Step-by-step solution
Steps 65
Estimated time 65 – 98 min
Hardest technique Box/Line
Clues 23
Given digit (clue)
Solved digit
Placement (✓ RlCc=d)
Elimination (✗ RlCc≠d)
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 row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R3C1 = 5.
Scan the empty cells in this box where 3 could go.
Across the whole box, 3 has only one possible spot left.
So R5C4 = 3.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R5C6 = 9.
Scan the empty cells in this column where 5 could go.
Across the whole column, 5 has only one possible spot left.
So R5C8 = 5.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R6C1 = 9.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R6C9 = 6.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R7C4 = 4.
Scan the empty cells in this box where 5 could go.
Across the whole box, 5 has only one possible spot left.
So R8C5 = 5.
Look at cell R3C4.
Every other digit already appears in its row, column or box.
Only one option remains: R3C4 = 1.
Look at cell R1C4.
Every other digit already appears in its row, column or box.
Only one option remains: R1C4 = 2.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R1C8 = 1.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R1C9 = 4.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R2C7 = 2.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R2C8 = 9.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R4C5 = 2.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R5C1 = 2.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R7C7 = 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 column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R7C9 = 2.
Scan the empty cells in this box where 2 could go.
Across the whole box, 2 has only one possible spot left.
So R8C6 = 2.
Scan the empty cells in this box where 6 could go.
Across the whole box, 6 has only one possible spot left.
So R8C8 = 6.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R9C2 = 9.
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.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 7.
Scan the empty cells in this row where 6 could go.
Across the whole row, 6 has only one possible spot left.
So R9C6 = 6.
Spot R4C4 and R6C4 in this box.
These two cells can only hold 5 and 7: they reserve those digits.
5 and 7 are therefore removed from the other cells of the box.
(1) Find where 5 and 6 can go on this row. (2) Find where 4 and 8 can go on this column. (3) Find where 5 and 6 can go on this column. (4) Find where 5 and 6 can go in this box.
(1) These two digits only fit in R7C2 and R7C3 on the row. (2) These two digits only fit in R2C1 and R4C1 on the column. (3) These two digits only fit in R4C2 and R7C2 on the column. (4) These two digits only fit in R7C2 and R7C3 in the box.
(1) The other candidates in R7C2 and R7C3 are therefore eliminated. (2) The other candidates in R2C1 and R4C1 are therefore eliminated. (3) The other candidates in R4C2 and R7C2 are therefore eliminated. (4) The other candidates in R7C2 and R7C3 are therefore eliminated.
Look at where 1 can go on this row.
All its spots lie within a single box (R5C2 and R5C3).
1 is therefore removed from the rest of the box.
Spot R6C3 and R6C4 on this row.
These two cells can only hold 5 and 7: they reserve those digits.
5 and 7 are therefore removed from the other cells of the row.
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.
R9C5 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 (R7C5 and R7C6).
3 is therefore removed from that row outside the box.
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.
R3C9, R4C7 and R6C7 is seen by both free ends: 8 is therefore eliminated there.
Look at cell R3C9.
Every other digit already appears in its row, column or box.
Only one option remains: R3C9 = 3.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 1.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 7.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 8.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 8.
Look at cell R4C6.
Every other digit already appears in its row, column or box.
Only one option remains: R4C6 = 1.
Look at cell R4C7.
Every other digit already appears in its row, column or box.
Only one option remains: R4C7 = 7.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 8.
Look at cell R6C5.
Every other digit already appears in its row, column or box.
Only one option remains: R6C5 = 8.
Look at cell R7C6.
Every other digit already appears in its row, column or box.
Only one option remains: R7C6 = 3.
Look at cell R8C7.
Every other digit already appears in its row, column or box.
Only one option remains: R8C7 = 3.
Look at cell R9C5.
Every other digit already appears in its row, column or box.
Only one option remains: R9C5 = 1.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 7.
Look at cell R1C3.
Every other digit already appears in its row, column or box.
Only one option remains: R1C3 = 3.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 3.
Look at cell R4C4.
Every other digit already appears in its row, column or box.
Only one option remains: R4C4 = 5.
Look at cell R5C2.
Every other digit already appears in its row, column or box.
Only one option remains: R5C2 = 1.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 7.
Look at cell R6C3.
Every other digit already appears in its row, column or box.
Only one option remains: R6C3 = 5.
Look at cell R6C4.
Every other digit already appears in its row, column or box.
Only one option remains: R6C4 = 7.
Look at cell R7C3.
Every other digit already appears in its row, column or box.
Only one option remains: R7C3 = 6.
Look at cell R7C5.
Every other digit already appears in its row, column or box.
Only one option remains: R7C5 = 7.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 7.
Look at cell R9C1.
Every other digit already appears in its row, column or box.
Only one option remains: R9C1 = 3.
Look at cell R2C2.
Every other digit already appears in its row, column or box.
Only one option remains: R2C2 = 8.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 6.
Look at cell R4C3.
Every other digit already appears in its row, column or box.
Only one option remains: R4C3 = 4.
Look at cell R7C1.
Every other digit already appears in its row, column or box.
Only one option remains: R7C1 = 1.
Look at cell R7C2.
Every other digit already appears in its row, column or box.
Only one option remains: R7C2 = 5.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 4.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 1.
Look at cell R4C1.
Every other digit already appears in its row, column or box.
Only one option remains: R4C1 = 8.