hard nut to crack vs rub

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. 

rub

noun
  • A difficulty or problem. 

  • A loan. 

  • An act of rubbing. 

  • In the game of crown green bowls, any obstacle by which a bowl is diverted from its normal course. 

  • Any substance designed to be applied by rubbing. 

  • A mixture of spices applied to meat before it is barbecued. 

verb
  • To scour; to burnish; to polish; to brighten; to cleanse; often with up or over. 

  • To hinder; to cross; to thwart. 

  • To move (one object) while maintaining contact with another object over some area, with pressure and friction. 

  • To touch the jack with the bowl. 

  • To be rubbed against something. 

  • To rub something against (a second thing). 

  • To spread a substance thinly over; to smear. 

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