6
votes
1answer
225 views

Minimum number of lines covering n points

Let there be n points in the plane. I want to know the minimum number of horizontal and vertical lines covering all the points in the plane. My initial approach started like this, 1) for each point I ...
2
votes
1answer
142 views

minimum lines, maximum points

There are $P$ points in the 2-dimensional plane. Through each point, we draw two orthogonal lines: one horizontal (parallel to x axis), one vertical (parallel to y axis). Obviously, some of these ...
10
votes
1answer
233 views

Split up $n \in \mathbb{N}$ into sum of naturals with maximum LCM

Question: Given some natural number, we can of course split it up into various sums of other naturals (e.g. $7 = 6 + 1 = 1 + 4 + 2 = \ldots$) More precisely, for $n \in \mathbb{N}$, we can a find ...