MathDB
Problems
Contests
National and Regional Contests
China Contests
ASDAN Math Tournament
2014 ASDAN Math Tournament
9
2014 General #9
2014 General #9
Source:
July 4, 2022
2014
General Test
Problem Statement
The operation
⊘
\oslash
⊘
, called "reciprocal sum," is useful in many areas of physics. If we say that
x
=
a
⊘
b
x=a\oslash b
x
=
a
⊘
b
, this means that
x
x
x
is the solution to
1
x
=
1
a
+
1
b
\frac{1}{x}=\frac{1}{a}+\frac{1}{b}
x
1
=
a
1
+
b
1
Compute
4
⊘
2
⊘
4
⊘
3
⊘
4
⊘
4
⊘
2
⊘
3
⊘
2
⊘
4
⊘
4
⊘
3
4\oslash2\oslash4\oslash3\oslash4\oslash4\oslash2\oslash3\oslash2\oslash4\oslash4\oslash3
4
⊘
2
⊘
4
⊘
3
⊘
4
⊘
4
⊘
2
⊘
3
⊘
2
⊘
4
⊘
4
⊘
3
.
Back to Problems
View on AoPS