The Battle of Hogwarts

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Professor Dumbledore has just been informed that Lord Voldemort has gathered a huge army of Wizards and Witches and is marching towards Hogwarts to attack from the North. To prepare for the attack, Dumbledore ordered all the Wizards and Witches at Hogwarts to spread across the Northern border of the school. The border can be imagined as a straight line of length N units. At each unit a wizard is

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