Step-by-step solution
Steps 65
Estimated time 104 – 156 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 9 could go.
Across the whole row, 9 has only one possible spot left.
So R1C3 = 9.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C7 = 9.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R3C8 = 3.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R4C6 = 9.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R4C9 = 2.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R5C1 = 2.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C5 = 3.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R6C8 = 9.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R7C7 = 3.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R8C7 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C9 = 4.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R1C2 = 3.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C6 = 8.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R3C3 = 8.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R4C3 = 3.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R6C3 = 4.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R8C2 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R9C1 = 3.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C2 = 8.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R7C8 = 1.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R9C8 = 7.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R5C7 = 7.
Spot R9C4 and R9C6 in this box.
These two cells can only hold 1 and 5: they reserve those digits.
1 and 5 are therefore removed from the other cells of the box.
(1) Look at where 2 can go in this box. (2) Look at where 2 can go in this box.
(1) All its spots lie on a single row (R3C4 and R3C5). (2) All its spots lie on a single column (R7C3 and R8C3).
(1) 2 is therefore removed from that row outside the box. (2) 2 is therefore removed from that column outside the box.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R2C2 = 2.
Find 6 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 6.
R4C4, R4C5 and R5C8 is seen by both free ends: 6 is therefore eliminated there.
Look at where 6 can go in this box.
All its spots lie on a single row (R4C7 and R4C8).
6 is therefore removed from that row outside the box.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R6C2 = 6.
Find 5 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 5.
R2C3 and R3C9 is seen by both free ends: 5 is therefore eliminated there.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 7.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 5.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C1 = 9.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R8C1 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C4 = 9.
Find 5 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 5.
R2C6 and R1C9 is seen by both free ends: 5 is therefore eliminated there.
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.
R1C9 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 7.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 1.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 2.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 4.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 6.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 5.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 5.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 7.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 1.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 4.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 2.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 6.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 2.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 6.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 1.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 5.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 6.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 5.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 6.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 8.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 5.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 1.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 5.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 6.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 4.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 5.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 5.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 8.