MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
CMIMC Problems
2017 CMIMC
2017 CMIMC Algebra
8
2017 A8: Integer Linear Programming
2017 A8: Integer Linear Programming
Source:
January 29, 2017
2017
algebra
Problem Statement
Suppose
a
1
a_1
a
1
,
a
2
a_2
a
2
,
…
\ldots
…
,
a
10
a_{10}
a
10
are nonnegative integers such that
∑
k
=
1
10
a
k
=
15
and
∑
k
=
1
10
k
a
k
=
80.
\sum_{k=1}^{10}a_k=15\qquad\text{and}\qquad \sum_{k=1}^{10}ka_k = 80.
k
=
1
∑
10
a
k
=
15
and
k
=
1
∑
10
k
a
k
=
80.
Let
M
M
M
and
m
m
m
denote the maximum and minimum respectively of
∑
k
=
1
10
k
2
a
k
\sum_{k=1}^{10}k^2a_k
∑
k
=
1
10
k
2
a
k
. Compute
M
−
m
M-m
M
−
m
.
Back to Problems
View on AoPS