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Moldova Team Selection Test
1993 Moldova Team Selection Test
6
Combo seems Easy but I cannot Get
Combo seems Easy but I cannot Get
Source:
July 28, 2016
combinatorics
Problem Statement
The numbers
1
,
2
,
.
.
.
,
2
n
−
1
,
2
n
1,2,...,2n-1,2n
1
,
2
,
...
,
2
n
−
1
,
2
n
are divided into two disjoint sets,
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
. Prove that
∣
a
1
−
b
1
∣
+
∣
a
2
−
b
2
∣
+
.
.
.
+
∣
a
n
−
b
n
∣
=
n
2
.
|a_1 - b_1| + |a_2 - b_2| + ... + |a_n - b_n| = n^2.
∣
a
1
−
b
1
∣
+
∣
a
2
−
b
2
∣
+
...
+
∣
a
n
−
b
n
∣
=
n
2
.
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