Further Thoughts on a Paradoxical Tower

Abstract

What is the maximum overhang that can be obtained when a set of blocks of variable width are stacked so that there is one block at each level? First, we stack these blocks in a prescribed order, and describe infinite sets of blocks that yield towers with arbitrarily large overhang. We then stack the blocks in any order, and describe how they should be stacked to maximize their overhang.

ACKNOWLEDGMENTS

In preparing this article, I received valuable guidance from my supervisors: Burkard Polster, Heiko Dietrich, and Marty Ross. Thanks must also go to the anonymous referees whose suggestions have substantially improved this article. In particular, Theorem 8.1 was generously contributed by one of these referees.

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Notes on contributors

David Treeby

DAVID TREEBY is completing his Ph.D. at Monash University, Australia, while concurrently teaching at Presbyterian Ladies College. He has had less success teaching his toddler, who refuses to believe that any integer exceeds five.