# Maximum overhang

• Published in 2007
In the collections
How far can a stack of $n$ identical blocks be made to hang over the edge of a table? The question dates back to at least the middle of the 19th century and the answer to it was widely believed to be of order $\log n$. Recently, Paterson and Zwick constructed $n$-block stacks with overhangs of order $n^{1/3}$, exponentially better than previously thought possible. We show here that order $n^{1/3}$ is indeed best possible, resolving the long-standing overhang problem up to a constant factor.

### BibTeX entry

@article{Maximumoverhang,
title = {Maximum overhang},
abstract = {How far can a stack of {\$}n{\$} identical blocks be made to hang over the edge of
a table? The question dates back to at least the middle of the 19th century and
the answer to it was widely believed to be of order {\$}\log n{\$}. Recently,
Paterson and Zwick constructed {\$}n{\$}-block stacks with overhangs of order
{\$}n^{\{}1/3{\}}{\$}, exponentially better than previously thought possible. We show here
that order {\$}n^{\{}1/3{\}}{\$} is indeed best possible, resolving the long-standing
overhang problem up to a constant factor.},
url = {http://arxiv.org/abs/0707.0093v1 http://arxiv.org/pdf/0707.0093v1},
year = 2007,
author = {Mike Paterson and Yuval Peres and Mikkel Thorup and Peter Winkler and Uri Zwick},
comment = {},
urldate = {2021-03-15},
archivePrefix = {arXiv},
eprint = {0707.0093},
primaryClass = {math.HO},
collections = {basically-physics,easily-explained,fun-maths-facts,puzzles}
}