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Bundeswettbewerb Mathematik
2012 Bundeswettbewerb Mathematik
1
subdivision of {1,2,..,2n}
subdivision of {1,2,..,2n}
Source:
August 19, 2015
number theory
algebra
Problem Statement
given a positive integer
n
n
n
. the set
{
1
,
2
,
.
.
,
2
n
}
\{ 1,2,..,2n \}
{
1
,
2
,
..
,
2
n
}
is partitioned into
a
1
<
a
2
<
.
.
.
<
a
n
a_1<a_2<...<a_n
a
1
<
a
2
<
...
<
a
n
and
b
1
>
b
2
>
.
.
.
>
b
n
b_1>b_2>...>b_n
b
1
>
b
2
>
...
>
b
n
. find the value of :
∑
i
=
1
n
∣
a
i
−
b
i
∣
\sum_{i=1}^{n}|a_i - b_i|
∑
i
=
1
n
∣
a
i
−
b
i
∣
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