IMO 1988 LL FRA12

Show that there do not exist more than 27 half-lines (or rays)

IMO 1988 LL FRA12

Origin: FRA

Problem

Show that there do not exist more than 27 half-lines (or rays) emanating from the origin in 3-dimensional space such that the angle between each pair of rays is greater than of equal to \pi/4.