Problem representation scheme and rule based production system problem:

2) (40 points) A game is referred as Princess Romantica. Princess Romantica is known to have two persistent suitors, Charming Charles and Handsome Hans, them she instructs to take turns to visit her castle's garden (shown in Figure 2) to pick at most two roses from the rose bushes. Naturally this ceremony is meant to fathom the depth of their true love, so that she may later decide to whom she wants to award her hand in marriage. In the figure 1 Princess Romantica is smelling a beautiful rose that Charming Charles has picked from the largest bush. This "game" will continue until one of the suitors will be unable to bring a rose back, because there is eventually none left; upon which event he will despondently creep away to let the winner live happily ever after. Assuming the rose bushes (originally have 1, 3, 5,7, 9, and 11 roses respectively) in the castle's garden as shown in Figure 1. They are the only special rose bushes in the country. You as a unique advisor for Charming Charles please help him to win the important game: a) (20 points) Select a problem representation scheme that you have learned to represent the game. Select a problem solving method that you have learned to solve and win this game. Using this method to solve it. b) (20 points) Design a rule-based expert system/production system, which let Charming Charles to win this game. Given the rules /production set, the inference engine/control regime, and the contents in the working memory. (Hint: You may first consider simple cases which has 1 bush or 2 bushes, then consider the whole game as a recursive one. So your system may actually solve the problem having anyN> 6 bushes.)