Problem
1. By performing backtracking by hand, find all solutions to the problem of placing five queens on a 5 × 5 board. You may use the left-right symmetry of the first row by considering only the possibilities when the queen in row 1 is in one of columns 1, 2, or 3.
2. Run the eight-queens program on your computer:
(a) Write the missing Queens methods.
(b) Find out exactly how many board positions are investigated by including a counter that is incremented every time function solve_from is started. [Note that a method that placed all eight queens before it started checking for guarded squares would be equivalent to eight calls to solve_from.]
(c) Run the program for the number of queens ranging from 4 to 15. Try to find a mathematical function that approximates the number of positions investigated as a function of the number of queens.