I got another answer to the Puzzler (which president succeeded his successor?)
Richard Nixon.
His successor as Vice President was LBJ. And his predecessor as President was LBJ.
I admit this is kind of a trick answer, but then it’s fairly surprising that it’s happened.
I think that Bill Clinton would also be a valid answer to this puzzler. His situation was identical to Cleveland’s, but for the governorship of Arkansas rather than the presidency.