I have developed a fixed strategy that is able to solve all cases of scales problem in at most 6 steps. The program is a decision tree coded if if else statements. The running time is O(18) . You can have a look at the solution at the following:
It is indeed a high quality problem and I have developed a high quality solution(Time and memory optimized). I want that software people or students in general should study the problem and its solution so that they may sharpen their skills about computing algorithm and mathematics.
I am still studying different aspects of the problem. If doubts arise in one's mind he may send me a query. I do not guarantee to answer the query but I will try my level best.
Because there is everlasting scope of improvement that exists.