The leaning tower of Lire with variable block mass

Abstract

Editor's Note: A classic block-stacking puzzle becomes more interesting when the blocks have different masses. Readers discover how changing thickness or density can make the total overhang shrink, grow slowly, or even increase linearly. The “Lire Tower Transform,” a neat way to turn a mass sequence into an overhang pattern, is also introduced, which may be interesting for teaching sequences. By blending physical intuition, analytical results, and simple numerical tools, one may explore different stacking behaviors with ease.