Step-by-step solution
Steps 62
Estimated time 100 – 150 min
Hardest technique X-Wing
Clues 25
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 4.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 3.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 3.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 5.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 8.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R1C7 = 9.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R2C4 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C7 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R3C2 = 5.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R3C6 = 8.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R3C7 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C8 = 6.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R5C3 = 1.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R6C8 = 5.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R7C7 = 8.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R8C1 = 1.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R8C4 = 5.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C6 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R9C4 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R9C6 = 6.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R9C8 = 2.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 2.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R2C9 = 2.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R5C7 = 6.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C4 = 2.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R7C6 = 4.
(1) Look at where 4 can go in this box. (2) Look at where 4 can go in this box. (3) Look at where 7 can go in this box.
(1) All its spots lie on a single column (R1C9 and R3C9). (2) All its spots lie on a single column (R8C2 and R9C2). (3) All its spots lie on a single column (R8C7 and R9C7).
(1) 4 is therefore removed from that column outside the box. (2) 4 is therefore removed from that column outside the box. (3) 7 is therefore removed from that column outside the box.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R6C3 = 4.
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.
R4C8 is seen by both free ends: 3 is therefore eliminated there.
Find 8 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 8.
R4C1 is seen by both free ends: 8 is therefore eliminated there.
(1) Find where 8 appears on two rows: altogether, only two columns are involved (R2C2, R2C8, R4C2 and R4C8). (2) Find where 8 appears on two columns: altogether, only two rows are involved (R1C1, R6C1, R1C9 and R6C9).
(1) On each covered column, 8 must lie within one of these two rows. (2) On each covered row, 8 must lie within one of these two columns.
(1) 8 is therefore removed from those two columns outside the two X-Wing rows. (2) 8 is therefore removed from those two rows outside the two X-Wing columns.
Spot R6C2, R8C2 and R9C2 on this column.
These three cells share only 4, 7 and 9.
4, 7 and 9 are therefore removed from the rest of the column.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R5C8 = 9.
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.
R1C9 and R3C9 is seen by both free ends: 3 is therefore eliminated there.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 4.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 8.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 3.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 3.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 7.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 4.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 7.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 6.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 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 R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 8.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 6.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 9.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 8.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 3.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 9.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 6.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 7.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 3.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 9.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 4.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 7.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 2.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 4.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 2.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 7.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 8.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 3.