Question 8: In this question we use the notation from Question 7. Let n1 be an integer and consider the 1(2n+1) board B2n+1. We number the cells of this board, from left to right, as 1,2,3,,2n+1. a) Determine the number of tilings of B2n+1 where the rightmost red tile is at position 1. b) Let k be an integer 1kn. Determine the number of tilings of B2n+1 where the rightmost red tile is at position 2k+1. c) Use the results from above to prove that T2n+1=2n+k=1n2nkT2k. Question 9: (Bonus Question) Consider the following recursive algorithm: Let d be the value returned by Slowclid(x,y). (a) Prove that d is the GCD of x and y. (b) Find a (tight) upper bound on the number of times Swap(x,y) is called from an initial call to Slowclid (x,y). You may express this as a number seen in class