Step-by-step solution
Steps 68
Estimated time 112 – 168 min
Hardest technique X-Wing
Clues 23
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R1C4 = 1.
Scan the empty cells in this column where 9 could go.
Across the whole column, 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 R2C5 = 7.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R3C2 = 7.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R3C6 = 3.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R4C4 = 7.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R4C6 = 2.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C1 = 1.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C6 = 5.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R6C5 = 1.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C6 = 7.
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.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 4.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R1C9 = 7.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R8C2 = 2.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R9C7 = 2.
Spot R7C2 and R7C6 on this row.
These two cells can only hold 4 and 8: they reserve those digits.
4 and 8 are therefore removed from the other cells of the row.
(1) Look at where 6 can go in this box. (2) Look at where 9 can go in this box. (3) Look at where 8 can go in this box.
(1) All its spots lie on a single column (R2C3 and R3C3). (2) All its spots lie on a single column (R5C4 and R6C4). (3) All its spots lie on a single row (R8C7, R8C8 and R8C9).
(1) 6 is therefore removed from that column outside the box. (2) 9 is therefore removed from that column outside the box. (3) 8 is therefore removed from that row outside the box.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 3.
Look at where 9 can go on this column.
All its spots lie within a single box (R5C2 and R6C2).
9 is therefore removed from the rest of the box.
Find where 6 and 9 can go on this row.
These two digits only fit in R6C2 and R6C4 on the row.
The other candidates in R6C2 and R6C4 are therefore eliminated.
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.
R5C2 is seen by both free ends: 4 is therefore eliminated there.
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.
R6C1 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 row (R4C1, R4C2 and R4C3).
4 is therefore removed from that row outside the box.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R2C7 = 4.
Look at where 5 can go in this box.
All its spots lie on a single column (R1C8 and R2C8).
5 is therefore removed from that column outside the box.
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.
R4C2 is seen by both free ends: 8 is therefore eliminated there.
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.
R6C1 is seen by both free ends: 8 is therefore eliminated there.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 3.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R4C7 = 3.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C7 = 5.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C7 = 8.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 6.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 4.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 8.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 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 R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 4.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 8.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 8.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 9.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 5.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 8.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 9.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 5.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 8.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 2.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 9.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 4.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 4.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 6.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 5.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 4.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 8.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 6.
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 = 2.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 9.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 6.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 8.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 4.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 1.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 3.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 6.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 5.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 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 R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 1.