When it comes to describing a problem or situation that is difficult to solve or understand, there are plenty of synonyms for the phrase "hard nut to crack." Some of the most common alternatives for this phrase include "tough nut to crack," "difficult puzzle," "enigma," "conundrum," "mystery," "challenge," "obstacle," "riddle," and "headache." Each of these synonyms emphasizes the idea of something that is complex, hard to figure out, or requiring a lot of effort to overcome. Whether you're dealing with a complicated project at work, a thorny personal problem, or a challenging academic assignment, you can use any of these phrases to describe the situation.