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1990 IMO Longlists
71
n-dimensional space - ILL 1990 PRK5
n-dimensional space - ILL 1990 PRK5
Source:
September 18, 2010
geometry proposed
geometry
Problem Statement
Given a point
P
=
(
p
1
,
p
2
,
…
,
p
n
)
P = (p_1, p_2, \ldots, p_n)
P
=
(
p
1
,
p
2
,
…
,
p
n
)
in
n
n
n
-dimensional space . Find point
X
=
(
x
1
,
x
2
,
…
,
x
n
)
X = (x_1, x_2, \ldots, x_n)
X
=
(
x
1
,
x
2
,
…
,
x
n
)
, such that
x
1
≤
x
2
≤
⋯
≤
x
n
x_1 \leq x_2 \leq\cdots \leq x_n
x
1
≤
x
2
≤
⋯
≤
x
n
and
(
x
1
−
p
1
)
2
+
(
x
2
−
p
2
)
2
+
⋯
+
(
x
n
−
p
n
)
2
\sqrt{(x_1-p_1)^2 + (x_2-p_2)^2+\cdots+(x_n-p_n)^2}
(
x
1
−
p
1
)
2
+
(
x
2
−
p
2
)
2
+
⋯
+
(
x
n
−
p
n
)
2
is minimal.
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