Step-by-step solution
Steps 71
Estimated time 116 – 174 min
Hardest technique X-Wing
Clues 23
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R1C2 = 4.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R4C6 = 1.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R5C5 = 7.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R6C8 = 7.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R7C1 = 7.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R7C8 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R8C1 = 1.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R1C6 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R2C8 = 2.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R3C2 = 2.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R3C6 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R7C2 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R9C8 = 3.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R9C9 = 2.
Spot R8C2 and R8C8 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.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 5.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R7C6 = 5.
(1) Find where 2 and 4 can go on this column. (2) Find where 1 and 7 can go on this column. (3) Find where 1 and 7 can go in this box. (4) Find where 2 and 4 can go in this box.
(1) These two digits only fit in R4C1 and R5C1 on the column. (2) These two digits only fit in R1C3 and R3C3 on the column. (3) These two digits only fit in R1C3 and R3C3 in the box. (4) These two digits only fit in R4C1 and R5C1 in the box.
(1) The other candidates in R4C1 and R5C1 are therefore eliminated. (2) The other candidates in R1C3 and R3C3 are therefore eliminated. (3) The other candidates in R1C3 and R3C3 are therefore eliminated. (4) The other candidates in R4C1 and R5C1 are therefore eliminated.
(1) Look at where 6 can go in this box. (2) Look at where 3 can go in this box. (3) Look at where 3 can go in this box.
(1) All its spots lie on a single column (R1C1 and R3C1). (2) All its spots lie on a single row (R1C7 and R1C9). (3) All its spots lie on a single column (R4C3 and R5C3).
(1) 6 is therefore removed from that column outside the box. (2) 3 is therefore removed from that row outside the box. (3) 3 is therefore removed from that column outside the box.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R2C1 = 3.
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.
R4C3 is seen by both free ends: 6 is therefore eliminated there.
Find 6 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 6.
R6C6 is seen by both free ends: 6 is therefore eliminated there.
Look at where 6 can go on this row.
All its spots lie within a single box (R6C2 and R6C3).
6 is therefore removed from the rest of the box.
Find where 5 and 6 can go on this column.
These two digits only fit in R6C3 and R9C3 on the column.
The other candidates in R6C3 and R9C3 are therefore eliminated.
Find 6 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 6.
R5C9 is seen by both free ends: 6 is therefore eliminated there.
Look at where 6 can go in this box.
All its spots lie on a single row (R4C8 and R4C9).
6 is therefore removed from that row outside the box.
Find where 5 and 6 can go on this column.
These two digits only fit in R1C5 and R3C5 on the column.
The other candidates in R1C5 and R3C5 are therefore eliminated.
Spot R1C5 and R3C5 in this box.
These two cells can only hold 5 and 6: they reserve those digits.
5 and 6 are therefore removed from the other cells of 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.
R6C6 is seen by both free ends: 9 is therefore eliminated there.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 8.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 4.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 8.
Spot R6C1 and R9C1 on this column.
These two cells can only hold 5 and 9: they reserve those digits.
5 and 9 are therefore removed from the other cells of the column.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 9.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 4.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 9.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 6.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 9.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 8.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 4.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 6.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 9.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 6.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 5.
Look at cell R9C3.
Every other digit already appears in its row, column or box.
Only one option remains: R9C3 = 6.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 8.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 2.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 3.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 9.
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 = 5.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 9.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 9.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 5.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 4.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 3.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 2.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 6.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 8.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 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 R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 3.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 9.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 6.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 7.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 5.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 8.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 8.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 1.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 7.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 6.