SARAH MILLS  IT was partly thanks to a bet with her sister that Agatha Christie wrote her first detective novel, and 100 years since it was published she is as popular as ever. Christie was 30 when in February 1920 "The Mysterious Affair at Styles" was serialised in a British newspaper. The book was published in America in October and the following year in Britain. Now, according to Guinness World Records, Christie is the world's best-selling fiction writer and her crime novels have sold 2 billion copies. "She did that as a woman at the time when women did not…