Step-by-step solution
Steps 66
Estimated time 108 – 162 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 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C6 = 9.
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 7 could go.
Across the whole box, 7 has only one possible spot left.
So R2C6 = 7.
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 row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R4C4 = 9.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R4C8 = 3.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R7C9 = 9.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C8 = 6.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R9C4 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C9 = 5.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C5 = 6.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R5C6 = 6.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R9C5 = 1.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R7C6 = 5.
Spot R9C1 and R9C2 in this box.
These two cells can only hold 4 and 6: they reserve those digits.
4 and 6 are therefore removed from the other cells of the box.
(1) Find where 6 and 7 can go on this row. (2) Find where 6 and 7 can go in this box.
(1) These two digits only fit in R4C1 and R4C2 on the row. (2) These two digits only fit in R4C1 and R4C2 in the box.
(1) The other candidates in R4C1 and R4C2 are therefore eliminated. (2) The other candidates in R4C1 and R4C2 are therefore eliminated.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R4C3 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C1 = 2.
Find where 2 and 9 can go on this row.
These two digits only fit in R2C2 and R2C7 on the row.
The other candidates in R2C2 and R2C7 are therefore eliminated.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R1C2 = 5.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R1C7 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R2C2 = 2.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C7 = 9.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C2 = 9.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R3C1 = 7.
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 column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R4C2 = 7.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R9C1 = 4.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R9C2 = 6.
(1) Look at where 4 can go in this box. (2) Look at where 3 can go in this box.
(1) All its spots lie on a single column (R1C3 and R3C3). (2) All its spots lie on a single column (R1C4 and R3C4).
(1) 4 is therefore removed from that column outside the box. (2) 3 is therefore removed from that column outside the box.
Look at where 1 can go on this row.
All its spots lie within a single box (R4C7 and R4C9).
1 is therefore removed from the rest of the box.
Find 3 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 3.
R5C2 is seen by both free ends: 3 is therefore eliminated there.
(1) Find where 3 appears on two rows: altogether, only two columns are involved (R5C3, R5C5, R7C3 and R7C5). (2) Find where 3 appears on two columns: altogether, only two rows are involved (R6C2, R8C2, R6C6 and R8C6).
(1) On each covered column, 3 must lie within one of these two rows. (2) On each covered row, 3 must lie within one of these two columns.
(1) 3 is therefore removed from those two columns outside the two X-Wing rows. (2) 3 is therefore removed from those two rows outside the two X-Wing columns.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R1C1 = 3.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R3C4 = 3.
Find 8 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 8.
R1C8, R2C8 and R8C7 is seen by both free ends: 8 is therefore eliminated there.
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 column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R7C8 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C2 = 8.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 4.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 4.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 5.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 3.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 2.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 3.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 4.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 2.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 3.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 1.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 8.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 4.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 4.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 1.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 5.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 8.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 3.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 4.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 1.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 1.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 5.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 4.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 8.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 1.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 8.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 1.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 8.