Block-stacking problem

In statics, the block stacking problem (also the book stacking problem, or a number of other similar terms) is the following puzzle:

Place $N$ rigid rectangular blocks in a stable stack on a table edge in such a way as to maximize the overhang.

Writing in the American Journal of Physics, physicist John F. Hall of Caltech discusses this problem and several variants including nonzero friction forces between adjacent blocks.

The single-wide problem involves having only one block at any given level. In the ideal case of perfectly rectangular blocks, the maximal overhang tends to infinity as $N$ increases. Hall discusses this result and shows that it is robust to nonidealizations such as rounded block corners and finite precision of block placing.

The solution to the simple ideal case is that the maximum overhang is given by $\sum _{i=1}^{N}{\frac {1}{2i}}$, where each block is one unit wide.

Hall shows that a multiwide stack (one that uses counterbalancing) can give larger overhangs than a single width stack. Hall presents a system of $N=40$ blocks with an overhang of 2.892 and claims that this is optimal.