1988 IMO Problems/Problem 2

Problem

Let $n$ be a positive integer and let $A_1, A_2, \cdots, A_{2n+1}$ be subsets of a set $B$ .

Suppose that

(a) Each $A_i$ has exactly $2n$ elements,

(b) Each $A_i\cap A_j$ $(1\le i<j\le 2n+1)$ contains exactly one element, and

(c) Every element of $B$ belongs to at least two of the $A_i$ .

For which values of $n$ can one assign to every element of $B$ one of the numbers $0$ and $1$ in such a way that $A_i$ has $0$ assigned to exactly $n$ of its elements?

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1988 IMO Problems/Problem 2

Problem