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Some years ago i asked myself a question that I still can not answer. Here it is:

A given tower consists of finite homogeneous cubic blocks staying one on another and equal to each other. What is the condition for stability of such tower?

First one can consider 2-dimensional analogue of this problem where 2-dimensional tower is staying on a real line.

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  • $\begingroup$ On the other hand, it is also possible make problem harder considering not a queue-tower which i meant in the beginning but more complicated towers with more than one cube in each stage. $\endgroup$
    – Alexei Fedotov
    Commented May 6, 2016 at 11:24

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Stability

For all $k$ up to the total number of blocks $n$: the center of mass of the top $k$ blocks must lie above the surface of the $k+1$ block supporting them.

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  • $\begingroup$ Thank you very much for the answer. I think it is right. $\endgroup$
    – Alexei Fedotov
    Commented May 8, 2016 at 18:19
  • $\begingroup$ I have a PhD in Physics and was a professor of physics for years, so frankly I do know this stuff. You can get a mathematical treatment of the greatest overhang possible by searching "greatest overhanging blocks physics." $\endgroup$
    – David G. Stork
    Commented May 8, 2016 at 19:40

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