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Q 3 . Consider the 2 X 2 Rubik's cube shown below: ( a ) Develop a list - based state representation for the 2
Q Consider the X Rubik's cube shown below:
a Develop a listbased state representation for the Rubik's cube so that a search algorithm
can be applied to solving it Keep it simple! Explain your state representation.
b Any state in which all pieces on each of the sides all have the same number as each other
is a goal state eg as in the picture above Can your representation represent more than one
such goal state or is it unique? Show the goal state or states and explain why or why not.
c Any state that is not a goal state is a potential start state for the search. Show and explain two
different start states.
d A move for the rubric cube is a rotation of one of the faces by either degrees left,
degrees right or degrees direction doesn't matter Since there are faces, that makes
times possible moves. Present the transition model, mapping the state before the move to the
state after the move, for all the moves but just for one side.
e Assuming you have moves for all sides, what is the branching factor for this search?
f Can you propose a modification of the action model to reduce this complexity? Be sure to
explain how it reduces the complexity.
g To apply A search to this problem we need to have an admissible heuristic. Explain in detail
whether the following is or is not an admissible heuristic:
sum the number mismatched pieces each side
Eg if all the numbers on a side are different, then are mismatched; if are the same, then are
mismatched; if are the same then is mismatched.
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