Math Challenge Problem

The Math Challenge problem has returned to UNC's School of Mathematical Sciences! This is a problem that everyone is welcomed to try their hand at. New problems monthly.  

September Challenge

Subsets of Subsets

Consider the set [n] = {1, 2, 3, ..., n}.  It is fairly easy to see that there are 2different subsets B of [n].  For each such subset, we can also count the number of subsets A of B, which will be 2where k is the size of B.  We would like to combine these to count the numbers of pairs (A, B) such that A is a subset of B which is a subset of [n].

The Challenge: Find an elegant formula for the number of such pairs (A, B).  Bonus: express this formula in as many ways as possible, and explain why they all make sense.

challenge art

Submit solutions to Ross 2239G or by email to oscar.levin@unco.edu.
Deadline: Friday, September 29.

Win PRIZES! A winner will be selected from all correct answers received for each challenge problem to receive a fun math prize of his or her choice.

 

Previous Problems

2016-2017

September Challenge | October Challenge | November Challenge | January Challenge | February Challenge | March Challenge | April Challenge

2015-2016

September Challenge 1 | September Challenge 2 | October Challenge 1 | October Challenge 2 | November Challenge 1 | November Challenge 2 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2 | April Challenge

2014-2015

September Challenge 1 | September Challenge 2 | October Challenge 1 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2 | April Challenge 1 | April Challenge 2

2013-2014

September Challenge 1 | September Challenge 2 | October Challenge 1 | October Challenge 2 | November Challenge 1 | November Challenge 2 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 2 | April Challenge 1 | April Challenge 2

2012 - 2013

September Challenge | October ChallengeNovember Challenge | January Challenge | February Challenge  | March Challenge  | April Challenge

2011 - 2012

September Challenge | October Challenge | November Challenge | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge | April Challenge