Step-by-step solution
Steps 67
Estimated time 108 – 162 min
Hardest technique X-Wing
Clues 22
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 R1C6 = 3.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C9 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R3C7 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R3C9 = 2.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R5C8 = 2.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C4 = 7.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R7C8 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C8 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R9C8 = 7.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R5C5 = 7.
Scan the empty cells in this column where 3 could go.
Across the whole column, 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 R8C5 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R9C4 = 4.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R5C3 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R8C1 = 3.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C9 = 9.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R9C1 = 2.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R9C2 = 9.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R9C9 = 3.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C1 = 9.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R1C3 = 2.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C5 = 9.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R4C3 = 9.
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.
(1) Find where 7 and 8 can go on this row. (2) Find where 7 and 8 can go in this box.
(1) These two digits only fit in R2C1 and R2C2 on the row. (2) These two digits only fit in R2C1 and R2C2 in the box.
(1) The other candidates in R2C1 and R2C2 are therefore eliminated. (2) The other candidates in R2C1 and R2C2 are therefore eliminated.
(1) Look at where 1 can go on this row. (2) Look at where 5 can go on this row.
(1) All its spots lie within a single box (R5C1 and R5C2). (2) All its spots lie within a single box (R7C1, R7C2 and R7C3).
(1) 1 is therefore removed from the rest of the box. (2) 5 is therefore removed from the rest of the box.
Spot R1C2 and R8C2 on this column.
These two cells can only hold 1 and 6: they reserve those digits.
1 and 6 are therefore removed from the other cells of the column.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 8.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 6.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 7.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 1.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R4C6 = 4.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R6C1 = 7.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R6C6 = 8.
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.
R3C4 is seen by both free ends: 1 is therefore eliminated there.
Look at where 1 can go in this box.
All its spots lie on a single row (R2C4 and R2C5).
1 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.
R7C1 is seen by both free ends: 6 is therefore eliminated there.
(1) Spot R7C1 and R7C2 on this row. (2) Spot R7C1 and R7C2 in this box.
(1) These two cells can only hold 4 and 5: they reserve those digits. (2) These two cells can only hold 4 and 5: they reserve those digits.
(1) 4 and 5 are therefore removed from the other cells of the row. (2) 4 and 5 are therefore removed from the other cells of the box.
(1) Find where 6 appears on two rows: altogether, only two columns are involved (R6C3, R6C9, R7C3 and R7C9). (2) Find where 6 appears on two columns: altogether, only two rows are involved (R3C1, R4C1, R3C8 and R4C8).
(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.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 5.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 2.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 5.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 1.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 6.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 1.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 5.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 6.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 6.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 5.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 1.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 6.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 1.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 6.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 5.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 1.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 4.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 6.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 1.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 2.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 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 R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 1.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 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 R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 5.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 4.