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