Locked Candidates
Use the intersection of boxes and lines to eliminate candidates. These techniques leverage the constraint that numbers must appear exactly once in each row, column, and box.
Before you start
Understanding Sudoku Constraints
Before diving into locked candidates, let's review how Sudoku constraints work:
Row Constraint
Each horizontal line must contain digits 1-9 exactly once
Column Constraint
Each vertical line must contain digits 1-9 exactly once
Box Constraint
Each 3×3 box must contain digits 1-9 exactly once
Locked Candidates Pointing
When a number can only appear in one row or column within a box, eliminate that number from the rest of that row or column. This technique uses the intersection between box and line constraints.
Worked example
Pointing in Action
Box Analysis
"In this house, 2 can only be in cells in one row"
Magic Sudoku identifies when a number is restricted to a single row or column within a box.
Box Constraint
"Because this house must contain a 2, we know that it has to be one of these cells"
Shows how the box constraint forces the number into specific cells.
Row/Column Impact
"Since 2 must be in one of these cells, it can't appear elsewhere in this row"
Extends the constraint to eliminate candidates in the same row or column outside the box.
Candidates to Remove
"In this row, only these cells contain a 2 as a candidate"
Shows which specific candidates will be eliminated outside the box.
Elimination
"Therefore we can rule out 2 as a candidate from these cells"
Removes the impossible candidates, potentially creating new solving opportunities.
When to use pointing
- Look for numbers that can only appear in one row or column within a box
- Check if that same number appears as a candidate elsewhere in that row/column
- Most effective after placing several numbers to create constraints
Locked Candidates Claiming
When all candidates for a number in a row or column are confined to a single box, eliminate that number from other cells in the box.
Worked example
Claiming in Action
Row/Column Analysis
"In this row, all candidates for digit 9 are in the same house"
Magic Sudoku identifies when all instances of a number in a line are within one box.
Line Constraint
"Since 9 must be in one of these cells, it can't appear elsewhere in this house"
The row/column constraint forces the number into specific cells within the box.
Box Elimination
"Remove 9 as a candidate from these cells in the same house"
Eliminates the number from other cells in the box, creating new solving opportunities.
When to use claiming
- Scan rows and columns for numbers that appear only within one box
- Check if that number appears elsewhere in the same box
- Often reveals hidden singles after eliminating candidates
Side by side
Understanding the Difference
Pointing
- Start with
- A box constraint
- Pattern
- Number restricted to one row/column in box
- Eliminate from
- Rest of that row/column
- Direction
- Box → Line
Claiming
- Start with
- A line constraint
- Pattern
- All candidates in line are in one box
- Eliminate from
- Rest of that box
- Direction
- Line → Box
Ready to Practice?
Locked candidates are powerful intermediate techniques that unlock many puzzles. Practice identifying the key patterns with Magic Sudoku's intelligent hints.