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Mathematician Hannah Fry has analysed every Christmas broadcast that the Queen has given since her reign began. Taking each year’s message, Hannah and a colleague have compared the number of words she has used to the number of unique words used by rappers and singers in their music. Hannah also explains that she has found a way of generating her own Queen’s Christmas Speech, using a simple algorithm to suggest passages that the Queen might say judged on her previous messages. Tim Harford finds out more. First broadcast on 18 December 2016.