Step-by-step solution
Steps 65
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 3 could go.
Across the whole row, 3 has only one possible spot left.
So R3C2 = 3.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R3C5 = 8.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R5C1 = 2.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R5C3 = 8.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C1 = 5.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R8C3 = 1.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R8C7 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R9C5 = 3.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R5C6 = 3.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R6C8 = 3.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R8C8 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R9C8 = 6.
(1) Look at where 1 can go in this box. (2) Look at where 6 can go in this box. (3) Look at where 4 can go in this box. (4) Look at where 5 can go in this box. (5) Look at where 6 can go in this box. (6) Look at where 2 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 row (R6C1, R6C2 and R6C3). (3) All its spots lie on a single column (R5C5 and R6C5). (4) All its spots lie on a single column (R5C9 and R6C9). (5) All its spots lie on a single row (R7C1 and R7C2). (6) All its spots lie on a single column (R7C9 and R8C9).
(1) 1 is therefore removed from that row outside the box. (2) 6 is therefore removed from that row outside the box. (3) 4 is therefore removed from that column outside the box. (4) 5 is therefore removed from that column outside the box. (5) 6 is therefore removed from that row outside the box. (6) 2 is therefore removed from that column outside the box.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 6.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R5C4 = 6.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R5C9 = 5.
Spot R1C6, R1C8 and R1C9 on this row.
These three cells share only 2, 4 and 7.
2, 4 and 7 are therefore removed from the rest of the row.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R2C2 = 2.
Look at where 4 can go in this box.
All its spots lie on a single row (R3C1 and R3C3).
4 is therefore removed from that row outside the box.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 5.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 8.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 1.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 4.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R2C1 = 8.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R4C8 = 1.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R8C6 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R9C1 = 4.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R9C2 = 8.
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 box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R4C2 = 4.
Spot R7C1 and R7C2 on this row.
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 row.
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.
R3C8 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.
R6C3 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.
R3C4 is seen by both free ends: 7 is therefore eliminated there.
Find where 5 and 7 can go on this column.
These two digits only fit in R4C4 and R6C4 on the column.
The other candidates in R4C4 and R6C4 are therefore eliminated.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C8 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C9 = 7.
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 R3C6 = 7.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R3C8 = 2.
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 7 could go.
Across the whole box, 7 has only one possible spot left.
So R5C8 = 7.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R6C5 = 1.
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 box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C5 = 7.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 2.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 7.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 9.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 1.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 5.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 7.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 5.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 6.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 9.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 1.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 2.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 9.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 9.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 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 R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 7.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 6.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 9.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 2.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 5.