The phrase "known conundrum" refers to a problem or situation that is well-known and yet remains difficult to solve or understand. There are several synonyms for this phrase, including "perplexing dilemma," "puzzling enigma," and "confounding mystery." Other words that can be used to describe a known conundrum include "enigmatic," "cryptic," and "unsolvable." When faced with a known conundrum, it may be helpful to approach it with a fresh perspective or by seeking counsel from others who have encountered similar challenges. Ultimately, the key to solving a known conundrum lies in careful analysis, persistence, and an open mind.