Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

Already signed up?
New to KöMaL?

Problem A. 558. (March 2012)

A. 558. Prove that there exists a constant C>0 for which the following statement holds: if n is a positive integer and $A_1,A_2,\ldots,A_N\subset\{1,2,\ldots,n\}$ are sets such that every two of them has at least two, and every three of them has at most three elements in common, then N<Cn².

(Proposed by: Z. Gyenes, Budapest)

(5 pont)

Deadline expired on April 10, 2012.

Statistics:

2 students sent a solution.

5 points: Ágoston Tamás, Janzer Olivér.

Problems in Mathematics of KöMaL, March 2012

2 students sent a solution.
5 points:	Ágoston Tamás, Janzer Olivér.