PUZZLEBOXX

The least number of moves is four.

You may notice that I have followed a pattern

(always a good way to solve problems).

First I turned over coins 1, 2, 3

Then I turned over coins 2, 3, 4

Then coins 3, 4, 1

Then coins 4, 1, 2

You may wish to try the same challenge starting with 5 coins!