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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1976 AMC 12/AHSME
28
28
Part of
1976 AMC 12/AHSME
Problems
(1)
100 Lines, all distinct
Source: 1976 AHSME Problem 28
5/19/2014
Lines
L
1
,
L
2
,
…
,
L
100
\mathit{L}_1,\mathit{L}_2,\dots,\mathit{L}_{100}
L
1
,
L
2
,
…
,
L
100
are distinct. All lines
L
4
n
\mathit{L}_{4n}
L
4
n
,
n
n
n
a positive integer, are parallel to each other. All lines
L
4
n
−
3
\mathit{L}_{4n-3}
L
4
n
−
3
,
n
n
n
a positive integer, pass through a given point
A
\mathit{A}
A
. The maximum number of points of intersection of pairs of lines from the complete set
{
L
1
,
L
2
,
…
,
L
100
}
\{\mathit{L}_1,\mathit{L}_2,\dots,\mathit{L}_{100}\}
{
L
1
,
L
2
,
…
,
L
100
}
is
<
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>
(
A
)
<
/
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4350
<
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>
(
B
)
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4351
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>
(
C
)
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>
4900
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x
−
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′
>
(
D
)
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>
4901
<
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>
(
E
)
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>
9851
<span class='latex-bold'>(A) </span>4350\qquad<span class='latex-bold'>(B) </span>4351\qquad<span class='latex-bold'>(C) </span>4900\qquad<span class='latex-bold'>(D) </span>4901\qquad <span class='latex-bold'>(E) </span>9851
<
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(
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)
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4350
<
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′
>
(
B
)
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>
4351
<
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=
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′
>
(
C
)
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>
4900
<
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a
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−
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′
>
(
D
)
<
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>
4901
<
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a
ss
=
′
l
a
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x
−
b
o
l
d
′
>
(
E
)
<
/
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p
an
>
9851
AMC