Initial order of first $n$ numbers

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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.
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Re: Initial order of first $n$ numbers

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

There is a parity of every permutation: try to define it in useful terms.
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