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US Math Competition Association
2021 USMCA
7
2021 USMCA National Championship #7
2021 USMCA National Championship #7
Source:
May 9, 2021
Problem Statement
Find the expected value of
max
(
min
(
a
,
b
)
,
min
(
c
,
d
)
,
min
(
e
,
f
)
)
\max(\min(a,b),\min(c,d),\min(e,f))
max
(
min
(
a
,
b
)
,
min
(
c
,
d
)
,
min
(
e
,
f
))
over all permutations
(
a
,
b
,
c
,
d
,
e
,
f
)
(a,b,c,d,e,f)
(
a
,
b
,
c
,
d
,
e
,
f
)
of
(
1
,
2
,
3
,
4
,
5
,
6
)
(1,2,3,4,5,6)
(
1
,
2
,
3
,
4
,
5
,
6
)
.
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