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Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2001 National Olympiad First Round
30
30
Part of
2001 National Olympiad First Round
Problems
(1)
P30 [Combinatorics] - Turkish NMO 1st Round - 2001
Source:
4/23/2014
There are
n
n
n
airports which form a regular
n
n
n
-gon. In the beginnig, there is exactly one plane at only
k
k
k
airports. Each of the planes flies to one of the nearest airport each day. For which of the following ordered pairs
(
n
,
k
)
(n,k)
(
n
,
k
)
, it is impossible to gather all planes at a airport on one day however the planes are arranged initially?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
(
10
,
6
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
(
10
,
4
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
(
11
,
3
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
(
11
,
5
)
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
(
13
,
8
)
<span class='latex-bold'>(A)</span>\ (10,6) \qquad<span class='latex-bold'>(B)</span>\ (10,4) \qquad<span class='latex-bold'>(C)</span>\ (11,3) \qquad<span class='latex-bold'>(D)</span>\ (11,5) \qquad<span class='latex-bold'>(E)</span>\ (13,8)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
(
10
,
6
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
(
10
,
4
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
(
11
,
3
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
(
11
,
5
)
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
(
13
,
8
)