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  We can generalize from twins to triples.
  
  Skinny triples.  AKA 2 x 3 circles.
  
  Imagine we have:
  

1 2 3 4 5 6 7 8 9 .---------.---------.---------..---------.---------.---------..---------.---------.---------. a | | | || | | || | | | a b | | | || | | || | | | b c | | | || | | || | | | c |---------+---------+---------++---------+---------+---------++---------+---------+---------| d | | | || 2 4 | 4 7 | 2 7 || | | | d e | | | || | | || | | | e f | | | || | | || | | | f |---------+---------+---------++---------+---------+---------++---------+---------+---------| g | | | || | | || | | | g h | | | || | | || | | | h i | | | || | | || | | | i '---------'---------'---------''---------'---------'---------''---------'---------'---------' 1 2 3 4 5 6 7 8 9

d4 = 2 iff d6 = 7 iff d5 = 4. d4 = 4 iff d5 = 7 iff d6 = 2. so in either case all the digits 2,4,7 are monopolized by d4, d5, and d6.

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