NMC 2015 Problem 4
- Answer
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 even, one may take the top volumes and put them in the bottom of the stack without changing the order.
(ii) For odd, one may take the top 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?
Dataset text NuminaMath olympiads. Quoted with source.
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(1000!)^2
Solutions
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