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)
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R3C3 = 4.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R5C7 = 9.
Spot R4C1 and R4C8 on this row.
These two cells can only hold 1 and 2: they reserve those digits.
1 and 2 are therefore removed from the other cells of the row.
Find where 4 and 6 can go on this column.
These two digits only fit in R5C1 and R8C1 on the column.
The other candidates in R5C1 and R8C1 are therefore eliminated.
(1) Look at where 7 can go in this box. (2) Look at where 3 can go in this box. (3) Look at where 1 can go in this box.
(1) All its spots lie on a single row (R1C2 and R1C3). (2) All its spots lie on a single column (R5C3 and R6C3). (3) All its spots lie on a single column (R4C8, R5C8 and R6C8).
(1) 7 is therefore removed from that row outside the box. (2) 3 is therefore removed from that column outside the box. (3) 1 is therefore removed from that column outside the box.
(1) Look at where 2 can go on this column. (2) Look at where 3 can go on this column.
(1) All its spots lie within a single box (R7C7, R8C7 and R9C7). (2) All its spots lie within a single box (R8C7 and R9C7).
(1) 2 is therefore removed from the rest of the box. (2) 3 is therefore removed from the rest of the box.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 8.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 5.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R1C2 = 9.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C3 = 7.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R1C8 = 8.
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 box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C8 = 9.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R5C2 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C2 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C8 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R9C4 = 7.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 8.
Find 2 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 2.
R7C3 and R9C6 is seen by both free ends: 2 is therefore eliminated there.
Find 2 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 2.
R1C1 is seen by both free ends: 2 is therefore eliminated there.
Look at where 2 can go in this box.
All its spots lie on a single row (R2C1 and R2C2).
2 is therefore removed from that row outside the box.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R4C5 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R4C6 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R5C4 = 8.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R7C4 = 2.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C5 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C6 = 8.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 3.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 2.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 1.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 1.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 3.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 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 R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 2.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 6.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 4.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 4.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 6.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 1.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 5.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 2.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 3.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 2.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 6.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 1.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 4.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 3.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 2.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 1.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 4.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 6.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 5.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 3.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 2.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 6.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 1.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 3.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 1.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 6.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 3.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 4.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 5.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 1.