Step-by-step solution
Steps 70
Estimated time 112 – 168 min
Hardest technique X-Wing
Clues 23
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 3.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C1 = 5.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R2C5 = 8.
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 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C5 = 3.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R4C8 = 2.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R4C9 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R5C4 = 9.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R5C8 = 5.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R6C4 = 7.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R8C7 = 5.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 8.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 3.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 5.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 9.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R2C7 = 3.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R4C1 = 9.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R5C6 = 1.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R6C1 = 3.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R7C2 = 8.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R8C9 = 8.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R5C2 = 2.
(1) Spot R6C2 and R6C9 on this row. (2) Spot R1C2 and R2C2 on this column. (3) Spot R4C7 and R6C9 in this box.
(1) These two cells can only hold 4 and 6: they reserve those digits. (2) These two cells can only hold 1 and 9: they reserve those digits. (3) These two cells can only hold 4 and 6: they reserve those digits.
(1) 4 and 6 are therefore removed from the other cells of the row. (2) 1 and 9 are therefore removed from the other cells of the column. (3) 4 and 6 are therefore removed from the other cells of the box.
Find where 1 and 9 can go on this row.
These two digits only fit in R2C2 and R2C8 on the row.
The other candidates in R2C2 and R2C8 are therefore eliminated.
(1) Find where 7 appears on two rows: altogether, only two columns are involved (R1C5, R1C8, R9C5 and R9C8). (2) Find where 7 appears on two columns: altogether, only two rows are involved (R2C6, R7C6, R2C9 and R7C9).
(1) On each covered column, 7 must lie within one of these two rows. (2) On each covered row, 7 must lie within one of these two columns.
(1) 7 is therefore removed from those two columns outside the two X-Wing rows. (2) 7 is therefore removed from those two rows outside the two X-Wing columns.
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.
R7C1 and R9C8 is seen by both free ends: 4 is therefore eliminated there.
Look at where 4 can go in this box.
All its spots lie on a single row (R7C8 and R7C9).
4 is therefore removed from that row outside the box.
Find 6 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 6.
R2C6 is seen by both free ends: 6 is therefore eliminated there.
Look at where 6 can go in this box.
All its spots lie on a single column (R2C4 and R3C4).
6 is therefore removed from that column outside the box.
Find 4 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 4.
R9C5 is seen by both free ends: 4 is therefore eliminated there.
Find 4 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 4.
R1C7 is seen by both free ends: 4 is therefore eliminated there.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 9.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 1.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 8.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 9.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 1.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 9.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R3C8 = 8.
Find 4 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 4.
R8C1 is seen by both free ends: 4 is therefore eliminated there.
Look at where 4 can go in this box.
All its spots lie on a single row (R9C1 and R9C2).
4 is therefore removed from that row outside the box.
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.
R9C5 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 7.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 3.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 4.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 7.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 1.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 7.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 6.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 4.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 6.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 4.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 2.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 7.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 6.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 4.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 6.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 6.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 5.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 4.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 2.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 4.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 5.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 4.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 4.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 3.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 6.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 1.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 6.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 2.