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 box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C7 = 4.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R1C8 = 5.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R2C1 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C3 = 5.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R4C6 = 4.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R4C7 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C1 = 5.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R6C2 = 4.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R6C4 = 2.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R6C9 = 6.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C8 = 4.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R9C1 = 2.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R9C8 = 8.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 9.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 7.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R9C5 = 4.
Spot R8C5 and R8C7 on this row.
These two cells can only hold 7 and 9: they reserve those digits.
7 and 9 are therefore removed from the other cells of the row.
Find where 1 and 2 can go on this column.
These two digits only fit in R1C5 and R7C5 on the column.
The other candidates in R1C5 and R7C5 are therefore eliminated.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R1C4 = 6.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R1C5 = 1.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R7C4 = 1.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C5 = 2.
(1) Look at where 8 can go in this box. (2) Look at where 3 can go in this box. (3) Look at where 9 can go in this box.
(1) All its spots lie on a single row (R2C4 and R2C5). (2) All its spots lie on a single column (R4C8 and R5C8). (3) All its spots lie on a single column (R7C2 and R9C2).
(1) 8 is therefore removed from that row outside the box. (2) 3 is therefore removed from that column outside the box. (3) 9 is therefore removed from that column outside the box.
Spot R2C9 and R7C9 on this column.
These two cells can only hold 7 and 9: they reserve those digits.
7 and 9 are therefore removed from the other cells of the column.
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.
R3C6 is seen by both free ends: 7 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.
R2C5 is seen by both free ends: 7 is therefore eliminated there.
Find 7 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 7.
R1C6 is seen by both free ends: 7 is therefore eliminated there.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R2C4 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C5 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C7 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C9 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C7 = 9.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 9.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 1.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 1.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C1 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C6 = 9.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C1 = 9.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R3C6 = 2.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R4C1 = 1.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R4C2 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R4C4 = 8.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C4 = 5.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R5C6 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C6 = 5.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C1 = 6.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C2 = 5.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R9C4 = 9.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 3.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 9.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 9.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 3.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 3.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 8.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 3.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 6.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 3.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 8.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 6.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 9.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 3.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 8.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 6.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 2.