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## NPTEL An Introduction to Artificial Intelligence Week 6 Assignment Answers

**Q1. Mona is performing a backtracking search for solving CSPs. At each step, she is unable to decide which variable to assign next. Which of the following methods would you recommend to her to speed up the search?**

i. Randomly select a variable from remaining choices

ii. Choose the variable with the fewest legal values remaining

iii. Choose the variable with the most number of legal values remaining

iv. Choose the variable with the most constraints on remaining variables

**Answer:** (b),(c)&(d)

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**Q2. Select the correct options regarding forward consistency check.**

**Answer:** (a)&(c)

**Q3. Which of the following options are not correct?**

**Answer:** (a),(c)&(d)

**Q4.** **Consider the following cryptarithmetic problem where TWO and FOUR are three and four digit numbers respectively. Which of the following constraint(s) is/are correct for modeling this problem? Assume that X1, X2 & X3 are carry overs resulting from the additions at the unit, tens and the hundreds place. Also, all digits are distinct.**

**Answer:** (a),(b)&(c)

**Q5. Bennet wishes to perform a graph coloring problem (with four colors) on a map of Australia. He is given the following map of Australia and to help him, his friend Fischl has already performed some steps of a Backtracking CSP. Following the Minimum Remaining Values Heuristic with Degree Heuristic used as Tie Breaking, which variable(state) would be assigned next?**

**Answer:** (c)

**Q6. In the following 2 problems, our goal is to assign numbers from 1 to 8 to each node in the given undirected graph such that no two nodes have the same assigned number and no two neighboring nodes have consecutive values.**

**Answer:** Answer this question yourself.

**Q7. What value would be assigned after the one in the 6th question? If you think the answer is the variable C would be assigned 4, then type: C,4**

**Answer:** Answer this question yourself.

**Q8. Which of the following are true for iterative min-conflicts?**

**Answer:** (a),(c)&(d)

**Q9. Mention the worst-case time complexity for solving a CSP with S variables where the domain of each variable has a size of V?**

**Answer:** (c)

**Q10. Which of the following statement(s) is/are true for CSPs?**

**Answer:** (a),(b)&(c)

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