hard nut to crack vs puzzle

hard nut to crack

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

  • A problem that is challenging to solve. 

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

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

  • An amount that is difficult to finance. 

puzzle

noun
  • Anything that is difficult to understand or make sense of. 

  • A riddle. 

  • The state of being puzzled; perplexity. 

  • A game for one or more people that is more or less difficult to work out or complete. 

  • A jigsaw puzzle. 

  • A crossword puzzle. 

verb
  • To think long and carefully, in bewilderment. 

  • To perplex, confuse, or mystify; to cause (someone) to be faced with a mystery, without answers or an explanation. 

  • To make intricate; to entangle. 

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