IMO Shortlist 1998 problem C4
Kvaliteta:
Avg: 0,0Težina:
Avg: 7,0 Let
, where
. A subset
of
is said to be split by an arrangement of the elements of
if an element not in
occurs in the arrangement somewhere between two elements of
. For example, 13542 splits
but not
. Prove that for any
subsets of
, each containing at least 2 and at most
elements, there is an arrangement of the elements of
which splits all of them.













Izvor: Međunarodna matematička olimpijada, shortlist 1998