Step-by-step solution
Steps 65
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 24
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
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 row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R2C9 = 5.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R3C6 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R4C5 = 4.
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 row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R6C3 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C7 = 5.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R9C8 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R1C4 = 2.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C6 = 8.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R5C5 = 1.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C6 = 5.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R6C2 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C1 = 5.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C3 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R9C4 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C5 = 5.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 2.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 6.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R2C1 = 4.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R3C1 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R3C3 = 2.
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 box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C9 = 2.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R8C9 = 4.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R9C1 = 2.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R9C3 = 4.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R2C3 = 3.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R7C2 = 9.
Look at where 3 can go on this column.
All its spots lie within a single box (R1C8 and R3C8).
3 is therefore removed from the rest 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.
R3C8 is seen by both free ends: 1 is therefore eliminated there.
Find where 1 appears on two rows: altogether, only two columns are involved (R3C2, R3C9, R9C2 and R9C9).
On each covered column, 1 must lie within one of these two rows.
1 is therefore removed from those two columns outside the two X-Wing rows.
Find where 1 and 9 can go on this column.
These two digits only fit in R3C9 and R9C9 on the column.
The other candidates in R3C9 and R9C9 are therefore eliminated.
Look at where 3 can go in this box.
All its spots lie on a single column (R8C7 and R9C7).
3 is therefore removed from that column outside the box.
Spot R5C3 and R5C7 on this row.
These two cells can only hold 6 and 7: they reserve those digits.
6 and 7 are therefore removed from the other cells of the row.
Find where 7 appears on two columns: altogether, only two rows are involved (R1C1, R4C1, R1C9 and R4C9).
On each covered row, 7 must lie within one of these two columns.
7 is therefore removed from those two rows outside the two X-Wing columns.
Find 7 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 7.
R8C7 is seen by both free ends: 7 is therefore eliminated there.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 3.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 9.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 1.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 9.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 7.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 7.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 3.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 6.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 7.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 1.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 3.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 1.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 7.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 1.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 6.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 6.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 7.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 1.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 6.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 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 R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 7.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 8.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 6.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 3.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 6.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 8.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 3.