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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 $x_1+\ldots +x_n=1$?


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 ( 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.

When you submit your solutions, please provide a detailed reasoning rather than just an answer. Also, please include some short info about yourself for our records.

Previous Problems and Solutions

  • Problem 2 Partial solutions received from Yuqiao Huang, Maxwell T Meyers, and Matthew Pressimone.
  • Problem 1 Solved by John Giaccio and Yuqiao Huang.
pow/start.txt · Last modified: 2020/10/27 00:49 by mazur