Reserve in packing cubes into the unit cube
Janusz Januszewski, Łukasz Zielonka · Bulletin of the Polish Academy of Sciences Mathematics · 2023
Any collection of $d$-dimensional cubes of total volume not greater than $2^{1-d}$ can be packed into the unit $d$-dimensional cube $I^d$ so that the uncovered part of $I^d$ contains a cube of edge length $1-\sqrt[d]{2}/2$. To achieve this result, the wel