Problem A. 658. (December 2015)

A. 658. We call a bar of width \(\displaystyle w\) on the surface \(\displaystyle S^2\) of the unit sphere in \(\displaystyle 3\)-dimension, centered at the origin a spherical zone which has width \(\displaystyle w\) and is symmetric with respect to the origin. Prove that there exists a constant \(\displaystyle c>0\) such that for every positive integer \(\displaystyle n\) the surface \(\displaystyle S^2\) can be covered with \(\displaystyle n\) bars of the same width so that every point is contained in no more than \(\displaystyle c\sqrt{n}\) bars.

Miklós Schweitzer competition, 2015

(5 pont)

Deadline expired on January 11, 2016.

Statistics:

1 student sent a solution.
2 points:	1 student.

Problems in Mathematics of KöMaL, December 2015