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Creating Rectangular Prisms with Given Surface Area

Creation of this resource was inspired by this problem from Robert Kaplinsky. Goal here: Adjust the dimensions of the rectangular prism shown below to create one with the given surface area. For simplicity sake, the edge lengths of this prism are positive integers ranging from 1 to 9. Given this, the number of possible unique solutions for each problem is provided. Note: The number of UNIQUE solutions is given. Thus, a prism having LENGTH = 4, WIDTH = 5, and HEIGHT = 6 is equivalent to a prism having LENGTH = 6, WIDTH = 4, and HEIGHT = 5.