Step-by-step solution
Steps 66
Estimated time 68 – 102 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 3 could go.
Across the whole box, 3 has only one possible spot left.
So R1C4 = 3.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R1C6 = 6.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R2C7 = 6.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R4C5 = 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 5 could go.
Across the whole box, 5 has only one possible spot left.
So R7C7 = 5.
Scan the empty cells in this row where 7 could go.
Across the whole row, 7 has only one possible spot left.
So R7C9 = 7.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R8C6 = 8.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R9C5 = 6.
Scan the empty cells in this row where 8 could go.
Across the whole row, 8 has only one possible spot left.
So R4C1 = 8.
Scan the empty cells in this column where 3 could go.
Across the whole column, 3 has only one possible spot left.
So R4C7 = 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.
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 4 could go.
Across the whole box, 4 has only one possible spot left.
So R9C8 = 4.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R9C9 = 3.
(1) Spot R3C1 and R3C9 on this row. (2) Spot R7C2 and R7C6 on this row. (3) Spot R7C6 and R9C4 in this box.
(1) These two cells can only hold 2 and 5: they reserve those digits. (2) These two cells can only hold 2 and 9: they reserve those digits. (3) These two cells can only hold 2 and 9: they reserve those digits.
(1) 2 and 5 are therefore removed from the other cells of the row. (2) 2 and 9 are therefore removed from the other cells of the row. (3) 2 and 9 are therefore removed from the other cells of the box.
(1) Find where 4 and 8 can go on this row. (2) Find where 7 and 8 can go on this column. (3) Find where 7 and 8 can go in this box. (4) Find where 4 and 8 can go in this box.
(1) These two digits only fit in R5C4 and R5C5 on the row. (2) These two digits only fit in R1C8 and R2C8 on the column. (3) These two digits only fit in R1C8 and R2C8 in the box. (4) These two digits only fit in R5C4 and R5C5 in the box.
(1) The other candidates in R5C4 and R5C5 are therefore eliminated. (2) The other candidates in R1C8 and R2C8 are therefore eliminated. (3) The other candidates in R1C8 and R2C8 are therefore eliminated. (4) The other candidates in R5C4 and R5C5 are therefore eliminated.
(1) Look at where 5 can go in this box. (2) Look at where 5 can go in this box. (3) Look at where 1 can go in this box.
(1) All its spots lie on a single column (R1C5 and R2C5). (2) All its spots lie on a single column (R1C9, R2C9 and R3C9). (3) All its spots lie on a single row (R6C4 and R6C5).
(1) 5 is therefore removed from that column outside the box. (2) 5 is therefore removed from that column outside the box. (3) 1 is therefore removed from that row outside the box.
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.
R6C2 is seen by both free ends: 9 is therefore eliminated there.
Look at where 9 can go in this box.
All its spots lie on a single column (R4C3 and R6C3).
9 is therefore removed from that column outside the box.
Find where 4 and 9 can go on this row.
These two digits only fit in R2C1 and R2C9 on the row.
The other candidates in R2C1 and R2C9 are therefore eliminated.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R2C5 = 5.
Find 2 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 2.
R1C1 and R3C1 is seen by both free ends: 2 is therefore eliminated there.
Look at cell R3C1.
Every other digit already appears in its row, column or box.
Only one option remains: R3C1 = 5.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 2.
Look at cell R4C9.
Every other digit already appears in its row, column or box.
Only one option remains: R4C9 = 1.
Look at cell R8C9.
Every other digit already appears in its row, column or box.
Only one option remains: R8C9 = 9.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 9.
Look at cell R2C9.
Every other digit already appears in its row, column or box.
Only one option remains: R2C9 = 4.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 2.
Look at cell R8C8.
Every other digit already appears in its row, column or box.
Only one option remains: R8C8 = 1.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 5.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 9.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 2.
Look at cell R9C4.
Every other digit already appears in its row, column or box.
Only one option remains: R9C4 = 9.
Look at cell R5C1.
Every other digit already appears in its row, column or box.
Only one option remains: R5C1 = 1.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 9.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 2.
Look at cell R1C1.
Every other digit already appears in its row, column or box.
Only one option remains: R1C1 = 4.
Scan the empty cells in this row where 1 could go.
Across the whole row, 1 has only one possible spot left.
So R1C3 = 1.
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 8 could go.
Across the whole box, 8 has only one possible spot left.
So R2C8 = 8.
Spot R6C4 and R6C5 on this row.
These two cells can only hold 1 and 2: they reserve those digits.
1 and 2 are therefore removed from the other cells of the row.
Look at cell R6C8.
Every other digit already appears in its row, column or box.
Only one option remains: R6C8 = 5.
Look at cell R4C8.
Every other digit already appears in its row, column or box.
Only one option remains: R4C8 = 2.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 6.
Look at cell R3C2.
Every other digit already appears in its row, column or box.
Only one option remains: R3C2 = 8.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 7.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 9.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 5.
Look at cell R5C6.
Every other digit already appears in its row, column or box.
Only one option remains: R5C6 = 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 R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 9.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 2.
Look at cell R1C5.
Every other digit already appears in its row, column or box.
Only one option remains: R1C5 = 8.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 7.
Look at cell R2C4.
Every other digit already appears in its row, column or box.
Only one option remains: R2C4 = 2.
Look at cell R3C3.
Every other digit already appears in its row, column or box.
Only one option remains: R3C3 = 6.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 5.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 2.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 4.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 1.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 2.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 4.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 1.
Look at cell R5C4.
Every other digit already appears in its row, column or box.
Only one option remains: R5C4 = 8.