Virginia Mathematics Teacher Fall 2016

HEXA Cha l l enge

Problems created by: Dr. Oscar Tagiyev

October Challenge: It is 2016. If we continue writing the digits, 2, 0, 1, 6, in this order N times, we’ll GET a different number K=201620162016...2016 where the digits 2, 0,1, 6 are repeated N times. Prove that K can not be a perfect square of any integer number.

November Challenge: There are N people that live in a city, where there are two main competing companies. Out of these people, n know each other, because they work for the same company. m people also know each other because they work in the same city, but in a rival company. Personal relationships between workers at rival companies are not allowed. What portion of the population of the city, does not work for either of these companies, but can knows exactly 1 person from each company.

December Challenge: Given an infinitely large set of different types of triangles, if one randomly selects a triangle, what are the chances of this triangle being obtuse?

Contest Alert!

Virginia Mathematics Teacher is conducting a contest for educators and students who can solve the greatest number of problems cor­ rectly by 2/29/2017 The winner will receive a prize and will be featured in the next issue of the VMT. Send your solutions to vmt@radford.edu with the email subject line: Hexa Challenge

Virginia Mathematics Teacher vol. 43, no. 1

14