Golden-Oldie(s)

Re-visiting some old faves today…:

Yesterday Presh Talwalkar covered one of my favorite math puzzles with a sort of update using the real-life example of Nigeria:

http://mindyourdecisions.com/blog/2014/07/28/monday-puzzle-nigerias-sex-ratio/#.U9ZpW6jrnKk

I covered this math conundrum a couple of years back when Richard Wiseman ran it as one of his Friday puzzles:

http://richardwiseman.wordpress.com/2012/01/16/answer-to-the-friday-puzzle-139/

Here is Richard's verbatim statement of the puzzle:

"Imagine there is a country with a lot of people. These people do not die, the people consists of monogamous families only, and there is no limit to the maximum amount of children each family can have. With every birth there is a 50% chance its a boy and a 50% chance it is a girl.  Every family wants to have one son: they get children until they give birth to a son, then they stop having children. This means that every family eventually has one father, one mother, one son and a variable number of daughters.  What percent of the children in that country are male?"

Richard's presentation drew 270+ comments at the time, and what I love about this particular riddle is that it tends to divide people into two groups: those who see the answer fairly quickly, and indeed, sometimes don't even understand what is puzzling about it… and those who have real trouble seeing "50%" as the correct solution to the puzzle, and must be meticulously shown the math involved before they can accept it.

Anyway, if you're not familiar with it I advise going back and reading Richard's post (and comments) first, then coming back and checking out Presh's rendition from yesterday.

By an odd coincidence, if the above doesn't give you enough of a mental workout, then physicist Sean Carroll almost certainly will. He also covered one of the classic math paradoxes on his blog yesterday, "The Sleeping Beauty Problem" (so far with just 30+ 50+ comments ;-):

http://www.preposterousuniverse.com/blog/2014/07/28/quantum-sleeping-beauty-and-the-multiverse/

Again, this is a topic I've touched upon before HERE (and it too divides people into at least two opposing camps), but seeing Sean apply it to cosmological theory is fascinating.