Questions, Problems, & Conjectures

From Visiting Lecturers to the 2005 ReSEARCH Group

1. Is it true that: Whenever the collection S={1,2,3,..., 100} is divided into 2 disjoint collections A and B, then either A contains a pair of integers x and y such that |x-y|=2 or B contains a pair of integers x and y such that |x-y|=2?