Step-by-step solution
Steps 66
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 R1C9 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R2C2 = 7.
Scan the empty cells in this column where 7 could go.
Across the whole column, 7 has only one possible spot left.
So R4C1 = 7.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R4C3 = 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.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R6C7 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C3 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C8 = 8.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R9C2 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R9C7 = 5.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R1C4 = 5.
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 column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R3C2 = 5.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R3C3 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C7 = 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 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C7 = 9.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R7C9 = 6.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R9C3 = 1.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R9C9 = 3.
Scan the empty cells in this row where 2 could go.
Across the whole row, 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 R5C4 = 2.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R5C6 = 7.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C4 = 7.
(1) Find where 3 and 6 can go on this column. (2) Find where 1 and 2 can go in this box.
(1) These two digits only fit in R2C5 and R6C5 on the column. (2) These two digits only fit in R3C8 and R3C9 in the box.
(1) The other candidates in R2C5 and R6C5 are therefore eliminated. (2) The other candidates in R3C8 and R3C9 are therefore eliminated.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R4C5 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R6C2 = 1.
Spot R3C8 and R3C9 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 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.
R9C5 is seen by both free ends: 9 is therefore eliminated there.
Find where 9 appears on two columns: altogether, only two rows are involved (R1C3, R5C3, R1C5 and R5C5).
On each covered row, 9 must lie within one of these two columns.
9 is therefore removed from those two rows outside the two X-Wing columns.
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.
R3C4 is seen by both free ends: 9 is therefore eliminated there.
Find where 9 appears on two rows: altogether, only two columns are involved (R3C1, R3C6, R9C1 and R9C6).
On each covered column, 9 must lie within one of these two rows.
9 is therefore removed from those two columns outside the two X-Wing rows.
Find where 8 and 9 can go on this column.
These two digits only fit in R3C6 and R9C6 on the column.
The other candidates in R3C6 and R9C6 are therefore eliminated.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C7 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R2C7 = 4.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R3C7 = 6.
Find 4 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 4.
R3C1 is seen by both free ends: 4 is therefore eliminated there.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 9.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 8.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 4.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 8.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 9.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 4.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 9.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 4.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 9.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 4.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 6.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 9.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 1.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 4.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 3.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 6.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 1.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 2.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 8.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 9.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 3.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 4.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 4.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 1.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 2.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 1.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 4.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 8.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 9.