a tough nut

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a tough nut (to crack)

A person, thing, situation, or problem that is particularly difficult to understand, solve, or deal with. I've been dating Jenny for over a year, and I still think she's a tough nut to crack! Figuring out the best way to modernize our product without alienating existing customers is definitely a tough nut to crack. The spy we captured is a tough nut; he hasn't said a thing since we began the interrogation.
See also: nut, tough

a tough nut

or

a hard nut

INFORMAL
If you call someone a tough nut or a hard nut, you mean they have a strong character and are very determined. That Bridget would sort anyone out — she's a tough nut.
See also: nut, tough

a tough (or hard) nut (to crack)

someone who is difficult to deal with or hard to beat; a formidable person. informal
See also: nut, tough

a hard/tough ˈnut (to ˈcrack)

(informal) a very difficult problem to solve; a very difficult person to deal with: Persuading drivers to leave their cars at home and use public transport will be a very tough nut to crack.You’ll find it difficult to make him change his mind. He’s a tough nut.
See also: hard, nut, tough