I have been thinking about this question for a long time, but I can't solve it. Here is the question:
We have $9$ cards, with numbers one to nine written on them (in the order $1, 2, \ldots , 9$).
You can move $n$ cards, if they are located next to each other (physically, not numerically).
First, I have to show how to make it $9, 8, 7, \ldots, 1$ in five moves and then prove that it is possible.
Sorry for any spelling and grammar errors, improper tags or any other mistake.
An example of a valid move:
We pick cards $1,2,3,4$ and put them between $7$ and $8$. The sequence after the move looks like this: $$5,6,7,1,2,3,4,8,9.$$