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}} | ||
+ | |||
+ | == See Also == {{IMO box|year=1973|num-b=1|num-a=3}} | ||
+ | [[Category:Olympiad Geometry Problems]] | ||
+ | [[Category:3D Geometry Problems]] |
Revision as of 15:47, 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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See Also
1973 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |