Step-by-step solution
Steps 64
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 24
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 9.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C1 = 6.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R1C4 = 5.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C6 = 7.
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.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R4C4 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C3 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R5C6 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R6C4 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C7 = 6.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R7C2 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R8C5 = 2.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R8C6 = 1.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 3.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 8.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 7.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 7.
(1) Spot R3C4 and R9C4 on this column. (2) Spot R7C5 and R9C4 in this box.
(1) These two cells can only hold 3 and 4: they reserve those digits. (2) These two cells can only hold 3 and 4: they reserve those digits.
(1) 3 and 4 are therefore removed from the other cells of the column. (2) 3 and 4 are therefore removed from the other cells of the box.
(1) Find where 3 and 9 can go on this row. (2) Find where 6 and 7 can go on this row. (3) Find where 3 and 9 can go in this box.
(1) These two digits only fit in R6C8 and R6C9 on the row. (2) These two digits only fit in R7C3 and R7C4 on the row. (3) These two digits only fit in R6C8 and R6C9 in the box.
(1) The other candidates in R6C8 and R6C9 are therefore eliminated. (2) The other candidates in R7C3 and R7C4 are therefore eliminated. (3) The other candidates in R6C8 and R6C9 are therefore eliminated.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R4C9 = 5.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R1C9 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R3C2 = 1.
Look at where 3 can go on this row.
All its spots lie within a single box (R1C7 and R1C8).
3 is therefore removed from the rest of the box.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 9.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 3.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 9.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R3C3 = 9.
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.
R9C3 is seen by both free ends: 3 is therefore eliminated there.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 2.
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.
R7C1 is seen by both free ends: 3 is therefore eliminated there.
Look at where 3 can go in this box.
All its spots lie on a single row (R8C1 and R8C3).
3 is therefore removed from that row outside the box.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 4.
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.
R9C2 and R7C5 is seen by both free ends: 4 is therefore eliminated there.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 3.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 1.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 9.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 4.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 3.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 4.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 3.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 2.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 5.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 9.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 3.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 1.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 4.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 2.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 8.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 4.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 5.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 7.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 6.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 7.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 3.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 5.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 6.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 4.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 2.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 5.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 3.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 2.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 8.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 2.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 7.