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Problems
Contests
National and Regional Contests
Russia Contests
Russian Team Selection Tests
Russian TST 2014
P4
P4
Part of
Russian TST 2014
Problems
(1)
Pairs of subsets with certain properties
Source: Russian TST 2014, Day 10 P4 (Groups A & B)
1/8/2024
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
.
combinatorics
counting