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All-Russian Olympiad
1990 All Soviet Union Mathematical Olympiad
517
ASU 517 All Soviet Union MO 1990 max |...| |a_1 - a_2| - a_3| - ... - a_{1990}|
ASU 517 All Soviet Union MO 1990 max |...| |a_1 - a_2| - a_3| - ... - a_{1990}|
Source:
August 14, 2019
inequalities
maximum
algebra
absolute value
Problem Statement
What is the largest possible value of
∣
.
.
.
∣
∣
a
1
−
a
2
∣
−
a
3
∣
−
.
.
.
−
a
1990
∣
|...| |a_1 - a_2| - a_3| - ... - a_{1990}|
∣...∣∣
a
1
−
a
2
∣
−
a
3
∣
−
...
−
a
1990
∣
, where
a
1
,
a
2
,
.
.
.
,
a
1990
a_1, a_2, ... , a_{1990}
a
1
,
a
2
,
...
,
a
1990
is a permutation of
1
,
2
,
3
,
.
.
.
,
1990
1, 2, 3, ... , 1990
1
,
2
,
3
,
...
,
1990
?
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