BMT 2014 Spring - Geometry 5
Source:
December 29, 2021
geometry
Problem Statement
In a 100-dimensional hypercube, each edge has length . The box contains hyperspheres with the same radius . The center of one hypersphere is the center of the hypercube, and it touches all the other spheres. Each of the other hyperspheres is tangent to faces of the hypercube. Thus, the hyperspheres are tightly packed in the hypercube. Find .