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Putnam
2018 Putnam
B1
Putnam 2018 B1
Putnam 2018 B1
Source:
December 2, 2018
Putnam
Putnam 2018
Problem Statement
Let
P
\mathcal{P}
P
be the set of vectors defined by
P
=
{
(
a
b
)
|
0
≤
a
≤
2
,
0
≤
b
≤
100
,
and
a
,
b
∈
Z
}
.
\mathcal{P} = \left\{\begin{pmatrix} a \\ b \end{pmatrix} \, \middle\vert \, 0 \le a \le 2, 0 \le b \le 100, \, \text{and} \, a, b \in \mathbb{Z}\right\}.
P
=
{
(
a
b
)
0
≤
a
≤
2
,
0
≤
b
≤
100
,
and
a
,
b
∈
Z
}
.
Find all
v
∈
P
\mathbf{v} \in \mathcal{P}
v
∈
P
such that the set
P
∖
{
v
}
\mathcal{P}\setminus\{\mathbf{v}\}
P
∖
{
v
}
obtained by omitting vector
v
\mathbf{v}
v
from
P
\mathcal{P}
P
can be partitioned into two sets of equal size and equal sum.
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