Establish if there exists a finite set $M$ of points in space, not all situated in the same plane, so that for any straight line $d$ which contains at least two points from M there exists another straight line $d'$, parallel with $d,$ but distinct from $d$, which also contains at least two points from $M$.
Problem
Source: IMO ShortList 1973, Poland 1, IMO 1973, Day 1, Problem 2
Tags: combinatorics, point set, 3D geometry, straight lines, parallel, IMO, IMO 1973