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 box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R6C7 = 4.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R8C4 = 1.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R8C5 = 2.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R8C9 = 4.
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.
Find where 6 and 8 can go on this row.
These two digits only fit in R9C1 and R9C7 on the row.
The other candidates in R9C1 and R9C7 are therefore eliminated.
(1) Look at where 5 can go in this box. (2) Look at where 3 can go in this box. (3) Look at where 7 can go in this box. (4) Look at where 3 can go in this box.
(1) All its spots lie on a single row (R3C4 and R3C5). (2) All its spots lie on a single row (R4C7 and R4C9). (3) All its spots lie on a single column (R5C8 and R6C8). (4) All its spots lie on a single row (R7C4 and R7C5).
(1) 5 is therefore removed from that row outside the box. (2) 3 is therefore removed from that row outside the box. (3) 7 is therefore removed from that column outside the box. (4) 3 is therefore removed from that row outside the box.
Spot R7C3 and R7C8 on this row.
These two cells can only hold 8 and 9: they reserve those digits.
8 and 9 are therefore removed from the other cells of the row.
Find where 5 and 7 can go in this box.
These two digits only fit in R8C7 and R9C9 in the box.
The other candidates in R8C7 and R9C9 are therefore eliminated.
Look at where 9 can go in this box.
All its spots lie on a single column (R7C8 and R8C8).
9 is therefore removed from that column outside the box.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 1.
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 column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R4C9 = 1.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R6C6 = 1.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 9.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 8.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R6C4 = 8.
(1) Spot R1C7 and R8C7 on this column. (2) Spot R5C8 and R6C8 on this column. (3) Spot R2C6 and R3C6 in this box.
(1) These two cells can only hold 5 and 7: they reserve those digits. (2) These two cells can only hold 2 and 7: they reserve those digits. (3) These two cells can only hold 3 and 7: they reserve those digits.
(1) 5 and 7 are therefore removed from the other cells of the column. (2) 2 and 7 are therefore removed from the other cells of the column. (3) 3 and 7 are therefore removed from the other cells of the box.
(1) Find where 2 and 8 can go on this row. (2) Find where 1 and 4 can go on this column.
(1) These two digits only fit in R2C1 and R2C7 on the row. (2) These two digits only fit in R3C1 and R5C1 on the column.
(1) The other candidates in R2C1 and R2C7 are therefore eliminated. (2) The other candidates in R3C1 and R5C1 are therefore eliminated.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R2C1 = 2.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R2C4 = 6.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C7 = 8.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R3C1 = 4.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R3C2 = 1.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R3C3 = 8.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R3C7 = 2.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C8 = 6.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R4C1 = 6.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R5C1 = 1.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R5C3 = 4.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R5C5 = 6.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R5C8 = 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 7 could go.
Across the whole box, 7 has only one possible spot left.
So R6C8 = 7.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C3 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R7C8 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C3 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C8 = 9.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R9C1 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R9C7 = 6.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 3.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 2.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 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 R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 3.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R7C4 = 3.
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.
Spot R3C4 and R3C5 on this row.
These two cells can only hold 5 and 9: they reserve those digits.
5 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.
R8C2 is seen by both free ends: 7 is therefore eliminated there.
Look at cell R8C2.
Every other digit already appears in its row, column or box.
Only one option remains: R8C2 = 5.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 7.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 5.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 5.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 9.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 7.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 5.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 9.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 7.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 9.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 7.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 7.
Look at cell R2C6.
Every other digit already appears in its row, column or box.
Only one option remains: R2C6 = 3.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 9.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 5.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 9.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 7.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 3.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 5.