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 row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R2C3 = 5.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R3C2 = 6.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R3C4 = 7.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R4C1 = 5.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C2 = 3.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R4C7 = 2.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R4C9 = 6.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R5C5 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C6 = 5.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R5C8 = 3.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R6C5 = 9.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C6 = 6.
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 column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R7C3 = 6.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R8C5 = 6.
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.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R1C1 = 3.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C3 = 7.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R2C7 = 7.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R7C4 = 5.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R8C9 = 2.
Spot R3C5 and R4C5 on this column.
These two cells can only hold 1 and 4: they reserve those digits.
1 and 4 are therefore removed from the other cells of the column.
(1) Find where 2 and 9 can go on this column. (2) Find where 2 and 9 can go in this box.
(1) These two digits only fit in R7C2 and R9C2 on the column. (2) These two digits only fit in R7C2 and R9C2 in the box.
(1) The other candidates in R7C2 and R9C2 are therefore eliminated. (2) The other candidates in R7C2 and R9C2 are therefore eliminated.
Find where 8 appears on two rows: altogether, only two columns are involved (R3C1, R3C7, R8C1 and R8C7).
On each covered column, 8 must lie within one of these two rows.
8 is therefore removed from those two columns outside the two X-Wing rows.
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.
R1C6 and R2C6 is seen by both free ends: 4 is therefore eliminated there.
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 box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R4C4 = 4.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 1.
(1) Spot R3C1 and R8C1 on this column. (2) Spot R8C4 and R9C4 in this box.
(1) These two cells can only hold 1 and 8: they reserve those digits. (2) These two cells can only hold 1 and 9: they reserve those digits.
(1) 1 and 8 are therefore removed from the other cells of the column. (2) 1 and 9 are therefore removed from the other cells of the box.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R5C3 = 4.
Look at where 1 can go on this row.
All its spots lie within a single box (R7C8 and R7C9).
1 is therefore removed from the rest of the box.
Find 8 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 8.
R9C9 is seen by both free ends: 8 is therefore eliminated there.
Find 8 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 8.
R2C8 is seen by both free ends: 8 is therefore eliminated there.
Find where 4 and 8 can go on this row.
These two digits only fit in R2C2 and R2C9 on the row.
The other candidates in R2C2 and R2C9 are therefore eliminated.
Find where 8 appears on two rows: altogether, only two columns are involved (R2C2, R2C9, R5C2 and R5C9).
On each covered column, 8 must lie within one of these two rows.
8 is therefore removed from those two columns outside the two X-Wing rows.
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.
R3C1, R1C8 and R1C9 is seen by both free ends: 1 is therefore eliminated there.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 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 R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 9.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 1.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 9.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 8.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 8.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 1.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 4.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 2.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 8.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 1.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 1.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 8.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 1.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 2.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 9.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 4.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 3.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 1.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 8.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 4.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 1.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 2.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 3.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 7.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 8.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 9.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 4.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 9.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 7.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 2.