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In their amazing paper Overhang (Amer. Math. Monthly 116 (2009), 19–44), Mike Paterson and Uri Zwick revisited the old chestnut of how much of an overhang one can achieve by stacking bricks at the edge of a table. Crucial to their new results was the idea that a brick can have more than one other brick placed directly on top of it, thus serving as a counterweight.

I am curious about earlier examples of people who considered the possibility of stacking more than one brick on top of a given brick. Paterson and Zwick mention a few such precursors on the second page of their paper, but I have found one other instance not mentioned by them. In the book Ingenious Mathematical Problems and Methods by L. A. Graham, there are several pictures of arrangements that stack more than one brick on another brick. These were sent in by Graham's readers; curiously, Graham did not bother to analyze them, but breezily dismissed them all as "marvels of graceful instability."

Are there other precursors of Paterson and Zwick's work?

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  • $\begingroup$ That is freakin' awesome! I especially like their point that nobody ever thought to codify the "one brick per layer" rule; it was just taken for granted. $\endgroup$ Jul 7 at 12:27

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