One additional idea:   
      
   You have a system with the following characteristics:   
      
   1) Its current state is represented by 9 (1001) on a K-map.   
   2) A desired state is F (1111)   
   3) You have rules that can change the current state.   
      
   If you look for rules that result in a state between 9 and F,   
   (within 9 union F = 1XX1), then you have avoided a combinatorial   
   explosion.  You can tell that a change brings you directly closer   
   to the desired result.   
      
   The down-side is that the only possible solution(s) may require you   
   to change state outsite of 1XX1, namely within 0XXX or XXX0.   
      
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