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National and Regional Contests
Russia Contests
Russian Team Selection Tests
Russian TST 2014
Russian TST 2014
Part of
Russian Team Selection Tests
Subcontests
(4)
P4
1
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Pairs of subsets with certain properties
For a natural number
n
,
n{},
n
,
determine the number of ordered pairs
(
S
,
T
)
(S,T)
(
S
,
T
)
of subsets of
{
1
,
2
,
…
,
n
}
\{1,2,\ldots,n\}
{
1
,
2
,
…
,
n
}
for which
s
>
∣
T
∣
s>|T|
s
>
∣
T
∣
for any element
s
∈
S
s\in S
s
∈
S
and
t
>
∣
S
∣
t>|S|
t
>
∣
S
∣
for any element
t
∈
T
.
t\in T.
t
∈
T
.
P2
5
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P1
10
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P3
5
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