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National and Regional Contests
Turkey Contests
National Olympiad First Round
2006 National Olympiad First Round
8
8
Part of
2006 National Olympiad First Round
Problems
(1)
Turkey NMO 2006 1st Round - P08 (Combinatorics)
Source:
2/2/2013
Let
d
1
d_1
d
1
and
d
2
d_2
d
2
be parallel lines in the plane. We are marking
11
11
11
black points on
d
1
d_1
d
1
, and
16
16
16
white points on
d
2
d_2
d
2
. We are drawig the segments connecting black points with white points. What is the maximum number of points of intersection of these segments that lies on between the parallel lines (excluding the intersection points on the lines) ?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
5600
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
5650
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
6500
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
6560
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
6600
<span class='latex-bold'>(A)</span>\ 5600 \qquad<span class='latex-bold'>(B)</span>\ 5650 \qquad<span class='latex-bold'>(C)</span>\ 6500 \qquad<span class='latex-bold'>(D)</span>\ 6560 \qquad<span class='latex-bold'>(E)</span>\ 6600
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
5600
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
5650
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
6500
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
6560
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
6600