Finding synonyms for the phrase "difficult problem" can be challenging, as it depends on the context. However, some synonyms that come to mind are: complex issue, challenging predicament, vexing dilemma, thorny conundrum, demanding trouble, tricky situation, perplexing obstacle, daunting challenge, hardy puzzle, and formidable difficulty. Each of these synonyms highlights a different aspect of a difficult problem, whether it's its complexity, difficulty, or challenging nature. When faced with a difficult problem, using synonyms can help you articulate the issue more precisely, and potentially lead you to new solutions or perspectives.