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All-Russian Olympiad
1972 All Soviet Union Mathematical Olympiad
172
172
Part of
1972 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 172 All Soviet Union MO 1972 min of max of ... , x_n/(1+x_1+...+x_n)
Source:
7/3/2019
Let the sum of positive numbers
x
1
,
x
2
,
.
.
.
,
x
n
x_1, x_2, ... , x_n
x
1
,
x
2
,
...
,
x
n
be
1
1
1
. Let
s
s
s
be the greatest of the numbers
{
x
1
1
+
x
1
,
x
2
1
+
x
1
+
x
2
,
.
.
.
,
x
n
1
+
x
1
+
.
.
.
+
x
n
}
\left\{\frac{x_1}{1+x_1}, \frac{x_2}{1+x_1+x_2}, ..., \frac{x_n}{1+x_1+...+x_n}\right\}
{
1
+
x
1
x
1
,
1
+
x
1
+
x
2
x
2
,
...
,
1
+
x
1
+
...
+
x
n
x
n
}
What is the minimal possible
s
s
s
? What
x
i
x_i
x
i
correspond it?
minimum
maximum
algebra
inequalities