Step-by-step solution
Steps 67
Estimated time 108 – 162 min
Hardest technique X-Wing
Clues 24
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R1C1 = 1.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C2 = 8.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R1C3 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R2C5 = 4.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R3C4 = 1.
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 row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R5C6 = 4.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R5C8 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R6C2 = 4.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R6C6 = 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 column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R7C9 = 1.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R8C3 = 1.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 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 column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R8C5 = 6.
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.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R9C3 = 8.
(1) Spot R5C1 and R5C7 on this row. (2) Spot R7C6 and R9C6 on this column. (3) Spot R7C6 and R9C6 in this box.
(1) These two cells can only hold 5 and 9: they reserve those digits. (2) These two cells can only hold 2 and 7: they reserve those digits. (3) These two cells can only hold 2 and 7: they reserve those digits.
(1) 5 and 9 are therefore removed from the other cells of the row. (2) 2 and 7 are therefore removed from the other cells of the column. (3) 2 and 7 are therefore removed from the other cells of the box.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 9.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R1C4 = 7.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 2.
Find where 2 and 5 can go on this row.
These two digits only fit in R3C2 and R3C5 on the row.
The other candidates in R3C2 and R3C5 are therefore eliminated.
(1) Look at where 3 can go in this box. (2) Look at where 7 can go in this box.
(1) All its spots lie on a single row (R4C2 and R4C3). (2) All its spots lie on a single row (R4C1 and R4C2).
(1) 3 is therefore removed from that row outside the box. (2) 7 is therefore removed from that row outside the box.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 5.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 3.
Find 9 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 9.
R4C9, R6C9 and R8C7 is seen by both free ends: 9 is therefore eliminated there.
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.
R4C2 is seen by both free ends: 5 is therefore eliminated there.
Look at where 5 can go in this box.
All its spots lie on a single column (R4C1 and R5C1).
5 is therefore removed from that column outside the box.
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.
R3C7 is seen by both free ends: 9 is therefore eliminated there.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 7.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 2.
Spot R5C7 and R6C7 in this box.
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 box.
Find 9 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 9.
R2C2 is seen by both free ends: 9 is therefore eliminated there.
Find where 9 appears on two rows: altogether, only two columns are involved (R2C1, R2C9, R9C1 and R9C9).
On each covered column, 9 must lie within one of these two rows.
9 is therefore removed from those two columns outside the two X-Wing rows.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 5.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 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 R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 7.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 2.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 5.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 6.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 2.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 5.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 7.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 2.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 9.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 7.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 2.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 7.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 9.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 9.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 2.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 3.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 3.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 9.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 3.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 9.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 6.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 2.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 3.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 6.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 9.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 3.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 7.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 5.