Mathematical and Physical Journal
for High Schools
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# Problem A. 625. (October 2014)

A. 625. Let $\displaystyle n\ge2$, and let $\displaystyle \mathcal{S}$ be a family of some subsets of $\displaystyle \{1,2,\ldots,n\}$ with the property that $\displaystyle |A\cup B\cup C\cup D|\le n-2$ for all $\displaystyle A,B,C,D\in\mathcal{S}$. Show that $\displaystyle |\mathcal{S}|\le 2^{n-2}$.

(CIIM6, Costa Rica)

(5 pont)

Deadline expired on November 10, 2014.

### Statistics:

 5 students sent a solution. 5 points: Janzer Barnabás, Szabó 789 Barnabás, Williams Kada. 0 point: 2 students.

Problems in Mathematics of KöMaL, October 2014