Let S be a set of 100 points in the plane and the distance between any two points of S is at least 1. Show that these 100 points can be divided into 4 groups such that any two points in the same group has a distance strictly larger than 1.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .
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Let S be a set of 100 points in the plane and the distance between any two points of S is at least 1. Show that these 100 points can be divided into 4 groups such that any two points in the same group has a distance strictly larger than 1.

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