hard nut to crack vs mystery

hard nut to crack

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

  • A problem that is challenging to solve. 

  • 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. 

mystery

noun
  • Something secret or unexplainable; an unknown. 

  • Someone or something with an obscure or puzzling nature. 

  • A religious truth not understandable by the application of human reason alone (without divine aid). 

  • A particular event or series of events in the life of Christ. 

  • A sacrament. 

  • A secret religious celebration, admission to which was usually through initiation. 

  • A craft, art or trade; specifically a guild of craftsmen. 

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