Let suppose, initial position of element was **A** , and the position where it starts to repeat after some number of operation is **B**.

Now if we solve problem by hand and observe the pattern,the situtation is always like this

but why it can’t be like this

So , is there any way we can proof that 2nd secenerio will never happen ??

A permutation can always be decomposed into cycles.

Thnx … Got it.