A logical conundrum refers to a problem or situation that is difficult to solve logically. Synonyms for this phrase include perplexing puzzle, mind-boggling enigma, bewildering dilemma, and thorny predicament. These alternatives convey a similar sense of difficulty and complexity that requires analytical thought and reasoning. Other synonyms to consider include intricate quandary, mystifying paradox, complex puzzle, and convoluted mystery. In general, these terms capture the essence of a perplexing situation that challenges our understanding and requires a thoughtful approach to unravel. Whether you use logical conundrum or one of these synonyms, the goal is to convey a sense of intellectual challenge and difficulty.