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)
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 row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R1C1 = 4.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R3C6 = 3.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R3C7 = 4.
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 R5C7 = 3.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R6C2 = 3.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R7C6 = 8.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R7C8 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C4 = 4.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R8C5 = 1.
(1) Find where 5 and 9 can go on this column. (2) Find where 5 and 6 can go in this box.
(1) These two digits only fit in R5C6 and R6C6 on the column. (2) These two digits only fit in R2C5 and R3C5 in the box.
(1) The other candidates in R5C6 and R6C6 are therefore eliminated. (2) The other candidates in R2C5 and R3C5 are therefore eliminated.
(1) Spot R6C6 and R6C7 on this row. (2) Spot R2C5 and R3C5 on this column. (3) Spot R5C6 and R6C6 in this box.
(1) These two cells can only hold 5 and 9: they reserve those digits. (2) These two cells can only hold 5 and 6: they reserve those digits. (3) These two cells can only hold 5 and 9: they reserve those digits.
(1) 5 and 9 are therefore removed from the other cells of the row. (2) 5 and 6 are therefore removed from the other cells of the column. (3) 5 and 9 are therefore removed from the other cells of the box.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 1.
Spot R5C3 and R5C6 on this row.
These two cells can only hold 5 and 9: they reserve those digits.
5 and 9 are therefore removed from the other cells of the row.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 6.
Look at where 2 can go in this box.
All its spots lie on a single column (R4C5 and R6C5).
2 is therefore removed from that column outside the box.
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.
R2C8, R3C8 and R5C9 is seen by both free ends: 8 is therefore eliminated there.
Spot R5C9 and R7C9 on this column.
These two cells can only hold 1 and 7: they reserve those digits.
1 and 7 are therefore removed from the other cells of the column.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C8 = 7.
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.
R4C5 and R5C9 is seen by both free ends: 7 is therefore eliminated there.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 2.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 1.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 8.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 2.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 7.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 7.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 2.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 8.
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 = 8.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 1.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 2.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R3C3 = 1.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R4C7 = 7.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R4C8 = 6.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R8C2 = 7.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C6 = 6.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R9C6 = 7.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R9C8 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R9C9 = 6.
Spot R2C2 and R3C2 in this box.
These two cells can only hold 6 and 9: they reserve those digits.
6 and 9 are therefore removed from the other cells of 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.
R9C1 is seen by both free ends: 5 is therefore eliminated there.
Find 9 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 9.
R9C1 is seen by both free ends: 9 is therefore eliminated there.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 8.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 2.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 5.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 9.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 5.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 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 R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 8.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 9.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 3.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 2.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 8.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 6.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 5.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 9.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 5.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 9.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 9.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 5.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 5.
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 = 5.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 9.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 2.