Naked Sets
When groups of cells contain the same limited candidates, you can eliminate those numbers from other cells in the same unit. Master these powerful intermediate elimination techniques.
The idea
What Are Naked Sets?
Naked Sets occur when a group of cells (2, 3, or 4) in the same unit contain only the same limited set of candidates. Since these numbers must go in these cells, they can be eliminated from all other cells in that unit.
Naked Pairs
Two cells with the same two candidates
Naked Triples
Three cells sharing the same three candidates
Naked Quads
Four cells containing the same four candidates
Naked Pairs
Look for two cells in the same unit that contain exactly the same two candidates. Those two numbers are locked into those two cells.
Worked example
Naked Pair in Action
Identifying the Pattern
Look for two cells in the same unit that contain exactly the same two candidates. In this example, these cells both contain only candidates 1 and 8.
Understanding the Logic
Since these two cells can only contain 1 and 8, and there are exactly two cells, each number must go in one of these cells. This means 1 and 8 cannot appear anywhere else in that row.
Candidates to Remove
All other cells in row 4 that contain candidates 1 or 8 can have these numbers eliminated. The highlighted candidates show what will be removed.
After Elimination
After removing candidates 1 and 8 from other cells in the row, new solving opportunities may emerge. Notice how some cells now have fewer candidates.
How Larger Sets Work
The same principle applies to larger naked sets - the key is that the number of cells equals the number of candidates they collectively contain.
Worked example
Naked Triple
-
1
Identify the Pattern
In column 3, we have three cells with these candidates:
R2C3
R7C3
R9C3
Key insight: These three cells collectively contain exactly three unique numbers: {2, 5, 8}
-
2
Apply the Logic
Since we have 3 cells that can only contain the numbers {2, 5, 8}, these three numbers must be distributed among these three cells:
- R2C3 will be either 2 or 5
- R7C3 will be either 5 or 8
- R9C3 will be either 2 or 8
Therefore: Numbers 2, 5, and 8 cannot appear anywhere else in column 3!
-
3
Eliminate Candidates
Remove candidates 2, 5, and 8 from all other cells in column 3:
CellBeforeAfterR1C3 {1, 3, 5, 7} {1, 3, 7}R4C3 {2, 4, 6} {4, 6}R6C3 {1, 2, 8, 9} {1, 9}Result: R4C3 and R6C3 are each down to two candidates, so look for new pairs and singles in their rows and boxes.
Naked Triples
Three cells sharing exactly three candidates (like 2, 5, 8). Each cell might contain different combinations:
Cell A
Cell B
Cell C
Naked Quads
Four cells containing exactly four candidates (like 1, 4, 6, 9). More complex but same logic:
Cell A
Cell B
Cell C
Cell D
Putting it to work
Key Tips for Naked Sets
Recognition Patterns
- Look for cells with very few candidates (2-4)
- Check if multiple cells share the same candidates
- Count the total unique candidates across the cells
- The number of cells should equal the number of candidates
Application Strategy
- Start with naked pairs - they're easiest to spot
- Focus on units with many candidates filled in
- Check all three unit types: rows, columns, and boxes
- Apply eliminations immediately when found
Master Naked Sets
Practice identifying and applying naked sets in Magic Sudoku. The app will highlight these patterns and guide you through the elimination process.