Rock’n’Roll Suislide

Q. Each face of a convex polyhedron can serve as a base when the solid is placed on a horizontal plane. The center of gravity of a regular polyhedron is at the center, therefore it is stable on any face. Irregular polyhedrons are easily constructed that are unstable on certain faces; that is, when placed on a table with an unstable face as the base, they topple over. Is it possible to make a model of an irregular convex polyhedron that is unstable on every face?

Portrait of Luca Pacioli (1495)

Portrait of Luca Pacioli (1495)


A. No. If a convex polyhedron were unstable on every face, a perpetual motion machine could be built. Each time the solid toppled over onto a new base it would be unstable and would topple over again.

 — From “Ridiculous Questions” in Martin Gardner’s Mathematical Magical Show (1965), chapter 10.

Shick Shtick

Slightly adapted from Joseph Degrazia’s Math is Fun (1954):

Six Writers in a Railway Car

On their way to Chicago for a conference of authors and journalists, six writers meet in a railway club car. Three of them sit on one side facing the other three. Each of the six has his specialty. One writes short stories, one is a historian, another one writes humorous books, still another writes novels, the fifth is a playwright and the last a poet. Their names are Abbott, Blake, Clark, Duggan, Eccles and Farmer.* Each of them has brought one of his books and given it to one of his colleagues, so that each of the six is deep in a book which one of the other five has written.

Abbott reads a collection of short stories. Clark reads the book written by the colleague sitting just opposite him. Blake sits between the author of the short stories and the humorist. The short-story writer sits opposite the historian. Duggan reads a play. Blake is the brother-in-law of the novelist. Eccles sits next to the playwright. Abbott sits in a corner and is not interested in history. Duggan sits opposite the novelist. Eccles reads a humorous book. Farmer never reads poems.

These facts are sufficient to find each of the six authors’ specialties.


*In the original, the surnames were Blank, Bird, Grelly, George, Pinder and Winch.