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 row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R1C8 = 3.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R2C2 = 6.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R3C7 = 8.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R5C9 = 3.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R7C1 = 6.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C2 = 2.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R7C4 = 9.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R7C5 = 3.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R7C6 = 4.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C8 = 8.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R8C3 = 3.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R8C9 = 4.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R9C2 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R9C9 = 2.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R4C4 = 3.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R5C4 = 4.
(1) Spot R1C1 and R1C4 on this row. (2) Spot R1C4 and R3C5 in this box.
(1) These two cells can only hold 5 and 7: they reserve those digits. (2) These two cells can only hold 5 and 7: they reserve those digits.
(1) 5 and 7 are therefore removed from the other cells of the row. (2) 5 and 7 are therefore removed from the other cells of the box.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 4.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 8.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R2C5 = 4.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R4C3 = 4.
Find where 5 and 9 can go on this column.
These two digits only fit in R2C7 and R4C7 on the column.
The other candidates in R2C7 and R4C7 are therefore eliminated.
Look at where 5 can go in this box.
All its spots lie on a single row (R2C7 and R2C8).
5 is therefore removed from that row outside the box.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C6 = 5.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R9C3 = 5.
Find 9 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 9.
R4C1, R4C2 and R6C9 is seen by both free ends: 9 is therefore eliminated there.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 7.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 9.
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 row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R4C7 = 9.
(1) Find where 5 and 6 can go on this column. (2) Find where 5 and 6 can go in this box.
(1) These two digits only fit in R4C8 and R6C8 on the column. (2) These two digits only fit in R4C8 and R6C8 in the box.
(1) The other candidates in R4C8 and R6C8 are therefore eliminated. (2) The other candidates in R4C8 and R6C8 are therefore eliminated.
Look at where 2 can go in this box.
All its spots lie on a single row (R5C7 and R5C8).
2 is therefore removed from that row outside the box.
Find 1 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 1.
R6C5 is seen by both free ends: 1 is therefore eliminated there.
Find 7 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 7.
R2C8 is seen by both free ends: 7 is therefore eliminated there.
(1) Spot R2C6 and R2C8 on this row. (2) Spot R1C7 and R2C8 in this box.
(1) These two cells can only hold 1 and 2: they reserve those digits. (2) These two cells can only hold 1 and 2: they reserve those digits.
(1) 1 and 2 are therefore removed from the other cells of the row. (2) 1 and 2 are therefore removed from the other cells of the box.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 1.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 9.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 7.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 9.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 7.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 1.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 7.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 7.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 1.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 5.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 7.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 2.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 9.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 5.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 2.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 7.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 5.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 6.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 1.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 1.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 5.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 8.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 2.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 1.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 7.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 2.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 6.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 7.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 2.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 1.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 6.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 8.