4. (20 pts) On the British game show Countdown, the Numbers round consists of contestants getting six numbers and having to use a subset of those numbers together with the four standard arithmetic operations to come up with a given target value. (See example at the link.) In this question, you are to consider a program that will solve the numbers round (if possible). Note that each final solution can be thought of as a sequence of pairwise operations (e.g. for the solution given to the Wikipedia example, 75 + 50 = 125; 125 - 8 = 117; 117 * 7 = 819; 3 * 2 = 6; 819-6 = 813). a. What would be the state representation you would use for this problem? b. What is the initial state for the first example given at Wikipedia? c. What are your successor functions? Be specific. d. What is the branching factor of your approach? e. What is the maximum search depth of your approach? f. Imagine that instead you wanted to generate all possible three-digit numbers that can be achieved with a given initial set of six numbers, instead of just reaching a target. Would the answers to the previous parts change? If so, how? If not, why not? 4. (20 pts) On the British game show Countdown, the Numbers round consists of contestants getting six numbers and having to use a subset of those numbers together with the four standard arithmetic operations to come up with a given target value. (See example at the link.) In this question, you are to consider a program that will solve the numbers round (if possible). Note that each final solution can be thought of as a sequence of pairwise operations (e.g. for the solution given to the Wikipedia example, 75 + 50 = 125; 125 - 8 = 117; 117 * 7 = 819; 3 * 2 = 6; 819-6 = 813). a. What would be the state representation you would use for this problem? b. What is the initial state for the first example given at Wikipedia? c. What are your successor functions? Be specific. d. What is the branching factor of your approach? e. What is the maximum search depth of your approach? f. Imagine that instead you wanted to generate all possible three-digit numbers that can be achieved with a given initial set of six numbers, instead of just reaching a target. Would the answers to the previous parts change? If so, how? If not, why not