Step-by-step solution
Steps 68
Estimated time 112 – 168 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 row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R1C9 = 4.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R2C5 = 9.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R3C2 = 5.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R3C6 = 6.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R4C5 = 7.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C4 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R5C8 = 9.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R5C9 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C2 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C9 = 9.
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 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 7 could go.
Across the whole box, 7 has only one possible spot left.
So R9C7 = 7.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R7C6 = 5.
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 4 could go.
Across the whole row, 4 has only one possible spot left.
So R9C4 = 4.
Find where 5 and 6 can go in this box.
These two digits only fit in R6C7 and R6C9 in the box.
The other candidates in R6C7 and R6C9 are therefore eliminated.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C7 = 6.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R6C8 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C9 = 5.
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 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C9 = 6.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R2C7 = 5.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R5C3 = 6.
Spot R7C8 and R8C8 on this column.
These two cells can only hold 1 and 8: they reserve those digits.
1 and 8 are therefore removed from the other cells of the column.
Find where 4 and 8 can go on this row.
These two digits only fit in R4C1 and R4C6 on the row.
The other candidates in R4C1 and R4C6 are therefore eliminated.
Look at where 3 can go in this box.
All its spots lie on a single row (R3C7 and R3C8).
3 is therefore removed from that row outside the box.
(1) Look at where 8 can go on this column. (2) Look at where 3 can go on this column.
(1) All its spots lie within a single box (R8C2 and R9C2). (2) All its spots lie within a single box (R1C3 and R2C3).
(1) 8 is therefore removed from the rest of the box. (2) 3 is therefore removed from the rest of the box.
Spot R2C1 and R2C9 on this row.
These two cells can only hold 2 and 8: they reserve those digits.
2 and 8 are therefore removed from the other cells of the row.
Find 8 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 8.
R1C3 is seen by both free ends: 8 is therefore eliminated there.
Look at where 8 can go on this row.
All its spots lie within a single box (R1C5 and R1C6).
8 is therefore removed from the rest of the box.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R9C2 = 8.
Find 2 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 2.
R5C1 is seen by both free ends: 2 is therefore eliminated there.
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.
R8C5 is seen by both free ends: 2 is therefore eliminated there.
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.
R1C3 is seen by both free ends: 2 is therefore eliminated there.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 3.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 7.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 3.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 8.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 1.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 2.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 8.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 6.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 7.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 3.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 3.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 1.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 2.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 8.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 2.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 2.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 3.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 4.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 8.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 2.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 1.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 3.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 2.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 4.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 8.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 2.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 6.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 8.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 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 R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 8.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 3.