Using F#

1) Write an F# function shuffle xs that takes an even-length list, cuts it into two equal-sized pieces, and then interleaves the pieces:

 > shuffle [1;2;3;4;5;6;7;8];; val it : int list = [1; 5; 2; 6; 3; 7; 4; 8] 

(On a deck of cards, this is called a perfect out-shuffle.)

2) Write an F# function countshuffles n that counts how many calls to shuffle on a deck of n distinct "cards" it takes to put the deck back into its original order:

 > countshuffles 4;; val it : int = 2 

(To see that this result is correct, note that shuffle [1;2;3;4] = [1;3;2;4], and shuffle [1;3;2;4] = [1;2;3;4].) What is countshuffles 52?

Hint: Define an auxiliary function countaux(deck, target) that takes two lists and returns the number of shuffles it takes to make deck equal to target.