Step-by-step solution
Steps 67
Estimated time 108 – 162 min
Hardest technique X-Wing
Clues 23
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R2C2 = 6.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R4C2 = 2.
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 box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R5C8 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R5C9 = 9.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R6C2 = 8.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R6C5 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C7 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C8 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C1 = 8.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R8C3 = 9.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R8C4 = 6.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C9 = 6.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R4C1 = 6.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R4C5 = 9.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R6C3 = 3.
Look at where 3 can go in this box.
All its spots lie on a single column (R2C9 and R3C9).
3 is therefore removed from that column outside the box.
Look at where 3 can go on this row.
All its spots lie within a single box (R7C4 and R7C6).
3 is therefore removed from the rest of the box.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R2C5 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R3C9 = 3.
Look at where 1 can go in this box.
All its spots lie on a single column (R1C7 and R3C7).
1 is therefore removed from that column outside the box.
Spot R9C1, R9C2 and R9C8 on this row.
These three cells share only 3, 5 and 7.
3, 5 and 7 are therefore removed from the rest of the row.
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.
R8C2 is seen by both free ends: 7 is therefore eliminated there.
Look at where 7 can go in this box.
All its spots lie on a single row (R9C1 and R9C2).
7 is therefore removed from that row outside the box.
Find where 7 appears on two columns: altogether, only two rows are involved (R1C5, R8C5, R1C8 and R8C8).
On each covered row, 7 must lie within one of these two columns.
7 is therefore removed from those two rows outside the two X-Wing columns.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R5C3 = 7.
Spot R8C6, R9C4 and R9C6 in this box.
These three cells share only 1, 4 and 9.
1, 4 and 9 are therefore removed from the rest of 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.
R1C3 and R2C4 is seen by both free ends: 4 is therefore eliminated there.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 5.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 7.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 4.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 5.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 7.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C5 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C7 = 8.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C7 = 5.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R2C9 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C4 = 9.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R3C6 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R4C4 = 5.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C6 = 3.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C8 = 5.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R7C4 = 3.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R7C6 = 7.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R8C2 = 3.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C7 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C8 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C9 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C2 = 5.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R9C6 = 9.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R9C8 = 3.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R9C9 = 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 R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 8.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 1.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 2.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 4.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 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 R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 1.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 4.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 1.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 4.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 2.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 4.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 8.