Step-by-step solution
Steps 68
Estimated time 70 – 105 min
Hardest technique Box/Line
Clues 22
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R1C1 = 2.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R1C9 = 1.
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 R5C7 = 1.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R6C1 = 5.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C2 = 6.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R9C5 = 1.
(1) Spot R3C2 and R3C9 on this row. (2) Spot R5C6 and R6C6 on this column. (3) Spot R5C6 and R6C6 in this box.
(1) These two cells can only hold 7 and 9: they reserve those digits. (2) These two cells can only hold 2 and 3: they reserve those digits. (3) These two cells can only hold 2 and 3: they reserve those digits.
(1) 7 and 9 are therefore removed from the other cells of the row. (2) 2 and 3 are therefore removed from the other cells of the column. (3) 2 and 3 are therefore removed from the other cells of the box.
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 row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R5C6 = 2.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R6C6 = 3.
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.
Find where 1 and 8 can go in this box.
These two digits only fit in R7C2 and R7C3 in the box.
The other candidates in R7C2 and R7C3 are therefore eliminated.
Spot R7C2 and R7C3 on this row.
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 row.
(1) Look at where 6 can go in this box. (2) Look at where 4 can go in this box. (3) Look at where 3 can go in this box. (4) Look at where 9 can go in this box.
(1) All its spots lie on a single column (R1C7 and R2C7). (2) All its spots lie on a single row (R8C2 and R8C3). (3) All its spots lie on a single column (R7C4, R8C4 and R9C4). (4) All its spots lie on a single column (R7C4, R8C4 and R9C4).
(1) 6 is therefore removed from that column outside the box. (2) 4 is therefore removed from that row outside the box. (3) 3 is therefore removed from that column outside the box. (4) 9 is therefore removed from that column outside the box.
(1) Spot R9C7 and R9C8 on this row. (2) Spot R9C7 and R9C8 in this box.
(1) These two cells can only hold 8 and 9: they reserve those digits. (2) These two cells can only hold 8 and 9: they reserve those digits.
(1) 8 and 9 are therefore removed from the other cells of the row. (2) 8 and 9 are therefore removed from the other cells of the box.
Find where 2 and 4 can go on this column.
These two digits only fit in R6C7 and R7C7 on the column.
The other candidates in R6C7 and R7C7 are therefore eliminated.
Find where 4, 7 and 8 can go on this column.
These three digits only fit in R1C4, R4C4 and R5C4.
The other candidates in R1C4, R4C4 and R5C4 are therefore eliminated.
(1) Find where 5 and 6 can go on this row. (2) Find where 5 and 6 can go in this box.
(1) These two digits only fit in R4C5 and R4C6 on the row. (2) These two digits only fit in R4C5 and R4C6 in the box.
(1) The other candidates in R4C5 and R4C6 are therefore eliminated. (2) The other candidates in R4C5 and R4C6 are therefore eliminated.
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.
R2C4 is seen by both free ends: 5 is therefore eliminated there.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 6.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 3.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 6.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R1C7 = 6.
Scan the empty cells in this column where 6 could go.
Across the whole column, 6 has only one possible spot left.
So R4C5 = 6.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R4C6 = 5.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R7C6 = 6.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C8 = 5.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R8C1 = 6.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C7 = 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 R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 5.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 3.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 3.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 2.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 9.
Look at cell R7C7.
Every other digit already appears in its row, column or box.
Only one option remains: R7C7 = 4.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 2.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R1C8 = 7.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R2C7 = 5.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C2 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R3C7 = 8.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R3C9 = 9.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R4C8 = 9.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R6C5 = 9.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R6C8 = 4.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R6C9 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R9C7 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C8 = 8.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 3.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 5.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 3.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 5.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 8.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 1.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 9.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 4.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 8.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 8.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 9.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 4.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 4.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 1.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 7.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 4.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 3.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 7.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 8.