Ian Stewart’s (2005) book Game, Set and Math includes 12 puzzles linked to the 12 days of Christmas. A favourite is Five Gold Rings. The five gold rings are arranged to maximise the overlaps. At every overlap there is a diamond. You have diamonds of 1, 2, 3, 4, 5, 6, ... carats. Arrange the diamonds so the total number of carats on each ring is the same.
Try starting small—just two rings, two overlaps and each ring has a total of three carats (1 + 2). Now three rings, there are six overlaps, arrange diamonds of 1, 2, 3, 4, 5 and 6 carats so each ring has the same total.
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