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Let $n$ be a positive integer. A subset $S$ of points in plane satisfies the following conditions:

a) We can't find $n$ lines in plane, such that every element of $S$ belongs to at least one of these lines.

b) For every $X\in S$, we can find $n$ lines in plane, such that every element of $S-\{X\}$ belongs to at least one of these lines.

Find the maximum number of elements of $S$.

As you can see here, The problem can be solved using linear algebra. But is there a pure combinatorics way to prove it?

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