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10
max ||...||x_1 - x_2|- x_3| -... | - x_{2023}| (2023 Auckland MO p10)
max ||...||x_1 - x_2|- x_3| -... | - x_{2023}| (2023 Auckland MO p10)
Source:
March 26, 2024
algebra
inequalities
Problem Statement
Find the maximum of the expression
∣
∣
.
.
.
∣
∣
x
1
−
x
2
∣
−
x
3
∣
−
.
.
.
∣
−
x
2023
∣
,
||...||x_1 - x_2|- x_3| -... | - x_{2023}|,
∣∣...∣∣
x
1
−
x
2
∣
−
x
3
∣
−
...∣
−
x
2023
∣
,
where
x
1
,
x
2
,
.
.
.
,
x
2023
x_1,x_2,..., x_{2023}
x
1
,
x
2
,
...
,
x
2023
are distinct natural numbers between
1
1
1
and
2023
2023
2023
.
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