Consider the problem in the below figure. Your goal is to find the places of the digits from 0 to 9 in grey cells in such a way that if a number is given between adjacent cells, then the sum of the digits in these cells must be equal to that number. You can use each digit only once.
Formulate this problem as a mixed-integer linear program by defining binary decision variables. As you do not have an objective function, you can set it to 0. Implement your model using Python and Gurobi. Your code should output the resulting matrix, i.e., the values of the grey cells.