The cyclic quaternary ammonium hydroxide shown is heated (Hofmann elimination). The ring-opened tertiary amine is then exhaustively methylated, converted to the hydroxide and heated again. Which hydrocarbon is formed?

The salt is N,N-dimethylpiperidinium hydroxide. The first Hofmann elimination opens the ring to N,N-dimethylpent-4-en-1-amine, which is quaternised again. In the second elimination the beta-hydrogen on C-4 is removed, giving penta-1,4-diene (a conjugated diene would need a hydrogen that is not beta to nitrogen), with loss of trimethylamine.