Question 93
Over a period of $k$ consecutive days, a total of 2014 babies were born in a certain city, with at least one baby being born each day. Show that:
1. If $1014 \lt k \le 2014$, there must be a period of consecutive days during which exactly 100 babies were born.
2. By contrast, if $k = 1014$, such a period might not exist.
1. If $1014 \lt k \le 2014$, there must be a period of consecutive days during which exactly 100 babies were born.
2. By contrast, if $k = 1014$, such a period might not exist.