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 box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R1C1 = 6.
Scan the empty cells in this column where 8 could go.
Across the whole column, 8 has only one possible spot left.
So R1C2 = 8.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R1C5 = 5.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R2C4 = 3.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R3C4 = 8.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R3C6 = 1.
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 8 could go.
Across the whole column, 8 has only one possible spot left.
So R4C8 = 8.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R4C9 = 4.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R5C5 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C4 = 6.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R6C6 = 2.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R7C6 = 8.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 7.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 4.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 9.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 4.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R7C7 = 6.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C6 = 6.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R8C7 = 1.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R9C6 = 4.
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.
Look at cell R8C5.
Every other digit already appears in its row, column or box.
Only one option remains: R8C5 = 7.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 1.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R1C8 = 2.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R4C2 = 6.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R4C3 = 3.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R6C7 = 3.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R7C1 = 1.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R7C2 = 4.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R8C1 = 3.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R9C3 = 6.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R2C3 = 2.
(1) Look at where 2 can go in this box. (2) Look at where 9 can go in this box. (3) Look at where 2 can go in this box.
(1) All its spots lie on a single column (R4C1 and R5C1). (2) All its spots lie on a single row (R9C1 and R9C2). (3) All its spots lie on a single column (R8C9 and R9C9).
(1) 2 is therefore removed from that column outside the box. (2) 9 is therefore removed from that row outside the box. (3) 2 is therefore removed from that column outside the box.
Look at where 7 can go on this column.
All its spots lie within a single box (R7C9 and R9C9).
7 is therefore removed from the rest of the box.
Find 5 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 5.
R5C9 and R7C8 is seen by both free ends: 5 is therefore eliminated there.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 9.
Look at cell R7C8.
Every other digit already appears in its row, column or box.
Only one option remains: R7C8 = 9.
Spot R3C3 and R3C8 on this row.
These two cells can only hold 5 and 7: they reserve those digits.
5 and 7 are therefore removed from the other cells of the row.
Find where 5 appears on two columns: altogether, only two rows are involved (R2C1, R5C1, R2C7 and R5C7).
On each covered row, 5 must lie within one of these two columns.
5 is therefore removed from those two rows outside the two X-Wing columns.
Spot R2C2 and R2C6 on this row.
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 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.
R2C2 is seen by both free ends: 7 is therefore eliminated there.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 9.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 7.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 4.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 9.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 9.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 7.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 5.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 4.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 7.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 5.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 2.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 2.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 5.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 7.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 5.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 7.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 2.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 5.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 7.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 2.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 7.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 5.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 9.