[Solved]-Question 1 Consider Problem Solving Magic Triangle Shown Figuresiiii Csp Goal Place Number Q37250335

Question 1: Consider the problem of solving a magic triangle, shown in figuresiiii) below, as a CSP. The goal is to place each of the numbers from 1 to 6 in one of the circles along the sides of the triangle so that the sum of the three numbers on any side is the same total S (the magic sum). Possible solutions are shown for the cases of S-9 and S-10. We want to solve other puzzles e.g., for S-12, as shown. fi) dN (iii) 4 5 (S 10 12 4 2 3 2 (a) Provide a precise Constraint Satisfaction Problem (CSP) formulation in terms of the variables, their domain, and the equations that define all the problem constraints. Do not assume a particular S value. (1 mark) (b) Describe exactly how the Most Constraining Variable and Minimum- Remaining Value heuristics apply to this problem. State accordingly which one should be used to select variables. (3 marks) (c) Explain exactly how the Least Constraining Value heuristics works on this problem, using the first variable assignment as example. (3 marks) (d) Using your CSP formulation in part (a) and the best heuristics identified in part (b-c), apply the Depth-First Search algorithm with Forward Checking to find one possible solution to the puzzle. Use a table to show the variable instantiated at each step and the resulting domain for the remaining variables. Clearly indicate all backtracking steps, if any. (3 marks) (e) Explain briefly whether the above approach would scale up e.g., if we used a magic triangle of 9 circles instead of 6, or 12, or 15, etc. Hint: consider the variables, domains, constraints, heuristics… (2 marks) (12) Show transcribed image text Question 1: Consider the problem of solving a magic triangle, shown in figuresiiii) below, as a CSP. The goal is to place each of the numbers from 1 to 6 in one of the circles along the sides of the triangle so that the sum of the three numbers on any side is the same total S (the magic sum). Possible solutions are shown for the cases of S-9 and S-10. We want to solve other puzzles e.g., for S-12, as shown. fi) dN (iii) 4 5 (S 10 12 4 2 3 2 (a) Provide a precise Constraint Satisfaction Problem (CSP) formulation in terms of the variables, their domain, and the equations that define all the problem constraints. Do not assume a particular S value. (1 mark) (b) Describe exactly how the Most Constraining Variable and Minimum- Remaining Value heuristics apply to this problem. State accordingly which one should be used to select variables. (3 marks)
(c) Explain exactly how the Least Constraining Value heuristics works on this problem, using the first variable assignment as example. (3 marks) (d) Using your CSP formulation in part (a) and the best heuristics identified in part (b-c), apply the Depth-First Search algorithm with Forward Checking to find one possible solution to the puzzle. Use a table to show the variable instantiated at each step and the resulting domain for the remaining variables. Clearly indicate all backtracking steps, if any. (3 marks) (e) Explain briefly whether the above approach would scale up e.g., if we used a magic triangle of 9 circles instead of 6, or 12, or 15, etc. Hint: consider the variables, domains, constraints, heuristics… (2 marks) (12)

Expert Answer

---

Answer to Question 1: Consider the problem of solving a magic triangle, shown in figuresiiii) below, as a CSP. The goal is to plac… . . .