Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.