Step-by-step solution
Steps 64
Estimated time 104 – 156 min
Hardest technique X-Wing
Clues 25
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 9.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R1C2 = 1.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R1C9 = 2.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R2C3 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C6 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R3C3 = 5.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R3C8 = 4.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R4C1 = 4.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R4C6 = 2.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R5C3 = 9.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R5C5 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R6C9 = 4.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R7C2 = 5.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C3 = 7.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C4 = 2.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R8C1 = 8.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R8C4 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C7 = 5.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R8C8 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C4 = 5.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 3.
(1) Find where 7 and 8 can go in this box. (2) Find where 3 and 9 can go in this box.
(1) These two digits only fit in R5C6 and R6C6 in the box. (2) These two digits only fit in R7C9 and R9C7 in the box.
(1) The other candidates in R5C6 and R6C6 are therefore eliminated. (2) The other candidates in R7C9 and R9C7 are therefore eliminated.
Spot R5C6 and R6C6 on this column.
These two cells can only hold 7 and 8: they reserve those digits.
7 and 8 are therefore removed from the other cells of the column.
(1) Look at where 7 can go in this box. (2) Look at where 8 can go in this box.
(1) All its spots lie on a single column (R1C7 and R3C7). (2) All its spots lie on a single column (R7C8 and R9C8).
(1) 7 is therefore removed from that column outside the box. (2) 8 is therefore removed from that column outside the box.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R4C8 = 7.
(1) Look at where 1 can go on this column. (2) Look at where 6 can go on this column.
(1) All its spots lie within a single box (R5C4 and R6C4). (2) All its spots lie within a single box (R7C6 and R8C6).
(1) 1 is therefore removed from the rest of the box. (2) 6 is therefore removed from the rest of 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.
R2C9 is seen by both free ends: 1 is therefore eliminated there.
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.
R7C5 is seen by both free ends: 3 is therefore eliminated there.
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.
R7C5 is seen by both free ends: 9 is therefore eliminated there.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 8.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 6.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 1.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 8.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 9.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 1.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 3.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 6.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 9.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 9.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R1C5 = 9.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R4C3 = 1.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C3 = 6.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R6C4 = 1.
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.
R2C5 and R5C4 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 1.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 3.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 3.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 3.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 1.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 6.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 7.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 7.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 1.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 6.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 3.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 7.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 8.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 6.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 3.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 7.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 8.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 3.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 6.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 8.