2014 babies born over a period of k consecutive days, at least 1 each day
Source: Irmo 2014 p2 q10
September 15, 2018
combinatorics
Problem Statement
Over a period of consecutive days, a total of babies were born in a certain city, with at least one baby being born each day. Show that:
(a) If , there must be a period of consecutive days during which exactly babies were born.
(b) By contrast, if , such a period might not exist.