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2024-IMOC
A2
A2
Part of
2024-IMOC
Problems
(1)
Minimum value
Source: 2024 imocsl A2 (idependent quiz P3)
8/8/2024
Given integer
n
≥
3
n \geq 3
n
≥
3
and
x
1
x_1
x
1
,
x
2
x_2
x
2
, …,
x
n
x_n
x
n
be
n
n
n
real numbers satisfying
∣
x
1
∣
+
∣
x
2
∣
+
…
+
∣
x
n
∣
=
1
|x_1|+|x_2|+…+|x_n|=1
∣
x
1
∣
+
∣
x
2
∣
+
…
+
∣
x
n
∣
=
1
. Find the minimum of
∣
x
1
+
x
2
∣
+
∣
x
2
+
x
3
∣
+
…
+
∣
x
n
−
1
+
x
n
∣
+
∣
x
n
+
x
1
∣
.
|x_1+x_2|+|x_2+x_3|+…+|x_{n-1}+x_n|+|x_n+x_1|.
∣
x
1
+
x
2
∣
+
∣
x
2
+
x
3
∣
+
…
+
∣
x
n
−
1
+
x
n
∣
+
∣
x
n
+
x
1
∣.
Proposed by snap7822
algebra
IMOC
minimum value
inequalities
absolute value