zedoku

obvious pairs

level 3 - medium

also known as: naked pairs

what it means

two cells have the same two candidates. those two numbers must go in those two cells, so you can remove them from other cells in that row/column/box.

example 1: spot the pair

look at this row. two cells both have only [2, 8] as candidates.

1
9
4
 2     8 
6
7
 2     8 
3
5

the highlighted cells both contain only [2, 8]

example 2: before elimination

other cells in the same unit also have 2 or 8 as candidates. since the pair owns those numbers, we can eliminate 2 and 8 from everywhere else.

1
9
4
 2     8 
6
7
 2     8 
 23      
    5  8 
the pair [2, 8]2 or 8 will be eliminated

example 3: after elimination

2 and 8 are removed from other cells. notice how the last cell now has only one candidate left — a new single is revealed!

1
9
4
 2     8 
6
7
 2     8 
  3      
    5    
the pair [2, 8]new singles revealed!

key concept: they own those numbers

think of it like two friends ordering lunch. if alice and bob are the only ones who can eat the pizza and burger, and they both want exactly those two items, then:

  • alice gets either pizza or burger
  • bob gets the other one
  • nobody else can have pizza or burger!

the pair owns those two numbers for that unit.

the chain reaction

after eliminating candidates from an obvious pair, you often create a new obvious single (a cell with only one candidate left). this can trigger more eliminations and solve more of the puzzle!

before

 23   7  
 2     8 
 2  5    
 2     8 
  3  6   
1   5    
   4  7  
  3     9
1       9

after

  3   7  
 2     8 
    5    
 2     8 
  3  6   
1   5    
   4  7  
  3     9
1       9

removing 2 from cell 3 left only 5. that cell is now solved!

summary

  • find two cells with the exact same two candidates
  • those two numbers must occupy those two cells
  • remove those candidates from all other cells in the same row, column, or box
  • watch for new singles revealed by the elimination!
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