Walks, Paths and Connectivity · Challenge problem

Vertices $s=1$ and $t=2$ are joined by three internally-disjoint paths: $1\text{-}3\text{-}2$ (length $2$), $1\text{-}4\text{-}5\text{-}2$ (length $3$), and $1\text{-}6\text{-}7\text{-}8\text{-}2$ (length $4$), and by no other edges. What is the maximum number of pairwise internally-disjoint paths from $1$ to $2$?