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Balkan MO
1993 Balkan MO
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Part of
1993 Balkan MO
Problems
(1)
Six real numbers with sum 10
Source: Balkan MO 1993, Problem 1
4/25/2006
Let
a
,
b
,
c
,
d
,
e
,
f
a,b,c,d,e,f
a
,
b
,
c
,
d
,
e
,
f
be six real numbers with sum 10, such that
(
a
−
1
)
2
+
(
b
−
1
)
2
+
(
c
−
1
)
2
+
(
d
−
1
)
2
+
(
e
−
1
)
2
+
(
f
−
1
)
2
=
6.
(a-1)^2+(b-1)^2+(c-1)^2+(d-1)^2+(e-1)^2+(f-1)^2 = 6.
(
a
−
1
)
2
+
(
b
−
1
)
2
+
(
c
−
1
)
2
+
(
d
−
1
)
2
+
(
e
−
1
)
2
+
(
f
−
1
)
2
=
6.
Find the maximum possible value of
f
f
f
. Cyprus
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