Y by PhantomR, Adventure10, Mango247
The real numbers
satisfy
![\[x_1+x_2=2x_1',\ x_2+x_3=2x_2', \ \ldots, \ x_{2011}+x_1=2x_{2011}'\]](//latex.artofproblemsolving.com/7/e/d/7ed0c709cfa8469398b7f02bc8fca5cdf8cd1b7e.png)
where
is a permutation of
. Prove that
.

![\[x_1+x_2=2x_1',\ x_2+x_3=2x_2', \ \ldots, \ x_{2011}+x_1=2x_{2011}'\]](http://latex.artofproblemsolving.com/7/e/d/7ed0c709cfa8469398b7f02bc8fca5cdf8cd1b7e.png)
where



We have your learning goals covered with Spring and Summer courses available. Enroll today!
Something appears to not have loaded correctly.