Initial order of first $n$ numbers

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Masum
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Initial order of first $n$ numbers

Unread post by Masum » Sun Aug 09, 2015 9:42 pm

The integers $1,...,n$ are arranged in any order. In one step any two neighboring integers may be interchanged. Prove that the initial order can never be reached after an odd number of steps.
One one thing is neutral in the universe, that is $0$.

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*Mahi*
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Re: Initial order of first $n$ numbers

Unread post by *Mahi* » Sun Aug 09, 2015 10:07 pm

Hint:
There is a parity of every permutation: try to define it in useful terms.
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Nur Muhammad Shafiullah | Mahi

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