1975 IMO Problems/Problem 1
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Problem
Let 
be real numbers such that ![\[x_1\ge x_2\ge\cdots\ge x_n \text{ and } y_1\ge y_2\ge\cdots\ge y_n.\]](http://latex.artofproblemsolving.com/2/9/8/2986cacba9b25b367eec05bc85a10139b47e70ee.png)
Prove that, if 
is any permutation of 
then ![\[\sum^n_{i=1}(x_i-y_i)^2\le\sum^n_{i=1}(x_i-z_i)^2.\]](http://latex.artofproblemsolving.com/7/d/2/7d2ec052f76e524fbdaf5010c1b49882e5278b00.png)
Solution
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See Also
| 1975 IMO (Problems) • Resources | ||
| Preceded by First Question |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
