I found this problem:
There are 2n people seated around a circular table, and m cookies are distributed among them. The cookies may be passed around under the following rules:
• Each person may only pass cookies to his or her neighbours.
• Each time someone passes a cookie, he or she must also eat a cookie.
Let A be one of these people. Find the least m such that no matter how m cookies are distributed to begin with, there is a strategy to pass cookies so that A receives at least one cookie.
What I'm looking for is just an example, like a small case verification ( say n = 3 or 4 ), because What I see is that for n=3, taking m=6 is sufficient so that everyone gets a cookie, but they claim that the minimum is $2^n$. Can someone explain where I am wrong ?