MathDB
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 kk consecutive days, a total of 20142014 babies were born in a certain city, with at least one baby being born each day. Show that: (a) If 1014<k20141014 < k \le 2014, there must be a period of consecutive days during which exactly 100100 babies were born. (b) By contrast, if k=1014k = 1014, such a period might not exist.