Suppose that k ≥ 2 is a positive integer. An in-shuffle is performed on a list with 2k items to produce a new list of 2k items in the following way: • The first k items from the original are placed in the odd positions of the new list in the same order as they appeared in the original list. • The remaining k items from the original are placed in the even positions of the new list, in the same order as they appeared in the original list. For example, an in-shuffle performed on the list P Q R S T U gives the new list P S Q T R U. A second in-shuffle now gives the list P T S R Q U. Ping has a list of the 66 integers from 1 to 66, arranged in increasing order. He performs 1000 in-shuffles on this list, recording the new list each time. In how many of these 1001 lists is the number 47 in the 24th position?