Harry first faces Hagrid’s Puzzle. Hagrid believes that the best way to teach Harry about magical creatures is by getting him to interact with them. Hagrid decides to make this a little interesting. Hagrid takes Harry to the Enchanted Forest. Hagrid with some help from Dumbledore divides the forest into several cells, each with it’s own coordinates as shown below. Each charm has a magical creature. Harry will start at (8,10). A spell has been laid so that movement between these cells is restricted. If your position is (a,b), you can only move to (a,a+b), (a,a-b),(a+b,b), (a-b,b), (b-a,b) and (a,b-a). Harry can contin- ue until there is no other magical creature under his reach. Harry wants to make the most of this exercise and learn as much as possible. What is the largest possible number of Magical Creatures he will be able to meet?