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 box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C2 = 7.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R1C7 = 2.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R2C6 = 5.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R3C1 = 3.
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 column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R6C4 = 3.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R6C9 = 7.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R7C1 = 2.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C6 = 7.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R7C9 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C1 = 7.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R9C4 = 2.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R9C8 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C9 = 5.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 1.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R4C9 = 3.
Spot R9C2 and R9C3 in this box.
These two cells can only hold 6 and 9: they reserve those digits.
6 and 9 are therefore removed from the other cells of the box.
Find where 2 and 6 can go on this row.
These two digits only fit in R4C6 and R4C8 on the row.
The other candidates in R4C6 and R4C8 are therefore eliminated.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R4C8 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R5C6 = 2.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R5C8 = 1.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 6.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R4C1 = 1.
Find where 4 and 5 can go on this row.
These two digits only fit in R5C3 and R5C4 on the row.
The other candidates in R5C3 and R5C4 are therefore eliminated.
(1) Look at where 4 can go in this box. (2) Look at where 5 can go in this box. (3) Look at where 8 can go in this box.
(1) All its spots lie on a single row (R3C4 and R3C6). (2) All its spots lie on a single column (R5C3 and R6C3). (3) All its spots lie on a single column (R4C5 and R6C5).
(1) 4 is therefore removed from that row outside the box. (2) 5 is therefore removed from that column outside the box. (3) 8 is therefore removed from that column outside the box.
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.
R2C8 is seen by both free ends: 9 is therefore eliminated there.
Look at where 9 can go in this box.
All its spots lie on a single column (R1C9 and R3C9).
9 is therefore removed from that column outside the box.
Look at where 9 can go on this row.
All its spots lie within a single box (R2C1, R2C2 and R2C3).
9 is therefore removed from the rest of the box.
Find where 6 and 9 can go on this column.
These two digits only fit in R2C2 and R9C2 on the column.
The other candidates in R2C2 and R9C2 are therefore eliminated.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C5 = 9.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R2C3 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R3C6 = 4.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C9 = 9.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R4C2 = 4.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R4C5 = 8.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C3 = 5.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R5C4 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C5 = 5.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C5 = 4.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C6 = 9.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 1.
Find 8 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 8.
R1C3 and R5C1 is seen by both free ends: 8 is therefore eliminated there.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 9.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 8.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 9.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 3.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 1.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 6.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 8.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 8.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 9.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 6.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 1.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 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 R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 8.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 6.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 3.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 6.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 9.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 1.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 8.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 5.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 6.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 9.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 8.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 5.