Step-by-step solution
Steps 67
Estimated time 108 – 162 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 8 could go.
Across the whole column, 8 has only one possible spot left.
So R1C8 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C9 = 4.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R2C5 = 8.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C9 = 9.
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 column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R4C7 = 1.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C4 = 8.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R7C7 = 4.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R8C5 = 2.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R8C9 = 1.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 3.
Spot R8C1 and R9C2 in this box.
These two cells can only hold 5 and 6: they reserve those digits.
5 and 6 are therefore removed from the other cells of the box.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 9.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 7.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R9C8 = 9.
Spot R4C8 and R5C8 in this box.
These two cells can only hold 3 and 4: they reserve those digits.
3 and 4 are therefore removed from the other cells of the box.
(1) Spot R6C2 and R6C9 on this row. (2) Spot R5C9 and R6C9 on this column.
(1) These two cells can only hold 5 and 7: they reserve those digits. (2) These two cells can only hold 5 and 7: they reserve those digits.
(1) 5 and 7 are therefore removed from the other cells of the row. (2) 5 and 7 are therefore removed from the other cells of the column.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 8.
Look at where 6 can go in this box.
All its spots lie on a single row (R1C4, R1C5 and R1C6).
6 is therefore removed from that row 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.
R5C2 is seen by both free ends: 5 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.
R5C6 is seen by both free ends: 6 is therefore eliminated there.
Spot R5C6 and R5C9 on this row.
These two cells can only hold 5 and 7: they reserve those digits.
5 and 7 are therefore removed from the other cells of the row.
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.
R4C1 is seen by both free ends: 5 is therefore eliminated there.
Find 5 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 5.
R6C2 is seen by both free ends: 5 is therefore eliminated there.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 7.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 5.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 7.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 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 R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 7.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 5.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 7.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 5.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 6.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 2.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 5.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R2C7 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C1 = 7.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R3C7 = 5.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R4C3 = 5.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R4C5 = 7.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 6.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 2.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R1C5 = 6.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C1 = 3.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R4C4 = 6.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R4C8 = 4.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R5C1 = 8.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R5C3 = 6.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C4 = 1.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R5C5 = 4.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C8 = 3.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R6C1 = 1.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R6C3 = 4.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R6C4 = 3.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R6C5 = 9.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R9C1 = 4.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C3 = 8.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 2.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 3.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 9.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 1.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 2.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 2.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 3.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 1.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 3.