after a certain time each newborn in family has at least 1 direct ancestor
Source: 2021 Dürer Math Competition Finals Day2 E15 https://artofproblemsolving.com/community/c2749870_
January 8, 2022
combinatorics
Problem Statement
King Albrecht founded a family. In the family everyone has exactly children. The only, but really important rule is that among the grandchildren of any person at most can be named Bela. (None of Albrecht’s children is called Bela.) For which is it possible that after a certain time each newborn in the family has at least one direct ancestor in the Royal family called Bela.
No two of Albrecht’s descendants (including himself) have a common child.