enigma vs hard nut to crack

enigma

noun
  • A riddle, or a difficult problem. 

  • A species of grasshopper, Oedaleonotus enigma. 

  • Mysteriousness; obscurity; lack of clarity. 

  • The Talaud kingfisher, Todiramphus enigma. 

  • A rare species of moth, Heliothis enigma. 

  • A style of literature characterized by obscurity and hints of transcendental meaning. 

  • Something or someone puzzling, mysterious or inexplicable. 

  • A protein with three LIM domains (a conserved cysteine- and histidine-rich structure of two adjacent zinc fingers) at the C terminus that regulates protein phosphorylation. 

  • Riddles and puzzles, collectively. 

hard nut to crack

noun
  • A problem that is challenging to solve. 

  • Used other than figuratively or idiomatically: see hard, nut, crack. 

  • A situation, person, group, etc. which is difficult to overcome or deal with. 

  • A place, opportunity, etc. to which it is difficult to gain entry. 

  • An amount that is difficult to finance. 

How often have the words enigma and hard nut to crack occurred in a corpus of books? (source: Google Ngram Viewer )