please provide excel solution as well

In the XXVI Puzzle game, the idea is to arrange the numbers in such a way that each line of four pieces must total to 26, see Figure 1 below taken from Courtesy (2013). There are 12 pieces numbered from 1 to 12 , and no piece is allowed to be used twice and each position is allowed to have one piece only. As you can see from Figure 1, there are 6 lines, each line corresponding to the side of one of the two triangles. Figure 1. The XXVI Puzzle game (Courtesy, 2013) (i) Formulate the problem as a Linear Programming problem by defining clearly your decision variables, the objective function and constraints. (ii) Provide two possible combinations using Excel solver (include your formulation in excel as an appendix). Give your answer in a way that a non-specialist can understand it. (iii) Show briefly either empirically or otherwise why other values than 26 would lead to an infeasible problem. Hint: The question is how to assign the 12 numbers to the 12 fixed positions. This is an assignment problem with the additional constraints that the sum of the numbers in any line (there are 6 of them) must be exactly 26 and no number is allowed to be repeated and all positions have to be used. It is a one to one relationship