Need help in understanding arguement
Posted: Tue Feb 09, 2021 8:42 pm
Example 6 [New Zealand IMO Training, 2011]
There are 2n people seated around a circular table, and m cookies
are distributed among them. The cookies can be passed under the
following rules:
(a) Each person can only pass cookies to his or her neighbors
(b) 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 initially, there is a strategy to pass
cookies so that A receives at least one cookie.
Ref: Pranav Sriram Combii Chapter 1
He started by giving every $A_i cookies weight of 1/(2^i). What's the motivation behind such weighting scheme?
Please see The book from aops for a better understanding.
There are 2n people seated around a circular table, and m cookies
are distributed among them. The cookies can be passed under the
following rules:
(a) Each person can only pass cookies to his or her neighbors
(b) 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 initially, there is a strategy to pass
cookies so that A receives at least one cookie.
Ref: Pranav Sriram Combii Chapter 1
He started by giving every $A_i cookies weight of 1/(2^i). What's the motivation behind such weighting scheme?
Please see The book from aops for a better understanding.