Shortly after Charles Dickens's A Christmas Carol was released in 1843, a tradition of adaptation began which has continued seemingly unabated to the present day. Consequently, the tale has become so widely known that one is arguably as likely to have first encountered the iconic miser Scrooge through any number of audio-visual adaptations as through the original work itself. Significant critical attention has been paid to the nature of Scrooge's drastic change from miser to philanthropist. Many would argue that the change, happening both literally and figuratively overnight, is not representative of a genuine psychological transformation. On Christmas day, 2010, Stephen Moffat, Show-runner of the popular sci-fi series Doctor Who, became the latest adapter of the classic tale, with a Christmas themed episode of the series titled Doctor Who: A Christmas Carol. This paper addresses the Scrooge Problem, or the debated legitimacy of Scrooge's transformation. A study of A Christmas Carol and Doctor Who: A Christmas Carol reveals that Dickens in fact represents a genuine transformation based on one primary concept, time as a cyclical journey. This concept accommodates Dickens's belief in the transformative power of childhood memory and the nature of sympathy. Scrooge's transformation is brought to pass in part through his evolving understanding of the nature of time, a phenomenon which becomes even more apparent in Doctor Who: A Christmas Carol.