Step-by-step solution
Steps 67
Estimated time 68 – 102 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 8 could go.
Across the whole box, 8 has only one possible spot left.
So R1C1 = 8.
Scan the empty cells in this row where 2 could go.
Across the whole row, 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 R1C9 = 6.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R2C9 = 4.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R3C1 = 4.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R3C3 = 6.
Scan the empty cells in this row where 4 could go.
Across the whole row, 4 has only one possible spot left.
So R5C4 = 4.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R6C2 = 3.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R7C2 = 2.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R9C7 = 3.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R2C6 = 3.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R3C9 = 3.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R4C5 = 3.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R7C1 = 3.
(1) Spot R8C1 and R8C9 on this row. (2) Spot R5C9 and R8C9 on this column.
(1) These two cells can only hold 1 and 5: they reserve those digits. (2) These two cells can only hold 1 and 5: they reserve those digits.
(1) 1 and 5 are therefore removed from the other cells of the row. (2) 1 and 5 are therefore removed from the other cells of the column.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 6.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R5C1 = 6.
(1) Find where 6 and 7 can go on this column. (2) Find where 6 and 7 can go in this box.
(1) These two digits only fit in R4C8 and R6C8 on the column. (2) These two digits only fit in R4C8 and R6C8 in the box.
(1) The other candidates in R4C8 and R6C8 are therefore eliminated. (2) The other candidates in R4C8 and R6C8 are therefore eliminated.
Look at where 7 can go in this box.
All its spots lie on a single column (R2C2 and R3C2).
7 is therefore removed from that column outside the box.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R2C4 = 7.
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 2 could go.
Across the whole box, 2 has only one possible spot left.
So R4C6 = 2.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R5C5 = 7.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R5C7 = 2.
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 7 could go.
Across the whole box, 7 has only one possible spot left.
So R8C6 = 7.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R2C8 = 8.
Look at where 5 can go in this box.
All its spots lie on a single row (R6C5 and R6C6).
5 is therefore removed from that row outside the box.
(1) Look at where 9 can go on this column. (2) Look at where 8 can go on this column.
(1) All its spots lie within a single box (R1C2 and R2C2). (2) All its spots lie within a single box (R4C4 and R6C4).
(1) 9 is therefore removed from the rest of the box. (2) 8 is therefore removed from the rest of the box.
Find 1 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 1.
R4C1 and R6C1 is seen by both free ends: 1 is therefore eliminated there.
(1) Look at where 1 can go on this row. (2) Look at where 1 can go on this column.
(1) All its spots lie within a single box (R6C4, R6C5 and R6C6). (2) All its spots lie within a single box (R8C1 and R9C1).
(1) 1 is therefore removed from the rest of the box. (2) 1 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.
R4C1 is seen by both free ends: 5 is therefore eliminated there.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R4C3 = 5.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R4C7 = 1.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R5C9 = 5.
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 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C8 = 5.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R8C1 = 5.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R9C1 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R9C5 = 9.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 1.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 1.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 1.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 1.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 1.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 4.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 5.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 6.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 4.
Look at cell R9C6.
Every other digit already appears in its row, column or box.
Only one option remains: R9C6 = 8.
Look at cell R3C5.
Every other digit already appears in its row, column or box.
Only one option remains: R3C5 = 8.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 5.
Look at cell R3C7.
Every other digit already appears in its row, column or box.
Only one option remains: R3C7 = 9.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 8.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 9.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 1.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 6.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 7.
Look at cell R6C9.
Every other digit already appears in its row, column or box.
Only one option remains: R6C9 = 8.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 9.
Look at cell R1C6.
Every other digit already appears in its row, column or box.
Only one option remains: R1C6 = 1.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 5.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 7.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 6.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 9.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 5.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 9.