Step-by-step solution
Steps 65
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 22
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R1C3 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R2C3 = 4.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R2C6 = 2.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R5C2 = 8.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R5C7 = 4.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C9 = 3.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R6C5 = 8.
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 column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R7C3 = 2.
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 box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R7C8 = 4.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R8C4 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C9 = 8.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R9C9 = 2.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 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 R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 9.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C2 = 5.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R3C7 = 2.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R7C5 = 5.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R8C1 = 5.
Spot R6C3 and R6C7 on this row.
These two cells can only hold 6 and 7: they reserve those digits.
6 and 7 are therefore removed from the other cells of the row.
(1) Look at where 6 can go in this box. (2) Look at where 7 can go in this box. (3) Look at where 1 can go in this box. (4) Look at where 3 can go in this box.
(1) All its spots lie on a single column (R1C5, R2C5 and R3C5). (2) All its spots lie on a single column (R1C5 and R2C5). (3) All its spots lie on a single row (R9C4 and R9C5). (4) All its spots lie on a single column (R7C6 and R8C6).
(1) 6 is therefore removed from that column outside the box. (2) 7 is therefore removed from that column outside the box. (3) 1 is therefore removed from that row outside the box. (4) 3 is therefore removed from that column outside the box.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 4.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 3.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R3C3 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R7C1 = 3.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R7C2 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R8C6 = 3.
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.
R8C8 is seen by both free ends: 6 is therefore eliminated there.
Find where 6 appears on two rows: altogether, only two columns are involved (R6C3, R6C7, R8C3 and R8C7).
On each covered column, 6 must lie within one of these two rows.
6 is therefore removed from those two columns outside the two X-Wing rows.
Find 7 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 7.
R8C8 is seen by both free ends: 7 is therefore eliminated there.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 1.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C4 = 4.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R1C7 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R2C4 = 3.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R3C5 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R9C4 = 1.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R9C5 = 4.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R1C1 = 1.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R2C7 = 1.
Find 6 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 6.
R2C1 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 9.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 6.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 9.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 2.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 7.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 6.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 2.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 7.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 6.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 5.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 9.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 6.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 7.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 7.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 6.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 6.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 7.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 9.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 7.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 6.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 7.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 5.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 6.