I thought this question was classified as a word-meaning question. So, does "1 apart" mean 1/2 the side of the triangle?
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It looks to be referring to a distance of $1$ unit apart. – John Habert Feb 11 '14 at 13:39
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@JohnHabert, so this means that the distance between two points at least is 1 unit? – Feb 11 '14 at 13:41
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See this for a similar question. – John Habert Feb 11 '14 at 13:55
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@Kareem -- no. It means that the distance is at most one unit. – bubba Feb 11 '14 at 14:23
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If you put five points in this triangles, there will be two distinct points among them with a distance $\le 1$. Or: It is impossible to find five points in this triangle such that all pairwise distances are $>1$. (And yes, as the side length of the triangle, you can replace $1$ with "half the side length" here).
As a hint to the solution, partition the triangle into four suitable parts.
Hagen von Eitzen
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To say that two points are "less than or equal to 1 apart" means that the distance between the two points is less than or equal to 1 unit. Or, more briefly, the distance is at most one unit.
bubba
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