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 box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R1C4 = 5.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R1C8 = 3.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C8 = 5.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R2C9 = 1.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R3C2 = 4.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R3C3 = 3.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R4C3 = 9.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C5 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C1 = 3.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R5C6 = 5.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C8 = 1.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C3 = 5.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R7C2 = 5.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C3 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C7 = 5.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R9C4 = 3.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R1C5 = 4.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C5 = 9.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R4C4 = 1.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R7C5 = 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.
(1) Find where 4 and 6 can go on this column. (2) Find where 2 and 9 can go on this column. (3) Find where 4 and 6 can go in this box. (4) Find where 2 and 9 can go in this box.
(1) These two digits only fit in R5C4 and R6C4 on the column. (2) These two digits only fit in R8C9 and R9C9 on the column. (3) These two digits only fit in R5C4 and R6C4 in the box. (4) These two digits only fit in R8C9 and R9C9 in the box.
(1) The other candidates in R5C4 and R6C4 are therefore eliminated. (2) The other candidates in R8C9 and R9C9 are therefore eliminated. (3) The other candidates in R5C4 and R6C4 are therefore eliminated. (4) The other candidates in R8C9 and R9C9 are therefore eliminated.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R9C8 = 4.
(1) Look at where 2 can go in this box. (2) Look at where 2 can go in this box. (3) Look at where 6 can go in this box.
(1) All its spots lie on a single row (R2C1, R2C2 and R2C3). (2) All its spots lie on a single column (R5C5 and R6C5). (3) All its spots lie on a single row (R7C7 and R7C8).
(1) 2 is therefore removed from that row outside the box. (2) 2 is therefore removed from that column outside the box. (3) 6 is therefore removed from that row outside the box.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R3C4 = 2.
Look at where 2 can go on this row.
All its spots lie within a single box (R7C1 and R7C3).
2 is therefore removed from the rest of the box.
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.
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.
R3C7 is seen by both free ends: 7 is therefore eliminated there.
Look at where 7 can go in this box.
All its spots lie on a single column (R1C9 and R3C9).
7 is therefore removed from that column outside the box.
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.
R7C4 and R8C8 is seen by both free ends: 7 is therefore eliminated there.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 8.
Find where 8 appears on two columns: altogether, only two rows are involved (R4C2, R9C2, R4C6 and R9C6).
On each covered row, 8 must lie within one of these two columns.
8 is therefore removed from those two rows outside the two X-Wing columns.
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 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C4 = 8.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R3C7 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C9 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C6 = 8.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 8.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 6.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 7.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 7.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 6.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 7.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 9.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 7.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 6.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 7.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 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 R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 6.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 2.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 7.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 8.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 2.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 8.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 4.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 6.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 4.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 2.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 8.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 2.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 8.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 9.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 6.