#### Good Will Hunting Problem

Remember the Good Will Hunting movie, where a genius solves an MIT problem? Our artificial intelligence can solve that too!

#### Problem

```G
is the graph
vertex set V = {1,2,3,4}
edges E =
(1,2),(1,4),(2,3),(2,3),(2,4)
Find:
2) the matrix
giving the number of 3 step walks.
3) the generating function for walks from
point i → j.
4) the generating function for walks from points 1 → 3.```

#### Solution

```1) The adjacency matrix A is:

A = [[0, 1, 0, 1],
[1, 0, 2, 1],
[0, 2, 0, 0],
[1, 1, 0, 0]]

2) The matrix giving the number of 3 step walks is:

W3 = [[0, 0, 0, 0],
[0, 0, 2, 0],
[0, 2, 0, 0],
[0, 0, 0, 0]]

3) The generating function for walks from point i → j is:

G(i,j) = (A^3)_{ij}

4) The generating function for walks from points 1 → 3 is:

G(1,3) = (A^3)_{13}```

A.I. Evaluation of the Solution

The candidate's solution is correct and demonstrates a level of completeness. The approach is straightforward and easy to follow.

Evaluated at: 2022-10-15 15:37:44

#### Community solutions:

Check these solutions from our community and artificial intelligence:
The candidate's solution is correct. They have provided the adjacency matrix and have correctly found the number of 3 step walks and the generating function for walks from points 1-3.
The candidate's solution is complete and solves the problem. The candidate's approach is to first find the adjacency matrix A, then the matrix giving the number of 3 step walks, then the generating function for walks from point i → j, and finally the generating function for walks from points 1 → 3.