pow:start

# Problem of the Week

Problem 1 (due Monday, March 1)

We say that a vector in $\mathbb R^3$ is ${\rm positive}$ (${\rm negative}$) if all its coordinates are positive (resp. negative). Let $v_1,v_2,v_3,v_4$ be vectors in $\mathbb R^3$ such that the sum of any two of these vectors is either positive or negative. Prove that at least one of the vectors $v_1,v_2,v_3,v_4, v_1+v_2+v_3+v_4$ is either positive or negative.

## Overview

Every other Monday (starting 02/15/21), we will post a problem to engage our mathematical community in the problem solving activity and to enjoy mathematics outside of the classroom. Students (both undergraduate and graduate) are particularly encouraged to participate as there is no better way to practice math than working on challenging problems. If you have a solution and want to be a part of it, e-mail your solution to Marcin Mazur (mazur@math.binghamton.edu) by the due date. We will post our solutions as well as novel solutions from the participants and record the names of those who've got the most number of solutions throughout each semester.