Does a greedy best-first search produce an optimal solution when the   
   heuristic is admissible and consistent and the cost between nodes is   
   constant?  It seems intuitive to me that it does produce an optimal   
   solution when the cost between nodes is constant but I don't know how   
   to prove it.  How would I prove it?  Or, am I just wrong, are there   
   counter examples?   
      
   Thanks   
      
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