Step-by-step solution
Steps 64
Estimated time 65 – 98 min
Hardest technique Box/Line
Clues 25
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 R1C5 = 8.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R3C4 = 7.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R3C7 = 9.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R4C8 = 5.
Scan the empty cells in this row where 9 could go.
Across the whole row, 9 has only one possible spot left.
So R5C1 = 9.
Scan the empty cells in this column where 2 could go.
Across the whole column, 2 has only one possible spot left.
So R5C4 = 2.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R5C6 = 7.
Scan the empty cells in this box where 1 could go.
Across the whole box, 1 has only one possible spot left.
So R7C5 = 1.
Scan the empty cells in this box where 9 could go.
Across the whole box, 9 has only one possible spot left.
So R8C2 = 9.
Scan the empty cells in this row where 2 could go.
Across the whole row, 2 has only one possible spot left.
So R8C9 = 2.
Scan the empty cells in this column where 9 could go.
Across the whole column, 9 has only one possible spot left.
So R9C5 = 9.
Spot R3C6 and R3C8 on this row.
These two cells can only hold 4 and 6: they reserve those digits.
4 and 6 are therefore removed from the other cells of the row.
(1) Find where 2 and 4 can go on this column. (2) Find where 5 and 8 can go on this column. (3) Find where 5 and 8 can go in this box.
(1) These two digits only fit in R1C2 and R6C2 on the column. (2) These two digits only fit in R8C6 and R9C6 on the column. (3) These two digits only fit in R8C6 and R9C6 in the box.
(1) The other candidates in R1C2 and R6C2 are therefore eliminated. (2) The other candidates in R8C6 and R9C6 are therefore eliminated. (3) The other candidates in R8C6 and R9C6 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 R3C9 = 5.
(1) Find where 1 and 7 can go on this row. (2) Find where 1 and 7 can go in this box.
(1) These two digits only fit in R1C7 and R1C9 on the row. (2) These two digits only fit in R1C7 and R1C9 in the box.
(1) The other candidates in R1C7 and R1C9 are therefore eliminated. (2) The other candidates in R1C7 and R1C9 are therefore eliminated.
Look at where 1 can go in this box.
All its spots lie on a single row (R5C7 and R5C9).
1 is therefore removed from that row 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 R4C1 = 7.
Scan the empty cells in this column where 1 could go.
Across the whole column, 1 has only one possible spot left.
So R4C3 = 1.
Scan the empty cells in this box where 7 could go.
Across the whole box, 7 has only one possible spot left.
So R7C3 = 7.
Scan the empty cells in this box where 8 could go.
Across the whole box, 8 has only one possible spot left.
So R3C1 = 8.
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 R7C2 = 8.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R7C7 = 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 8 could go.
Across the whole box, 8 has only one possible spot left.
So R8C6 = 8.
Scan the empty cells in this row where 5 could go.
Across the whole row, 5 has only one possible spot left.
So R9C6 = 5.
Spot R2C7, R6C7 and R8C7 on this column.
These three cells share only 3, 4 and 6.
3, 4 and 6 are therefore removed from the rest of the column.
Find where 4 appears on two columns: altogether, only two rows are involved (R2C3, R5C3, R2C5 and R5C5).
On each covered row, 4 must lie within one of these two columns.
4 is therefore removed from those two rows outside the two X-Wing columns.
Scan the empty cells in this column where 4 could go.
Across the whole column, 4 has only one possible spot left.
So R8C7 = 4.
Scan the empty cells in this box where 4 could go.
Across the whole box, 4 has only one possible spot left.
So R9C4 = 4.
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.
R2C5 and R1C8 is seen by both free ends: 3 is therefore eliminated there.
Scan the empty cells in this row where 3 could go.
Across the whole row, 3 has only one possible spot left.
So R1C6 = 3.
Find 6 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 6.
R2C7 and R5C8 is seen by both free ends: 6 is therefore eliminated there.
Look at cell R2C7.
Every other digit already appears in its row, column or box.
Only one option remains: R2C7 = 3.
Look at cell R6C7.
Every other digit already appears in its row, column or box.
Only one option remains: R6C7 = 6.
Look at cell R6C6.
Every other digit already appears in its row, column or box.
Only one option remains: R6C6 = 4.
Look at cell R3C6.
Every other digit already appears in its row, column or box.
Only one option remains: R3C6 = 6.
Look at cell R3C8.
Every other digit already appears in its row, column or box.
Only one option remains: R3C8 = 4.
Look at cell R6C2.
Every other digit already appears in its row, column or box.
Only one option remains: R6C2 = 2.
Look at cell R1C2.
Every other digit already appears in its row, column or box.
Only one option remains: R1C2 = 4.
Look at cell R1C8.
Every other digit already appears in its row, column or box.
Only one option remains: R1C8 = 2.
Look at cell R2C3.
Every other digit already appears in its row, column or box.
Only one option remains: R2C3 = 5.
Look at cell R2C5.
Every other digit already appears in its row, column or box.
Only one option remains: R2C5 = 4.
Look at cell R2C8.
Every other digit already appears in its row, column or box.
Only one option remains: R2C8 = 6.
Look at cell R6C1.
Every other digit already appears in its row, column or box.
Only one option remains: R6C1 = 3.
Look at cell R8C1.
Every other digit already appears in its row, column or box.
Only one option remains: R8C1 = 5.
Look at cell R8C3.
Every other digit already appears in its row, column or box.
Only one option remains: R8C3 = 6.
Look at cell R8C4.
Every other digit already appears in its row, column or box.
Only one option remains: R8C4 = 3.
Look at cell R9C2.
Every other digit already appears in its row, column or box.
Only one option remains: R9C2 = 3.
Look at cell R9C8.
Every other digit already appears in its row, column or box.
Only one option remains: R9C8 = 8.
Look at cell R2C1.
Every other digit already appears in its row, column or box.
Only one option remains: R2C1 = 2.
Look at cell R4C2.
Every other digit already appears in its row, column or box.
Only one option remains: R4C2 = 6.
Look at cell R4C5.
Every other digit already appears in its row, column or box.
Only one option remains: R4C5 = 3.
Look at cell R5C3.
Every other digit already appears in its row, column or box.
Only one option remains: R5C3 = 4.
Look at cell R5C5.
Every other digit already appears in its row, column or box.
Only one option remains: R5C5 = 6.
Look at cell R5C8.
Every other digit already appears in its row, column or box.
Only one option remains: R5C8 = 3.
Look at cell R5C9.
Every other digit already appears in its row, column or box.
Only one option remains: R5C9 = 1.
Look at cell R7C4.
Every other digit already appears in its row, column or box.
Only one option remains: R7C4 = 6.
Look at cell R7C9.
Every other digit already appears in its row, column or box.
Only one option remains: R7C9 = 3.
Look at cell R9C7.
Every other digit already appears in its row, column or box.
Only one option remains: R9C7 = 7.
Look at cell R9C9.
Every other digit already appears in its row, column or box.
Only one option remains: R9C9 = 6.
Look at cell R1C7.
Every other digit already appears in its row, column or box.
Only one option remains: R1C7 = 1.
Look at cell R1C9.
Every other digit already appears in its row, column or box.
Only one option remains: R1C9 = 7.
Look at cell R5C7.
Every other digit already appears in its row, column or box.
Only one option remains: R5C7 = 8.