IMO 1982 LL FIN24

Origin: FIN

Problem

Prove that if a person a has infinitely many descendants (chil- dren, their children, etc.), then a has an infinite sequence a0, a1, . . . of descendants (i.e., a = a0 and for all n \geq1, an+1 is always a child of an). It is assumed that no-one can have infinitely many children. Variant 1. Prove that if a has infinitely many ancestors, then a has an infinite descending sequence of ancestors (i.e., a0, a1, . . . where a = a0 and an is always a child of an+1). Variant 2. Prove that if someone has infinitely many ancestors, then all people cannot descend from A(dam) and E(ve).