An upright symmetrical triangle is divided into four layers: The bottom layer consists of four (equally-spaced) dots, designated as A, B, C, and D. The next layer includes dots E, F, and G, and the following layer has dots H and I. The top layer has dot J. You want to invert the triangle (bottom layer has one dot and top layer has four) by moving the dots around as necessary.8

(a) Identify two feasible solutions.

(b) Determine the smallest number of moves needed to invert the triangle.