Challenge: Three States

What if there's a cooldown: after robbing a node, you must skip at least one level before robbing again? Now you need three states: $(rob, skip1, skip2+)$. $skip1$ = just skipped one level, $skip2+$ = skipped two or more.

Transition: $rob = value + skip2+_{children}$. $skip1 = rob_{children}$. $skip2+ = \max(skip1, skip2+)_{children}$. This pattern generalizes: more constraints = more states. The tree structure stays the same; only the state tuple grows.