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Rioplatense Mathematical Olympiad, Level 3
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Rioplatense Olympiad 2001 P3
Rioplatense Olympiad 2001 P3
Source: Rioplatense Olympiad 2001 P3
October 2, 2017
combinatorics
algebra
Problem Statement
Let
n
>
1
n>1
n
>
1
be an integer. For each numbers
(
x
1
,
x
2
,
…
,
x
n
)
(x_1, x_2,\dots, x_n)
(
x
1
,
x
2
,
…
,
x
n
)
with
x
1
2
+
x
2
2
+
x
3
2
+
⋯
+
x
n
2
=
1
x_1^2+x_2^2+x_3^2+\dots +x_n^2=1
x
1
2
+
x
2
2
+
x
3
2
+
⋯
+
x
n
2
=
1
, denote
m
=
min
{
∣
x
i
−
x
j
∣
,
0
<
i
<
j
<
n
+
1
}
m=\min\{|x_i-x_j|, 0<i<j<n+1\}
m
=
min
{
∣
x
i
−
x
j
∣
,
0
<
i
<
j
<
n
+
1
}
Find the maximum value of
m
m
m
.
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