This page has been one of the most hugely popular problem pages on the site.  Graeme, a perceptive and intuitive mathematician, gave us for many years math problems that perplexed and delighted visitors.  Be warned that many of these problems are not for the faint of heart; some of his solutions are longer than three or four solutions from other problem pages.  If you have the courage to face the challenge, dive in below and start solving!