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Bosnia Herzegovina Contests
Bosnia Herzegovina Team Selection Test
2011 Bosnia Herzegovina Team Selection Test
3
Old and easy sums
Old and easy sums
Source: Bosnia and Herzegovina 2011
May 16, 2011
absolute value
algebra proposed
algebra
Problem Statement
Numbers
1
,
2
,
.
.
.
,
2
n
1,2, ..., 2n
1
,
2
,
...
,
2
n
are partitioned into two sequences
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 number
W
=
∣
a
1
−
b
1
∣
+
∣
a
2
−
b
2
∣
+
.
.
.
+
∣
a
n
−
b
n
∣
W= |a_1-b_1|+|a_2-b_2|+...+|a_n-b_n|
W
=
∣
a
1
−
b
1
∣
+
∣
a
2
−
b
2
∣
+
...
+
∣
a
n
−
b
n
∣
is a perfect square.
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