12

Part of 1988 IMO Longlists

Problems(1)

27 half-lines (or rays) emanating from the origin

Source: IMO LongList 1988, France 4, Problem 12 of ILL

Show that there do not exist more than

27

half-lines (or rays) emanating from the origin in the

3

-dimensional space, such that the angle between each pair of rays is

\geq \frac{\pi}{4}

geometry3D geometryspherecombinatorics unsolvedcombinatorics