Step-by-step solution
Steps 69
Estimated time 112 – 168 min
Hardest technique X-Wing
Clues 23
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 R1C4 = 8.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R3C7 = 8.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R4C1 = 8.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R4C7 = 7.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R5C3 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R6C6 = 8.
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 R9C2 = 8.
Scan the empty cells in this row where 5 could go.
Across the whole row, 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 R6C2 = 4.
Spot R5C1 and R7C1 on this column.
These two cells can only hold 2 and 9: they reserve those digits.
2 and 9 are therefore removed from the other cells of the column.
Look at where 1 can go in this box.
All its spots lie on a single row (R7C4 and R7C6).
1 is therefore removed from that row outside the box.
Spot R4C5, R4C6 and R6C5 in this box.
These three cells share only 2, 5 and 9.
2, 5 and 9 are therefore removed from the rest of the box.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 6.
Find 7 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 7.
R2C9 and R8C8 is seen by both free ends: 7 is therefore eliminated there.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R7C9 = 7.
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.
R6C7 is seen by both free ends: 6 is therefore eliminated there.
(1) Find where 6 appears on two rows: altogether, only two columns are involved (R6C3, R6C8, R8C3 and R8C8). (2) Find where 6 appears on two columns: altogether, only two rows are involved (R5C2, R7C2, R5C7 and R7C7).
(1) On each covered column, 6 must lie within one of these two rows. (2) On each covered row, 6 must lie within one of these two columns.
(1) 6 is therefore removed from those two columns outside the two X-Wing rows. (2) 6 is therefore removed from those two rows outside the two X-Wing columns.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C6 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R2C9 = 4.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R3C9 = 6.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R5C4 = 4.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 1.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 4.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 1.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 3.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R1C8 = 7.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R7C4 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R8C4 = 3.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 2.
(1) Spot R5C1 and R5C9 on this row. (2) Spot R7C1 and R7C6 on this row.
(1) These two cells can only hold 2 and 9: they reserve those digits. (2) These two cells can only hold 2 and 9: they reserve those digits.
(1) 2 and 9 are therefore removed from the other cells of the row. (2) 2 and 9 are therefore removed from the other cells of the row.
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.
R9C3 is seen by both free ends: 2 is therefore eliminated there.
Look at where 2 can go on this row.
All its spots lie within a single box (R9C7, R9C8 and R9C9).
2 is therefore removed from the rest of the box.
Find 3 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 3.
R2C2 and R1C7 is seen by both free ends: 3 is therefore eliminated there.
Find 9 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 9.
R9C3 is seen by both free ends: 9 is therefore eliminated there.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 3.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 6.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 3.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 5.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 6.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 9.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 1.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 3.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 2.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 2.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 9.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 2.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 6.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 9.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 2.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 9.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 9.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 6.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 1.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 9.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 3.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 2.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 9.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 5.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 1.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 5.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 2.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 5.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 7.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 2.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 2.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 5.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 7.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 9.