Step-by-step solution
Steps 65
Estimated time 65 – 98 min
Hardest technique Box/Line
Clues 23
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 R1C4 = 3.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R4C2 = 5.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C9 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C2 = 3.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R5C5 = 8.
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 3 could go.
Across the whole box, 3 has only one possible spot left.
So R6C5 = 3.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C8 = 5.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C3 = 8.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R7C8 = 3.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R9C8 = 2.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C9 = 8.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 8.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R1C3 = 5.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R2C2 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R3C2 = 2.
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 8 could go.
Across the whole column, 8 has only one possible spot left.
So R3C6 = 8.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R4C4 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R6C3 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C1 = 2.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R8C5 = 2.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 7.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 1.
Spot R4C6 and R5C4 in this box.
These two cells can only hold 4 and 6: they reserve those digits.
4 and 6 are therefore removed from the other cells of the box.
Spot R6C6 and R7C6 on this column.
These two cells can only hold 7 and 9: they reserve those digits.
7 and 9 are therefore removed from the other cells of the column.
Find where 1 and 4 can go in this box.
These two digits only fit in R8C6 and R9C4 in the box.
The other candidates in R8C6 and R9C4 are therefore eliminated.
Look at where 9 can go in this box.
All its spots lie on a single row (R2C4 and R2C5).
9 is therefore removed from that row outside the box.
Find where 6 appears on two rows: altogether, only two columns are involved (R2C1, R2C4, R5C1 and R5C4).
On each covered column, 6 must lie within one of these two rows.
6 is therefore removed from those two columns outside the two X-Wing rows.
Look at where 6 can go on this row.
All its spots lie within a single box (R3C7 and R3C9).
6 is therefore removed from the rest of the box.
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.
R5C4 and R8C6 is seen by both free ends: 4 is therefore eliminated there.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 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 R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 4.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 6.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 4.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 6.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 4.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 1.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 6.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 4.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 7.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 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 R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 7.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 1.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 6.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 7.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 5.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 4.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 7.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 1.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 9.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 5.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 9.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 5.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 7.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 1.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 7.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 9.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 9.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 7.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 9.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 5.