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Dots in a Cube (Posted on 2010-01-27) Difficulty: 3 of 5
Let there be a cube with edge length of 9 units. Inside this cube there are 1981 points.
1. Prove that among these points there are at least 2 with the distance between them of less than 1 unit.
2. What's the biggest number of points that do not have the property stated at (1)?
2.1. How many points for the distance of 2 - 8 units?

No Solution Yet Submitted by TheKPAXian    
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  Subject Author Date
Some Thoughtspartial solutionDej Mar2010-01-28 03:01:22
Some Thoughtssolution for part 1; approximation for part 2Charlie2010-01-27 14:21:01
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