Step-by-step solution
Steps 66
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 R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 3.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R2C1 = 7.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R2C4 = 4.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R3C2 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C6 = 7.
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 7 could go.
Across the whole box, 7 has only one possible spot left.
So R5C4 = 7.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R5C6 = 1.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R6C5 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C9 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C2 = 7.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R9C7 = 8.
Spot R5C5 and R5C8 on this row.
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 row.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 9.
(1) Spot R2C3 and R5C3 on this column. (2) Spot R4C2 and R6C2 in this box.
(1) These two cells can only hold 3 and 8: they reserve those digits. (2) These two cells can only hold 1 and 6: they reserve those digits.
(1) 3 and 8 are therefore removed from the other cells of the column. (2) 1 and 6 are therefore removed from the other cells of the box.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 9.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 1.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R1C7 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C8 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R3C8 = 2.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R4C8 = 1.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R6C9 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R7C1 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C5 = 9.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C1 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R8C9 = 1.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 3.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 6.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 8.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 1.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 3.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R3C9 = 3.
Spot R2C7 and R6C7 on this column.
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 column.
Look at where 5 can go on this column.
All its spots lie within a single box (R7C6, R8C6 and R9C6).
5 is therefore removed from the rest of the box.
Find where 4 and 5 can go on this row.
These two digits only fit in R8C6 and R8C8 on the row.
The other candidates in R8C6 and R8C8 are therefore eliminated.
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.
R7C4 and R8C4 is seen by both free ends: 2 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.
R7C4 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 3.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 2.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 8.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 2.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 3.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 5.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 6.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 5.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 2.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 6.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 5.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 4.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 2.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 6.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 2.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 5.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 6.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 5.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 8.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 2.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 5.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 6.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 5.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 6.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 5.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 8.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 3.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 6.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 4.