Difference between revisions of "1971 IMO Problems/Problem 5"

(Created page with "Prove that for every natural number m; there exists a finite set S of points in a plane with the following property: For every point A in S; there are exactly m points in S which...")
 
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Prove that for every natural number m; there exists a finite set S of points
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Prove that for every natural number <math>m</math>; there exists a finite set <math>S</math> of points in a plane with the following property: For every point <math>A</math> in <math>S</math>; there are exactly <math>m</math> points in <math>S</math> which are at unit distance from <math>A</math>.
in a plane with the following property: For every point A in S; there are
 
exactly m points in S which are at unit distance from A.
 

Revision as of 14:06, 29 January 2021

Prove that for every natural number $m$; there exists a finite set $S$ of points in a plane with the following property: For every point $A$ in $S$; there are exactly $m$ points in $S$ which are at unit distance from $A$.

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