We have several cubes that are ordered as in the picture below:
What is the smallest number of moves with which we are able to reach every possible order?
Only the order of the cubes in the columns matters, the ordering of the columns on the desk is irrelevant. The height and the number of columns may change.
- In every step we may take a cube and put it on another cube or on the desk.
My attempt:If we put all cubes on the desk and then bring them together we will need $17$ moves so every case can be made using $17$ moves.I also got a combination that needs at least $16$ moves because it is a test the answer will be $17$ but I need a complete proof.So my question is which combination needs $17$ moves to be made?