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