MathDB
Problems
Contests
International Contests
KoMaL A Problems
KoMaL A Problems 2023/2024
A. 869
A. 869
Part of
KoMaL A Problems 2023/2024
Problems
(1)
Maximum distance of points on solids in R^n
Source: KoMaL A. 869
2/15/2024
Let
A
A
A
and
B
B
B
be given real numbers. Let the sum of real numbers
0
≤
x
1
≤
x
2
≤
…
≤
x
n
0\le x_1\le x_2\le\ldots \le x_n
0
≤
x
1
≤
x
2
≤
…
≤
x
n
be
A
A
A
, and let the sum of real numbers
0
≤
y
1
≤
y
2
≤
…
≤
y
n
0\le y_1\le y_2\le \ldots\le y_n
0
≤
y
1
≤
y
2
≤
…
≤
y
n
be
B
B
B
. Find the largest possible value of
∑
i
=
1
n
(
x
i
−
y
i
)
2
.
\sum_{i=1}^n (x_i-y_i)^2.
i
=
1
∑
n
(
x
i
−
y
i
)
2
.
Proposed by Péter Csikvári, Budapest
algebra
Inequality