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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 points)

Deadline expired on 11 January 2016.

Statistics on problem A. 658.
 1 student sent a solution. 2 points: 1 student.

• Problems in Mathematics of KöMaL, December 2015

•  Támogatóink: Morgan Stanley