1979 USAMO Problems/Problem 5

Problem

Let $A_1,A_2,...,A_{n+1}$ be distinct subsets of $[n]$ with $|A_1|=|A_2|=\cdots =|A_n|=3$ . Prove that $|A_i\cap A_j|=1$ for some pair $\{i,j\}$ .

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1979 USAMO (Problems • Resources)
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