The World of Sporcle.com

Who doesn't need a "Mentally Stimulating Diversion" from time to time?  One of my officemates introduced me to a website called Sporcle.  This sticky site hosts thousands of trivia quizzes of the form, "How many X can you name in Y minutes?"  Varied and random topics range from history to geography, movies to sports, and world scrambles to crytograms.  Even math trivia topics such as Digits of Pi and A in Math! 

I recently took the Mathematician Names trivia quiz (along with hundreds of others!).  This trivia quiz lists 50 well known mathematicians by last name and gives you eight minutes to enter their first names.  While most of the mathematicians' last names looked familiar, I can't claim I was on first name basis with any of them.  This trivia quiz was a struggle for me despite my background.  I managed to cough out a measly 20/50 first names which surprisingly placed me into the 95th percentile!  But more importantly, I learned something.  Thank you Lejeune Dirichlet, Pafnuty Chebyshev and Gottfried Leibniz!

Sporcle.com is a great site if you are training to be on Jeopardy or for a Spelling Bee, need a short break or just looking for a friendly competition between friends.  New trivia quizzes are added to the lot on a daily basis.  You can also upload your own user-generated trivia quizzes.  Have fun, but keep an eye on the timer... and the clock!

Back to School

With 4-6 inches of snow and only 6 plows, icy Atlanta transformed to Hoth-lanta last week, resulting in a 5-day extended winter break for University students.  Although there was a delay in the start of the semester, there was no delay in discussing interesting topics in my Combinatorics course this week. 

A Steiner system with parameters l, m, n such that l<m<n is an n-element set S with an m-element subset of S (called blocks) such that any l-element subset of S is contained in exactly one block.  To simplify, let l=2 and m=3 to form a Steiner triple system S(2,3,n).  For what n does a Steiner triple system exist?
 

This question inspired Reverend Thomas Kirkman and he solved a special case of this problem in 1847.  His solution is widely known as the Kirkman Schoolgirl Problem.  So in the spirit of a fresh, new semester, here is the riddle for you:  15 girls walk to school each day in five groups of three.  How many days does it take for each pair of girls to walk together exactly once?  Note this is a Steiner triple system S(2,3,n) where n is the number of days.  Hint:  See picture.

Wendy's Biggie Fries Container

Here is one to try on your next fast food date.  My husband and I were in the airport Wendy's enjoying our fries with ranch dressing and noticed the statement on the container read, "We figured out that there are 256 ways to personalize a Wendy's hamburger.  Luckily someone was paying attention in math class."  So naturally, we asked each other how many condiments does Wendy's offer to result in 256 combinations of burgers? 

I immediately answered 8 condiments, using the notion of power sets.  2 to the what equals 256?  Meanwhile, my husband attempted to solve the equation nC0 + nC1 + ... + nCn = 256 and also got 8 (after what seemed like hours after I gave my answer).  Alternatively, I suppose, you can just take a walk over to the fixings bar and count them.  Thanks Wendy's for making our layover so entertaining!

Monty Hall Problem

Yesterday I gave a mini-lecture in our teaching seminar on Bayes' theorem motivated by the "Monty Hall Problem":

Suppose you are on "Let's Make a Deal" gameshow, and you are given the choice of three doors: behind one door is a new car; behind the others are goats. You pick a door, say door #1, and Monty Hall, the host, who know knows what's behind the doors, opens another door, say door #3, and reveals a goat. He then says to you, "Do you want to stay with door #1, or switch to door #2?" Is it to your advantage to switch your choice?

If your initial guess is you have a 50/50 chance on winning the car regardless if you choose door #1 or door #2 knowing there is a goat behind door #3, think again. A simple application of Bayes' theorem will show that the probability of winning the new car by switching from door #1 to door #2 is 2/3. Therefore, it's to your advantage to switch your choice. Discuss.