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Korea Junior Mathematics Olympiad
2001 Korea Junior Math Olympiad
6
2001 KJMO P6
2001 KJMO P6
Source: 2001 KJMO P6
June 29, 2024
algebra
KJMO
Inequality
Problem Statement
For real variables
0
≤
x
,
y
,
z
,
w
≤
1
0 \leq x, y, z, w \leq 1
0
≤
x
,
y
,
z
,
w
≤
1
, find the maximum value of
x
(
1
−
y
)
+
2
y
(
1
−
z
)
+
3
z
(
1
−
w
)
+
4
w
(
1
−
x
)
x(1-y)+2y(1-z)+3z(1-w)+4w(1-x)
x
(
1
−
y
)
+
2
y
(
1
−
z
)
+
3
z
(
1
−
w
)
+
4
w
(
1
−
x
)
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