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scales: as Enchom mentioned, making a backtrack over the decision tree was probably the best idea (the difference between 36 and 6! seems too small for anything manual). 7 moves are doable quite well manually, sorting 4 numbers in 3 moves (min,nextmin,max) first and inserting the remaining two numbers in 2 moves each (if we have sorted 1,2,3,4,5, then median(2,4,6) leaves just 2 choices).
What about Google Code Jam?
Wrong week.