Here is a well-known beautiful problem I can’t solve. It probably has been already been asked but I couldn’t find it, so please either write a solution or write a link. Thanks.
Given $2^n$ integers around a circle. In a step you are able to change any two consecutive numbers to their average (so e.g. if 8 and 4.5 are next to each other, than you can delete both and write 6.25 and 6.25 instead of them). Is it always possible to make all numbers equal?