conundrum vs self-contradiction

conundrum

noun
  • A difficult question or riddle, especially one using a play on words in the answer. 

  • A difficult choice or decision that must be made. 

self-contradiction

noun
  • A statement that contains a contradiction, or a premise from which one could be derived 

How often have the words conundrum and self-contradiction occurred in a corpus of books? (source: Google Ngram Viewer )