Gordian knot vs tough nut to crack

Gordian knot

noun
  • Any intricate and complex problem having a simple solution. 

  • The legendary knot tied to a pole near the temple of Zeus in Gordium. 

tough nut to crack

noun
  • A problem that is challenging to solve. 

  • A situation, person, group, etc. which is difficult to 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 Gordian knot and tough nut to crack occurred in a corpus of books? (source: Google Ngram Viewer )