Problem
1. Write a backtracking algorithm for the n-Queens problem that uses a version of procedure expand instead of a version of procedure check node.
2. Write an algorithm that takes an integer n as input and determines the total number of solutions to the n-Queens problem.
3. Show that, without backtracking, 155 nodes must be checked before the first solution to the n = 4 instance of the n-Queens problem is found (in contrast to the 27 nodes in Figure 5.4).
