MathDB

An encyclopedia consists of

{2000}

numbered volumes. The volumes are stacked in order with number

{1}

on top and

{2000}

in the bottom. One may perform two operations with the stack: (i) For

{n}

even, one may take the top

{n}

volumes and put them in the bottom of the stack without changing the order. (ii) For

{n}

odd, one may take the top

{n}

volumes, turn the order around and put them on top of the stack again. How many different permutations of the volumes can be obtained by using these two operations repeatedly?

4

Problems(1)