IMO Shortlist 1979 problem 5
Dodao/la:
arhiva2. travnja 2012. Let
![n \geq 2](/media/m/2/1/f/21fe2458de6d1580c44fd06e0fac11bb.png)
be an integer. Find the maximal cardinality of a set
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
of pairs
![(j, k)](/media/m/0/7/a/07acb41848174cec8806556a22131a11.png)
of integers,
![1 \leq j < k \leq n](/media/m/0/3/0/0303e7ce3cbaa6d6b17cfcf0bb0068bf.png)
, with the following property: If
![(j, k) \in M](/media/m/2/b/0/2b0a769adc52241336b38bbbb9a76908.png)
, then
![(k,m) \not \in M](/media/m/5/7/a/57a85f1ef9fdccd79ad50f2886443f56.png)
for any
%V0
Let $n \geq 2$ be an integer. Find the maximal cardinality of a set $M$ of pairs $(j, k)$ of integers, $1 \leq j < k \leq n$, with the following property: If $(j, k) \in M$, then $(k,m) \not \in M$ for any $m.$
Izvor: Međunarodna matematička olimpijada, shortlist 1979