold 2 and 6: they reserve those digits.
2 and 6 are therefore removed from the other cells of the column.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 7.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R1C2 = 7.
Spot R4C6 and R4C9 on this row.
These two cells can only hold 4 and 8: they reserve those digits.
4 and 8 are therefore removed from the other cells of the row.
Look at where 6 can go on this row.
All its spots lie within a single box (R3C2 and R3C3).
6 is therefore removed from the rest of 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.
R3C3 and R9C1 is seen by both free ends: 2 is therefore eliminated there.
Find where 2 appears on two rows: altogether, only two columns are involved (R3C2, R3C7, R9C2 and R9C7).
On each covered column, 2 must lie within one of these two rows.
2 is therefore removed from those two columns outside the two X-Wing rows.
Find 3 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 3.
R5C4 is seen by both free ends: 3 is therefore eliminated there.
Look at where 3 can go in this box.
All its spots lie on a single row (R6C4 and R6C5).
3 is therefore removed from that row outside the box.
Find 3 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 3.
R3C3 is seen by both free ends: 3 is therefore eliminated there.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 6.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 2.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 6.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 8.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 4.
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 R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 8.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 4.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 2.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 6.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 3.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 6.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 2.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 4.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 3.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 8.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 6.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 3.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 3.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 2.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 6.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 7.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 3.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 4.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 7.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 6.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 3.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 7.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 8.