Step-by-step solution
Steps 66
Estimated time 108 – 162 min
Hardest technique X-Wing
Clues 24
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C2 = 8.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R3C3 = 6.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R3C5 = 8.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R4C7 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R5C1 = 8.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R7C4 = 3.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R8C7 = 4.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R9C6 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R9C9 = 7.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 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 R2C3 = 7.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R2C7 = 3.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R4C1 = 7.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C8 = 3.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C2 = 5.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R6C2 = 3.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R6C7 = 7.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R7C7 = 6.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C1 = 6.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R8C2 = 1.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R9C2 = 2.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R9C4 = 6.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 9.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 5.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 5.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 5.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 4.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 9.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R5C9 = 6.
(1) Spot R6C3 and R6C8 on this row. (2) Spot R4C5 and R5C4 in this box.
(1) These two cells can only hold 1 and 9: they reserve those digits. (2) These two cells can only hold 1 and 9: they reserve those digits.
(1) 1 and 9 are therefore removed from the other cells of the row. (2) 1 and 9 are therefore removed from the other cells of the box.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 5.
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.
R1C5 is seen by both free ends: 1 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.
R8C4 is seen by both free ends: 2 is therefore eliminated there.
Look at where 2 can go on this column.
All its spots lie within a single box (R1C4 and R3C4).
2 is therefore removed from the rest of the box.
Find 9 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 9.
R8C5 is seen by both free ends: 9 is therefore eliminated there.
Find where 1 and 9 can go on this column.
These two digits only fit in R4C5 and R7C5 on the column.
The other candidates in R4C5 and R7C5 are therefore eliminated.
Find where 9 appears on two columns: altogether, only two rows are involved (R4C5, R7C5, R4C9 and R7C9).
On each covered row, 9 must lie within one of these two columns.
9 is therefore removed from those two rows outside the two X-Wing columns.
Spot R1C6, R6C6 and R7C6 on this column.
These three cells share only 1, 2 and 6.
1, 2 and 6 are therefore removed from the rest of the column.
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.
R5C4 is seen by both free ends: 1 is therefore eliminated there.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 9.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 1.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 9.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 1.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 9.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 1.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 9.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 2.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 5.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 9.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 2.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 4.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 4.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 1.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 7.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 2.
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 = 6.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 4.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 9.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 1.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 2.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 5.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 6.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 2.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 7.