Step-by-step solution
Steps 67
Estimated time 108 – 162 min
Hardest technique X-Wing
Clues 22
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 6.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R4C5 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R5C5 = 2.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R6C4 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C4 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R7C5 = 1.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R7C6 = 3.
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 1 could go.
Across the whole box, 1 has only one possible spot left.
So R9C7 = 1.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 7.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 2.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R1C6 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R2C8 = 1.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R3C2 = 1.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R4C4 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C4 = 5.
Look at where 6 can go in this box.
All its spots lie on a single row (R7C7 and R7C8).
6 is therefore removed from that row outside the box.
Spot R4C7, R6C7 and R8C7 on this column.
These three cells share only 5, 8 and 9.
5, 8 and 9 are therefore removed from the rest of the column.
Spot R2C4 and R2C7 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 where 9 can go in this box.
All its spots lie on a single column (R1C9, R2C9 and R3C9).
9 is therefore removed from that column outside the box.
Find 5 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 5.
R6C3 is seen by both free ends: 5 is therefore eliminated there.
Find where 5 and 8 can go on this column.
These two digits only fit in R1C3 and R8C3 on the column.
The other candidates in R1C3 and R8C3 are therefore eliminated.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R8C8 = 3.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R9C3 = 3.
Find 8 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 8.
R7C1 and R8C7 is seen by both free ends: 8 is therefore eliminated there.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 5.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 9.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 8.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 5.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 8.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 5.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 3.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 4.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 9.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 5.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 6.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 3.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 4.
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 box where 6 could go.
Across the whole box, 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 R1C8 = 8.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R1C9 = 3.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C1 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R2C4 = 4.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R2C5 = 5.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R2C7 = 6.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C1 = 6.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R3C7 = 4.
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.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R7C8 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C9 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R9C2 = 6.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 9.
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.
R9C1 is seen by both free ends: 2 is therefore eliminated there.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 7.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 2.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 7.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 2.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 7.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 2.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 9.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 7.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 9.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 7.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 2.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 2.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 9.