1. Explain why it is a good heuristic to choose the variable that is most constrained but the value that is lost constraining in a CSP search. 2. Consider the problem of placing k knights on an nurn chessboard such that no two knights are attacking each other, where k is given and ks na. {a) Choose a CSP formulation. In your fornition, what are the variables? (b) What are the possible values of each variable? (c) What sets of variables are constrined, and how? 3. Consider the following classroom scheduling problem: There are 4 disses, CI, C2, C3, and C4 and 3 ss roos, R1, R2, and R3. The following table shows the cluss schedule: Cla Time 12 9.00 11:20 10:00 12:30 110011330 In addition, there are the following restrictions: Each class must the one of the 3 rooms. RI R2 R3. R3 is too small for C3. R2 and R3 are too snall for C4