2018 Putnam B Problems/Problem 1
Problem
Let 
be the set of vectors defined by
![\[\mathcal{P} = \left\{\begin{pmatrix} a \\ b \end{pmatrix} \, \middle\vert \, 0 \le a \le 2, 0 \le b \le 100, \, \text{and} \, a, b \in \mathbb{Z}\right\}.\]](http://latex.artofproblemsolving.com/b/4/5/b4565d582b99ce2ad0598541bf807376bb532d3c.png)
Find all 
such that the set 
obtained by omitting vector 
from can be partitioned into two sets of equal size and equal sum.
Solution
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