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2016 Online Math Open Problems
15
2015-2016 Spring OMO #15
2015-2016 Spring OMO #15
Source:
March 29, 2016
Online Math Open
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be four real numbers such that
a
+
b
+
c
+
d
=
20
a+b+c+d=20
a
+
b
+
c
+
d
=
20
and
a
b
+
b
c
+
c
d
+
d
a
=
16
ab+bc+cd+da=16
ab
+
b
c
+
c
d
+
d
a
=
16
. Find the maximum possible value of
a
b
c
+
b
c
d
+
c
d
a
+
d
a
b
abc+bcd+cda+dab
ab
c
+
b
c
d
+
c
d
a
+
d
ab
.Proposed by Yannick Yao
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