Difference between revisions of "1973 IMO Problems/Problem 2"
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| − | Determine whether or not there exists a finite set M of points in space not | + | ==Problem== |
| − | lying in the same plane such that, for any two points A and B of M; one can | + | Determine whether or not there exists a finite set <math>M</math> of points in space not lying in the same plane such that, for any two points A and <math>B</math> of <math>M</math>; one can select two other points <math>C</math> and <math>D</math> of <math>M</math> so that lines <math>AB</math> and <math>CD</math> are parallel and not coincident. |
| − | select two other points C and D of M so that lines AB and CD are parallel | + | |
| − | and not coincident. | + | ==Solution== |
{{solution}} | {{solution}} | ||
[[Category:Olympiad Geometry Problems]] | [[Category:Olympiad Geometry Problems]] | ||
[[Category:3D Geometry Problems]] | [[Category:3D Geometry Problems]] | ||
Revision as of 14:47, 29 January 2021
Problem
Determine whether or not there exists a finite set 
of points in space not lying in the same plane such that, for any two points A and 
of ; one can select two other points 
and 
of so that lines 
and 
are parallel and not coincident.
Solution
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