In the end, Captain Flamingo always seems to stumble upon a solution either through Lizbeth's cleverness, persistent refusal to give up, and constantly trying new novelty items and plans until he succeeds, or sheer luck (or, quite often, some combination of the three).
Ultimately, Captain Flamingo consistently solves problems either by leveraging Lizbeth's ingenuity, her unwavering determination, and her continuous exploration of new ideas and strategies until success is achieved, or through fortunate circumstances.