Step-by-step solution
Steps 64
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 23
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R2C1 = 7.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R4C3 = 7.
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 R6C5 = 7.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R7C6 = 9.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R7C8 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C4 = 5.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R9C7 = 4.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 6.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 5.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 2.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R7C1 = 5.
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.
(1) Spot R8C1 and R9C1 on this column. (2) Spot R7C5 and R9C5 on this column. (3) Spot R8C1 and R9C1 in this box.
(1) These two cells can only hold 8 and 9: they reserve those digits. (2) These two cells can only hold 3 and 8: they reserve those digits. (3) These two cells can only hold 8 and 9: they reserve those digits.
(1) 8 and 9 are therefore removed from the other cells of the column. (2) 3 and 8 are therefore removed from the other cells of the column. (3) 8 and 9 are therefore removed from the other cells of the box.
Find where 1 and 4 can go in this box.
These two digits only fit in R4C4 and R4C5 in the box.
The other candidates in R4C4 and R4C5 are therefore eliminated.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R1C5 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R2C2 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R5C1 = 2.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 6.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 4.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 1.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 4.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 8.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 5.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 1.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 9.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 1.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 8.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R2C4 = 4.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R5C2 = 4.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R5C7 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R7C2 = 1.
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 column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R8C9 = 1.
(1) Spot R2C6 and R5C6 on this column. (2) Spot R5C6 and R6C4 in this box.
(1) These two cells can only hold 3 and 6: they reserve those digits. (2) These two cells can only hold 3 and 6: they reserve those digits.
(1) 3 and 6 are therefore removed from the other cells of the column. (2) 3 and 6 are therefore removed from the other cells of the box.
Find 3 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 3.
R3C8 is seen by both free ends: 3 is therefore eliminated there.
Find where 3 appears on two columns: altogether, only two rows are involved (R2C6, R5C6, R2C8 and R5C8).
On each covered row, 3 must lie within one of these two columns.
3 is therefore removed from those two rows outside the two X-Wing columns.
Find 6 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 6.
R3C8 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 9.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 8.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 3.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 9.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 8.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 3.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 9.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 6.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 8.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 8.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 5.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 3.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 8.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 6.
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 = 3.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 6.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 3.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 2.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 9.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 3.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 6.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 5.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 8.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 6.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 5.