MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2016 Korea Junior Math Olympiad
7
maximum of
maximum of
Source: 2016 KJMO #7
November 13, 2016
algebra
inequalities
Problem Statement
positive integers
a
1
,
a
2
,
.
.
.
,
a
9
a_1, a_2, . . . , a_9
a
1
,
a
2
,
...
,
a
9
satisfying
a
1
+
a
2
+
.
.
.
+
a
9
=
90
a_1+a_2+ . . . +a_9 =90
a
1
+
a
2
+
...
+
a
9
=
90
find maximum of
1
a
1
⋅
2
a
2
⋅
.
.
.
⋅
9
a
9
a
1
!
⋅
a
2
!
⋅
.
.
.
⋅
a
9
!
\frac{1^{a_1} \cdot 2^{a_2} \cdot . . . \cdot 9^{a_9}}{a_1! \cdot a_2! \cdot . . . \cdot a_9!}
a
1
!
⋅
a
2
!
⋅
...
⋅
a
9
!
1
a
1
⋅
2
a
2
⋅
...
⋅
9
a
9
I was really shocked because there are no inequality problems at KJMO and the test difficulty even more lower...
Back to Problems
View on AoPS