Given a cube that has a side length of one, determine the greatest number of points that can be placed on the cube (located on faces or edges) so that for any 2 points they are at least one length apart from each other. To show that there is a x, number, you will have to draw x points that are all one length apart and provide mathematical proof that a collection of x+1 points has 2 points that are less then one apart. (This is a combinatorics and graph theory math problem)
Given a cube that has a side length of one, determine the greatest number of points that can be placed on the cube (located on faces or edges) so that for any 2 points they are at least one length apart from each other. To show that there is a x, number, you will have to draw x points that are all one length apart and provide mathematical proof that a collection of x+1 points has 2 points that are less then one apart.
(This is a combinatorics and graph theory math problem)
It is given that a cube has side length of 1.
The objective is to determine the greatest number of points that can be placed on the cube so that any 2 points are at least one length apart from each other.
The pigeonhole principle is used to prove the requirement.
The pigeonhole principle states that if objects are placed in holes with , then at least one hole must contain more than one object.
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