IMO Shortlist 1996 problem C3
Dodao/la:
arhiva2. travnja 2012. Let
![k,m,n](/media/m/e/b/0/eb02bdc155b91d7a4e7108860107a69d.png)
be integers such that
![1 < n \leq m - 1 \leq k.](/media/m/5/5/a/55adcb9f88fc2a46803c746c7bbcede7.png)
Determine the maximum size of a subset
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
of the set
![\{1,2,3, \ldots, k-1,k\}](/media/m/6/9/1/691c407928ded778f7b6df7e8f99ff0f.png)
such that no
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
distinct elements of
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
add up to
%V0
Let $k,m,n$ be integers such that $1 < n \leq m - 1 \leq k.$ Determine the maximum size of a subset $S$ of the set $\{1,2,3, \ldots, k-1,k\}$ such that no $n$ distinct elements of $S$ add up to $m.$
Izvor: Međunarodna matematička olimpijada, shortlist 1996