MathDB

71

Part of 1990 IMO Longlists

Problems(1)

n-dimensional space - ILL 1990 PRK5

Source:

9/18/2010
Given a point P=(p1,p2,…,pn)P = (p_1, p_2, \ldots, p_n) in nn-dimensional space . Find point X=(x1,x2,…,xn)X = (x_1, x_2, \ldots, x_n), such that x1≤x2≤⋯≤xnx_1 \leq x_2 \leq\cdots \leq x_n and (x1−p1)2+(x2−p2)2+⋯+(xn−pn)2\sqrt{(x_1-p_1)^2 + (x_2-p_2)^2+\cdots+(x_n-p_n)^2} is minimal.
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