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National and Regional Contests
Ireland Contests
Ireland National Math Olympiad
2005 Irish Math Olympiad
4
arrangements
arrangements
Source: Ireland 2005
July 6, 2009
combinatorics proposed
combinatorics
Problem Statement
Determine the number of arrangements
a
1
,
a
2
,
.
.
.
,
a
10
a_1,a_2,...,a_{10}
a
1
,
a
2
,
...
,
a
10
of the numbers
1
,
2
,
.
.
.
,
10
1,2,...,10
1
,
2
,
...
,
10
such that
a
i
>
a
2
i
a_i>a_{2i}
a
i
>
a
2
i
for
1
≤
i
≤
5
1 \le i \le 5
1
≤
i
≤
5
and a_i>a_{2i\plus{}1} for
1
≤
i
≤
4
1 \le i \le 4
1
≤
i
≤
4
.
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