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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2007 National Olympiad First Round
28
28
Part of
2007 National Olympiad First Round
Problems
(1)
Turkey NMO 2007 1st Round - P28 (Combinatorics)
Source:
10/5/2012
n
n
n
integers are arranged along a circle in such a way that each number is equal to the absolute value of the difference of the two numbers following that number in clockwise direction. If the sum of all numbers is
278
278
278
, how many different values can
n
n
n
take?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
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x
−
b
o
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>
(
A
)
<
/
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p
a
n
>
1
<
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c
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a
s
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=
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a
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x
−
b
o
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>
(
B
)
<
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a
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>
2
<
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c
l
a
s
s
=
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x
−
b
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>
(
C
)
<
/
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p
a
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>
4
<
s
p
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c
l
a
s
s
=
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a
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−
b
o
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>
(
D
)
<
/
s
p
a
n
>
139
<
s
p
a
n
c
l
a
s
s
=
′
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a
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x
−
b
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>
(
E
)
<
/
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>
None of the above
<span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ 139 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
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′
>
(
A
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
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′
>
(
B
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
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′
>
(
C
)
<
/
s
p
an
>
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
139
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of the above
absolute value