A lower bound for the number of moves is because This can be done as follows:


We need for the following reason:


No one seems to have made any progress, so here's the partial answer for 9:


The answer might be this: Considering that the picture can be of any scale in all diagrams i.e. : each cross (axes) may have different scales as scales or markings are not mentioned.


The sequence is: So a longer list includes:


I agree with Dmitry Kamenetsky that this looks like a programming competition, so I won't at this time give algorithms, just results. Fully $\frac{1}{2}$ of the possible input have no solution. The longest optimal solution for $N$ integers is of length $\big\lfloor{\frac{N}{2}}\big\rfloor$. The bit about a cyclic right shift is deceptive. You can do both ...


The solution is: Explanation:

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