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2006 AIME Problems
4
Permutations of numbers
Permutations of numbers
Source: 2006 AIME II 4
March 28, 2006
AMC
Problem Statement
Let
(
a
1
,
a
2
,
a
3
,
.
.
.
,
a
12
)
(a_1,a_2,a_3,...,a_{12})
(
a
1
,
a
2
,
a
3
,
...
,
a
12
)
be a permutation of
(
1
,
2
,
3
,
.
.
.
,
12
)
(1,2,3,...,12)
(
1
,
2
,
3
,
...
,
12
)
for which
a
1
>
a
2
>
a
3
>
a
4
>
a
5
>
a
6
and
a
6
<
a
7
<
a
8
<
a
9
<
a
10
<
a
11
<
a
12
.
a_1>a_2>a_3>a_4>a_5>a_6 \text{ and } a_6<a_7<a_8<a_9<a_{10}<a_{11}<a_{12}.
a
1
>
a
2
>
a
3
>
a
4
>
a
5
>
a
6
and
a
6
<
a
7
<
a
8
<
a
9
<
a
10
<
a
11
<
a
12
.
An example of such a permutation is
(
6
,
5
,
4
,
3
,
2
,
1
,
7
,
8
,
9
,
10
,
11
,
12
)
(6,5,4,3,2,1,7,8,9,10,11,12)
(
6
,
5
,
4
,
3
,
2
,
1
,
7
,
8
,
9
,
10
,
11
,
12
)
. Find the number of such permutations.
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