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## IMC 2014 Day 2 Problem 4

We say that a subset of ${\Bbb{R}^n}$ is ${k}$almost contained by a hyperplane if there are less than ${k}$ points in that set which do not belong to the hyperplane. We call a finite set of points ${k}$generic if there is no hyperplane that ${k}$-almost contains the set. For each pair of positive integers ${k}$ and ${n}$, find the minimal number ${d(k,n)}$ such that every finite ${k}$-generic set in ${\Bbb{R}^n}$ contains a ${k}$-generic subset with at most ${d(k,n)}$ elements.

IMC 2014 Day 2 Problem 4