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

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