## Monday, December 27, 2010

### A couple of puzzles

Since we just had a geometric puzzle, let's go numerical this time:

1. A probability puzzle

By the time the movie started, there were 91 men and 121 women in the theater. If the first moviegoer to enter the theater was a man wearing glasses, and the second was a woman not wearing glasses, then what is the probability that equal percentages of men and women in the theater were wearing glasses?

Solution here.

2. Fun(?) with fractions

I saw a survey in the newspaper once in which 33% of the people surveyed said "no" to something, while 67% said "yes." Whenever I see something like that, I always think, "Huh - I wonder if they only asked three people."

Well, suppose you saw it reported that 34% of people surveyed answered "no" to something, while 66% said "yes." What is the smallest number of people who could have participated in this survey? Assume that the people reporting these results have rounded their figures to the nearest whole percentage point.

Solution here.

***

I'll end with a graph that shows what the solution to puzzle #2 would be for any possible pair of percentages adding to 100%. Don't study the graph too carefully if you are going to solve the puzzle yourself!

Danimal said...

Hey Jason,

I tried #2. Fun and original puzzle! I haven't seen that one along those lines before. I agree with your graph values for p = 0.34 and p = 0.48.

It seems to be the kind of puzzle that you need to be able to tinker with mathematically to solve. I wound up using MS Excel, though a short computer program would work better and be more flexible. Is there some number theory or discrete math result that lets you go more directly to an answer? I doubt it, but I'm curious.

Hope you all had a merry christmas! Any chance of posting a recent photo of Abigail and/or Claire on Zimblog?

Dan

PS Natalia got a Kindle, and I'm back to doing crossword puzzles. No eraser needed for NYTimes Crosswords on the Kindle (not that I ever used one anyway of course... hahaha :-)

JasonZimba said...

Hey Dan, Merry Christmas to you and Natalia!

Glad you enjoyed #2 - a number theorist friend of mine liked it too. I don't suppose there's a more direct way to get to the answer than the approach you took. (I generated the graph with a computer program.) I'll follow up with another comment in my next post!

P.S. I love my Kindle too. I travel a lot these days, and the Kindle has made flying a lot more pleasant.

Danimal said...

Are you still teaching at Bennington these days? Just wondering when you say that you're traveling a lot...

Thought you might enjoy this link!
http://www.nytimes.com/interactive/2011/01/02/opinion/20110102_Windows.html?hp