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Problems
Contests
International Contests
JBMO ShortLists
2019 JBMO Shortlist
A3
A3
Part of
2019 JBMO Shortlist
Problems
(1)
JBMO Shortlist 2019 A3
Source:
9/12/2020
Let
A
A
A
and
B
B
B
be two non-empty subsets of
X
=
{
1
,
2
,
.
.
.
,
11
}
X = \{1, 2, . . . , 11 \}
X
=
{
1
,
2
,
...
,
11
}
with
A
∪
B
=
X
A \cup B = X
A
∪
B
=
X
. Let
P
A
P_A
P
A
be the product of all elements of
A
A
A
and let
P
B
P_B
P
B
be the product of all elements of
B
B
B
. Find the minimum and maximum possible value of
P
A
+
P
B
P_A +P_B
P
A
+
P
B
and find all possible equality cases.Proposed by Greece
algebra