# Using your Head is Permitted

## May 2008 solution

The answer is that a permutation can be found in both cases if and only if
*n* is even.
If *n* is odd, *T*_{n}-1=1+...+*n*-1 mod *n*=0,
so clearly no solution can exist.

If *n* is even, the following permutation can easily be shown to provide
a solution:

*S*_{i}=(-1)^{i}*i*
mod *n*

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