College of Arts and Sciences

Department of Mathematics

Problem of the Fortnight

March 7: Natural Numbers and Their Digits

Show that for all natural numbers   n, at least one of two numbers,  n  or   n +1, can be represented in the following form:  k+ S(k ) for some integer   k, where   S(k) is the sum of all digits in   k. For example,  21= 15+ (1+5). Answers are due by 5:00 PM on Friday, March 7. Please show all of your work. Good Luck!


February 14: Finding the Center of My Heart

A heart shape is formed from a square with sides 2 units long and two half-circles of radius 1 unit (see figure). Where should the heart be placed in the Cartesian plane so that the origin is at the center of the heart, i.e. so there is the same amount of area in each of the four quadrants? Answers are due by 5:00 PM on Friday, February 14. Please show all of your work. Happy Valintines Day!

 

 

 

 

 

 

How it Works

Every two weeks a new problem will be posted. Answers can be submitted to the Math Club mailbox, located next to the main Math Department office (Neill 103). A list of people who submitted correct answers will be posted after each problem. The person with the most correctly answered POTFs at the end of the semester will win a small prize!