Step-by-step solution
Steps 69
Estimated time 112 – 168 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 7 could go.
Across the whole column, 7 has only one possible spot left.
So R4C8 = 7.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R7C1 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C4 = 7.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R7C9 = 6.
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 3 could go.
Across the whole row, 3 has only one possible spot left.
So R8C6 = 3.
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.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R9C8 = 5.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R1C5 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C6 = 9.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R1C7 = 5.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C6 = 8.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R3C3 = 5.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C5 = 6.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R4C1 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R4C5 = 9.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R5C1 = 7.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R6C9 = 5.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R8C3 = 6.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R9C5 = 1.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C2 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C9 = 8.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R2C4 = 5.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C1 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R3C2 = 8.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R4C4 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C2 = 1.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R5C6 = 5.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R9C2 = 9.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 4.
(1) Spot R2C2 and R2C5 on this row. (2) Spot R5C4 and R5C9 on this row.
(1) These two cells can only hold 2 and 4: they reserve those digits. (2) These two cells can only hold 2 and 4: they reserve those digits.
(1) 2 and 4 are therefore removed from the other cells of the row. (2) 2 and 4 are therefore removed from the other cells of the row.
Look at where 2 can go in this box.
All its spots lie on a single row (R6C1 and R6C2).
2 is therefore removed from that row outside the box.
Find 2 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 2.
R4C7 is seen by both free ends: 2 is therefore eliminated there.
Look at where 2 can go in this box.
All its spots lie on a single column (R4C9 and R5C9).
2 is therefore removed from that column outside the box.
Look at where 2 can go in this box.
All its spots lie on a single column (R1C8 and R3C8).
2 is therefore removed from that column outside the box.
Find 4 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 4.
R4C7 is seen by both free ends: 4 is therefore eliminated there.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 8.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 9.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 8.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R6C3 = 9.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R7C8 = 9.
Find where 3 appears on two rows: altogether, only two columns are involved (R2C1, R2C8, R6C1 and R6C8).
On each covered column, 3 must lie within one of these two rows.
3 is therefore removed from those two columns outside the two X-Wing rows.
Find 4 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 4.
R1C8 is seen by both free ends: 4 is therefore eliminated there.
Spot R1C1 and R1C8 on this row.
These two cells can only hold 1 and 2: they reserve those digits.
1 and 2 are therefore removed from the other cells of the row.
Look at where 4 can go in this box.
All its spots lie on a single row (R3C8 and R3C9).
4 is therefore removed from that row outside the box.
Find 4 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 4.
R4C6 is seen by both free ends: 4 is therefore eliminated there.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 2.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 4.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 2.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 4.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 2.
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 = 4.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 3.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 4.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 2.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 4.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 3.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 4.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 3.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 4.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 2.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 1.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 3.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 2.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 4.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 1.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 2.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 3.