1975 IMO Problems/Problem 1

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Problem

Let $x_i, y_i$ $(i=1,2,\cdots,n)$ be real numbers such that \[x_1\ge x_2\ge\cdots\ge x_n \text{ and } y_1\ge y_2\ge\cdots\ge y_n.\] Prove that, if $z_1, z_2,\cdots, z_n$ is any permutation of $y_1, y_2, \cdots, y_n,$ then \[\sum^n_{i=1}(x_i-y_i)^2\le\sum^n_{i=1}(x_i-z_i)^2.\]

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
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