Step-by-step solution
Steps 67
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 column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R1C2 = 1.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R2C7 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R3C4 = 8.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R4C9 = 8.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R5C4 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R5C9 = 6.
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 3 could go.
Across the whole box, 3 has only one possible spot left.
So R7C4 = 3.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R9C1 = 1.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C5 = 8.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 4.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 3.
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 box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R1C8 = 2.
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 box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R5C5 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C5 = 5.
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.
(1) Spot R7C2 and R7C6 on this row. (2) Spot R1C7 and R1C9 in this box.
(1) These two cells can only hold 4 and 9: they reserve those digits. (2) These two cells can only hold 7 and 9: they reserve those digits.
(1) 4 and 9 are therefore removed from the other cells of the row. (2) 7 and 9 are therefore removed from the other cells of the box.
Find where 3 and 5 can go on this column.
These two digits only fit in R5C7 and R9C7 on the column.
The other candidates in R5C7 and R9C7 are therefore eliminated.
Look at where 5 can go in this box.
All its spots lie on a single column (R7C3 and R9C3).
5 is therefore removed from that column outside the box.
Look at where 7 can go on this column.
All its spots lie within a single box (R4C8, R5C8 and R6C8).
7 is therefore removed from the rest of the box.
Find 4 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 4.
R4C8 is seen by both free ends: 4 is therefore eliminated there.
Find 4 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 4.
R4C2 is seen by both free ends: 4 is therefore eliminated there.
Look at where 4 can go in this box.
All its spots lie on a single column (R5C3 and R6C3).
4 is therefore removed from that column outside the box.
(1) Look at where 4 can go on this row. (2) Look at where 4 can go on this row.
(1) All its spots lie within a single box (R4C4 and R4C6). (2) All its spots lie within a single box (R9C8 and R9C9).
(1) 4 is therefore removed from the rest of the box. (2) 4 is therefore removed from the rest of the box.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R5C3 = 4.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R6C7 = 4.
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 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C2 = 3.
Find 9 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 9.
R2C2 is seen by both free ends: 9 is therefore eliminated there.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C7 = 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 5 could go.
Across the whole box, 5 has only one possible spot left.
So R4C6 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C7 = 5.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C8 = 3.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C3 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C9 = 5.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R8C3 = 6.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C7 = 7.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R8C9 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C3 = 5.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 7.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 7.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 3.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 9.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 4.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 9.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 7.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 4.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 9.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 7.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 3.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 1.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 9.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 9.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 4.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 4.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 5.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 9.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 4.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 3.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 7.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 5.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 1.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 9.