Sally wants all apples!

Computer Science Level 4

Sally loves apples, thus, she has an apple garden in her backyard, where she has grown \(25\) apples in the shape of a square of side \(5\). She is standing in the center of the garden, i.e. \(3^{\text{rd}}\) row and \(3^{\text{rd}}\) column. Now, she wants to move through the garden eating apple in every square, and she won't move into square without any apple. How many ways are there in which she can eat all the \(25\) apples?


If it were a \(3\times 3\) garden, and Sally would have started from center, i.e. (\(2,2)\) there would be \(8\) solutions as follows

\(1.\ (2,2),(3,2),(3,3),(2,3),(1,3),(1,2),(1,1),(2,1),(3,1)\) \(2.\ (2,2),(3,2),(3,1),(2,1),(1,1),(1,2),(1,3),(2,3),(3,3)\) \(3.\ (2,2),(2,3),(3,3),(3,2),(3,1),(2,1),(1,1),(1,2),(1,3)\) \(4.\ (2,2),(2,3),(1,3),(1,2),(1,1),(2,1),(3,1),(3,2),(3,3)\) \(5.\ (2,2),(1,2),(1,3),(2,3),(3,3),(3,2),(3,1),(2,1),(1,1)\) \(6.\ (2,2),(1,2),(1,1),(2,1),(3,1),(3,2),(3,3),(2,3),(1,3)\) \(7.\ (2,2),(2,1),(1,1),(3,2),(3,3),(2,3),(1,3),(1,2),(1,1)\) \(8.\ (2,2),(2,1),(1,1),(1,2),(1,3),(2,3),(3,3),(3,2),(3,1)\)


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