Neka je
. Koliko ima podskupova
skupa
takvih da za svako
vrijedi: ako
i
, onda barem jedan od brojeva
i
također pripada skupu
?
Let
. How many subsets
of
exist such that for all
holds: if
and
, then at least one of
and
is also in
?
[lang=hr]
Neka je $A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$. Koliko ima podskupova $B$ skupa $A$ takvih da za svako $n \in \{1, 2, 3, 4, 5, 6, 7, 8\}$ vrijedi: ako $n \in B$ i $n + 2 \in B$, onda barem jedan od brojeva $n + 1$ i $n + 3$ također pripada skupu $B$?
[/lang]
[lang=en]
Let $A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$. How many subsets $B$ of $A$ exist such that for all $n \in \{1, 2, 3, 4, 5, 6, 7, 8\}$ holds: if $n \in B$ and $n + 2 \in B$, then at least one of $n + 1$ and $n + 3$ is also in $B$?
[/lang]
