MathDB
BMT 2014 Spring - Geometry 5

Source:

December 29, 2021
geometry

Problem Statement

In a 100-dimensional hypercube, each edge has length 1 1. The box contains 2100+12^{100} + 1 hyperspheres with the same radius r r. 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 100100 faces of the hypercube. Thus, the hyperspheres are tightly packed in the hypercube. Find r r.