Suppose that k \geq 2 is a positive integer. An in-shuffle is performed on a list with 2 k items to produce a new list of 2 k 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 24 th position?
Answer Choices
A. 90
B. 71
C. 83
D. 72
E. 84