Step-by-step solution
Steps 65
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 24
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R1C4 = 5.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R1C6 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C8 = 9.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R2C8 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C2 = 9.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R4C3 = 9.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R4C8 = 5.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R5C2 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C3 = 5.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R7C3 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C6 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C7 = 5.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 8.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C5 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R4C4 = 8.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R4C5 = 2.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C5 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C9 = 8.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 2.
Spot R6C3 and R8C3 on this column.
These two cells can only hold 1 and 6: they reserve those digits.
1 and 6 are therefore removed from the other cells of the column.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R3C1 = 6.
(1) Look at where 3 can go in this box. (2) Look at where 6 can go in this box.
(1) All its spots lie on a single column (R4C1 and R5C1). (2) All its spots lie on a single row (R6C2 and R6C3).
(1) 3 is therefore removed from that column outside the box. (2) 6 is therefore removed from that row outside the box.
Spot R1C1, R1C2 and R1C5 on this row.
These three cells share only 1, 4 and 7.
1, 4 and 7 are therefore removed from the rest of the row.
Find 7 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 7.
R5C1 and R6C4 is seen by both free ends: 7 is therefore eliminated there.
Find 1 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 1.
R6C4 is seen by both free ends: 1 is therefore eliminated there.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C1 = 4.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R1C9 = 3.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R2C9 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R3C5 = 4.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R5C7 = 4.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R8C9 = 2.
Look at where 1 can go in this box.
All its spots lie on a single column (R2C7 and R3C7).
1 is therefore removed from that column outside the box.
Look at where 7 can go on this row.
All its spots lie within a single box (R5C5 and R5C6).
7 is therefore removed from the rest of the box.
Find 1 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 1.
R2C4 and R3C4 is seen by both free ends: 1 is therefore eliminated there.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 3.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 7.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 2.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 1.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 8.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 1.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 2.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 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 R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 8.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 3.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 7.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 1.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 7.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 7.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 7.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 3.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 6.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 1.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 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 R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 9.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 1.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 9.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 7.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 6.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 1.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 6.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 1.