Difference between revisions of "2018 Putnam B Problems/Problem 1"
(Created page with "==Problem== Let <math>\mathcal{P}</math> be the set of vectors defined by <cmath>\mathcal{P} = \left\{\begin{pmatrix} a \\ b \end{pmatrix} \, \middle\vert \, 0 \le a \le 2, 0...") |
(No difference)
|
Latest revision as of 23:37, 21 April 2019
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
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
