[Math Lair] Mazes

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Mazes are an interesting type of puzzle with a long history. Labyrinths or mazes are a very old recreation, dating from antiquity. The oldest labyrinths or mazes were ones that a person could walk through. Perhaps the world's most famous maze is found in ancient Minoan mythology, being one built by Daedalus to imprison the Minotaur. As well, Herodotus describes an ancient Egyptian labyrinth somewhere east of Lake Moeris. During the Middle Ages, pilgrims, on their hands and knees, would follow mazes in the pavements of churches as a form of penance. Typically, these mazes consisted of a single, forced path to the centre, with no dead ends. Around the seventeenth century or so, hedge mazes were popular among the wealthy. King Louis XIV of France had one constructed at Versailles that contained 39 fountains and cost the equivalent of over $3,000,000 to build. In England, around the same time, Sir Christopher Wren designed a maze at Hampton Court Palace, which is still around today. It was not until later that mazes became pencil and paper amusements, which is where they are seen most often today.

One strategy for solving a maze is known as the right-hand rule. From the start of the maze, simply follow the right-hand wall of the maze until you reach the end (alternately, you could follow along the left-hand wall, in which case the strategy would be called the left-hand rule). This works for some mazes but not others. Which mazes does it work for and which does it not? How can you tell?

Sources used (see bibliography page for titles corresponding to numbers): 45.