[Solved]-Question 1 Consider Problem Solving Magic Triangle Shown Figures Iii Csp Goal Place Number Q37214804

Question 1: Consider the problem of solving a magic triangle, shown in figures (-iii) 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. (iii) 10 12 Provide a precise Constraint Satisfaction Problem (CSP) formulation in terms of the variables, their domain, and the equations that define all the problenm constraints. Do not assume a particular S value. (1 mark) (a) (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) 1/4 (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-e), 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 eg. 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) 91 12) Show transcribed image text Question 1: Consider the problem of solving a magic triangle, shown in figures (-iii) 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. (iii) 10 12 Provide a precise Constraint Satisfaction Problem (CSP) formulation in terms of the variables, their domain, and the equations that define all the problenm constraints. Do not assume a particular S value. (1 mark) (a) (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) 1/4 (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-e), 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 eg. 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) 91 12)

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Answer to Question 1: Consider the problem of solving a magic triangle, shown in figures (-iii) below, as a CSP. The goal is to pl… . . .