Marinada '23

[lang = hr] Dano je $37$ intervala $[a_i,b_i]$ ( $0\leq a_i \leq b_i \leq 1$)gdje je $i$ element skupa $\{1,2,3,…,37\}$. Neovisno o odabiru $a$-ova i $b$-ova možemo garantirati da postoji $n$ intervala s zajedničkim elementom ili $n$ međusobno disjunktnih intervala. Koliko je $n$? [/lang] [lang = en] Given $37$ intervals $[a_i,b_i]$ ( $0\leq a_i \leq b_i \leq 1$) where $i$ is an element of the set $\{1,2,3,…,37\}$. Regardless of the choice of $a$ and $b$, we can guarantee that there are $n$ intervals with a common element or $n$ mutually disjoint intervals. How much is $n$? [/lang]