Step-by-step solution
Steps 68
Estimated time 70 – 105 min
Hardest technique Box/Line
Clues 24
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 1.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 7.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 2.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 8.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C2 = 4.
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 box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C2 = 6.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R3C7 = 5.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R4C4 = 5.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R4C6 = 2.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R4C7 = 4.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R5C2 = 7.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R5C9 = 6.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C1 = 6.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C2 = 5.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R6C4 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C1 = 7.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R7C2 = 2.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R7C5 = 4.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R7C8 = 6.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C1 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C4 = 7.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R8C8 = 2.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C9 = 5.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 3.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 1.
Look at cell R8C6.
Every other digit already appears in its row, column or box.
Only one option remains: R8C6 = 6.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C4 = 6.
(1) Spot R2C2 and R2C5 on this row. (2) Spot R3C3 and R6C3 on this column.
(1) These two cells can only hold 3 and 9: they reserve those digits. (2) These two cells can only hold 3 and 8: they reserve those digits.
(1) 3 and 9 are therefore removed from the other cells of the row. (2) 3 and 8 are therefore removed from the other cells of the column.
(1) Look at where 9 can go in this box. (2) Look at where 1 can go in this box.
(1) All its spots lie on a single row (R4C1 and R4C2). (2) All its spots lie on a single row (R6C8 and R6C9).
(1) 9 is therefore removed from that row outside the box. (2) 1 is therefore removed from that row outside the box.
Look at where 3 can go on this row.
All its spots lie within a single box (R5C4, R5C5 and R5C6).
3 is therefore removed from the rest of the box.
Find 3 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 3.
R3C8 is seen by both free ends: 3 is therefore eliminated there.
Look at where 3 can go in this box.
All its spots lie on a single row (R1C8 and R1C9).
3 is therefore removed from that row outside the box.
Spot R1C1, R1C6 and R1C7 on this row.
These three cells share only 1, 8 and 9.
1, 8 and 9 are therefore removed from the rest of the row.
Find 9 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 9.
R1C6 is seen by both free ends: 9 is therefore eliminated there.
Spot R1C6 and R2C4 in this box.
These two cells can only hold 1 and 8: they reserve those digits.
1 and 8 are therefore removed from the other cells of the box.
Spot R3C4 and R7C4 on this column.
These two cells can only hold 3 and 9: they reserve those digits.
3 and 9 are therefore removed from the other cells of the column.
Find 8 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 8.
R1C6 and R2C8 is seen by both free ends: 8 is therefore eliminated there.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 1.
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 = 1.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R3C1 = 1.
Find 8 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 8.
R3C8 and R5C7 is seen by both free ends: 8 is therefore eliminated there.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 9.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 9.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 8.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 3.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 3.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 8.
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 = 9.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 3.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 9.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 3.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 9.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 8.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 8.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 9.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 3.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 3.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 1.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 7.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 1.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 2.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 8.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 2.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 3.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 7.