Problem

Source: Federal Mathematical Competition of Serbia and Montenegro 2004

Tags: Sets, combinatorics



Let $A = \{1,2,3, . . . ,11\}$. How many subsets $B$ of $A$ are there, such that for each $n\in \{1,2, . . . ,8\}$, if $n$ and $n+2$ are in $B$ then at least one of the numbers $ n+1$ and $n+3$ is also in $B$?