Step-by-step solution
Steps 67
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 row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R1C2 = 3.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R2C3 = 1.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R2C4 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C5 = 9.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R2C6 = 2.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R2C9 = 3.
Scan the empty cells in this row where 6 could go.
Across the whole row, 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 R3C8 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R4C1 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R4C3 = 8.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R6C8 = 3.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C1 = 8.
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 1 could go.
Across the whole row, 1 has only one possible spot left.
So R1C6 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R3C9 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C6 = 3.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R5C8 = 6.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R7C5 = 3.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R7C8 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R7C9 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C6 = 8.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R9C3 = 3.
Spot R1C1 and R2C1 on this column.
These two cells can only hold 4 and 5: they reserve those digits.
4 and 5 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 R7C7 and R9C7 on the column. (2) These two digits only fit in R7C7 and R9C7 in the box.
(1) The other candidates in R7C7 and R9C7 are therefore eliminated. (2) The other candidates in R7C7 and R9C7 are therefore eliminated.
(1) Look at where 5 can go in this box. (2) Look at where 7 can go in this box. (3) Look at where 4 can go in this box.
(1) All its spots lie on a single column (R1C5 and R3C5). (2) All its spots lie on a single row (R3C5 and R3C6). (3) All its spots lie on a single column (R8C8 and R9C8).
(1) 5 is therefore removed from that column outside the box. (2) 7 is therefore removed from that row outside the box. (3) 4 is therefore removed from that column outside the box.
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.
R5C3 and R6C4 is seen by both free ends: 9 is therefore eliminated there.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R5C6 = 9.
Look at where 4 can go in this box.
All its spots lie on a single row (R4C4 and R4C5).
4 is therefore removed from that row outside the box.
Find 5 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 5.
R5C3 is seen by both free ends: 5 is therefore eliminated there.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 4.
Spot R7C3 and R7C7 on this row.
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 row.
Spot R9C4 and R9C7 on this row.
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 row.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R4C2 = 1.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R6C2 = 2.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R6C7 = 1.
Find where 5 appears on two columns: altogether, only two rows are involved (R5C2, R9C2, R5C9 and R9C9).
On each covered row, 5 must lie within one of these two columns.
5 is therefore removed from those two rows outside the two X-Wing columns.
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.
R5C2 and R8C1 is seen by both free ends: 7 is therefore eliminated there.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 5.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 7.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 9.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 2.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 9.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 9.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 5.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 2.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 9.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 2.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 5.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 5.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 7.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 5.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 4.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 7.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 5.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 7.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 4.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 7.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 4.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 4.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 5.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 7.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 7.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 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 R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 4.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 7.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 4.