crux vs hard nut to crack

crux

noun
  • A puzzle or difficulty. 

  • The basic, central, or essential point or feature. 

  • The critical or transitional moment or issue, a turning point. 

  • The hardest point of a climb. 

  • A cross on a coat of arms. 

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 crux and hard nut to crack occurred in a corpus of books? (source: Google Ngram Viewer )