The Freudenthal Problem and its Ramifications (Part I)

This is the second article (in a series of three) dedicated to the many variants and variations of the Freudenthal problem. The common crux in all these variants is how to draw the right conclusions from a strange conversation that mainly consists of “I-do-not-know” and “Now-I-do-know” statements. The Freudenthal problem dates back to the year 1969, when Hans Freudenthal posed it in the Nieuw Archief voor Wiskunde [5]. Nowadays the problem is famous all over the world. It regularly shows up in mathematical puzzle corners, and analyzing the flow of information in the underlying conversation has become a standard exercise for computer science students. In a predecessor paper [2], we have surveyed the Freudenthal problem in its classical form and some of its most basic variations. In the current paper, we continue our survey by discussing some of its more remote relatives. Each of the following seven sections introduces one relative or one class of relatives: We give a complete formulation of the respective problem. We state the respective solution. And we try to present a more or less complete derivation of the solution.