10

Part of 2021 Moldova EGMO TST

Problems(1)

Find the smallest positive integer $k$ with the property

Source: Moldova EGMO TST 2021

n\geq3

be an integer. Find the smallest positive integer

k

with the property that if in a group of

n

boys for each boy there are at least

k

other boys that are born in the same year with him, then all the boys are born in the same year.