pow:start

# Problem of the Week

Problem 5 (due Monday, November 9)

Recall that $\lfloor a \rfloor$ denotes the floor of $a$, i.e. the largest integer smaller or equal than $a$. What is the smallest possible value of $\displaystyle \left\lfloor \frac{1}{x_1}\right\rfloor+\left\lfloor\frac{1}{x_2}\right\rfloor+\ldots +\left \lfloor\frac{1}{x_n} \right\rfloor$, where $x_1,x_2,\ldots, x_n$ are positive real numbers such that $x_1+\ldots +x_n=1$?

## Overview

Every other Monday (starting 08/31/20), we will post a problem to encourage students (both undergraduate and graduate) to enjoy mathematics outside of the classroom and engage our mathematical community in the problem solving activity. 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 solutions (from us) as well as novel solutions from participants and record the names of those who've got the most number of solutions throughout each semester.