Friday Puzzle

For the probability buffs out there, here's a tricky problem from another site:

What is the probability that in a group of 31 people, NONE of them have birthdays in February or August? (assume equal probability of birthday for all days throughout the year)
Answer below.....
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the answer (I presume correct), 0.41%, is computed here:
http://tinyurl.com/7h3nh23

Delightful Math

I've seen this particular puzzle presented many times in the form of a typical word or story problem, but don't recall if I'd seen it rendered in poetical form before:

http://tinyurl.com/7j4dlcs

6 and Primes

It is an interesting fact that ALL prime numbers beyond 2 and 3 are either 1 more, or 1 less, than a multiple of 6. If you were unaware of this simple factoid you can check out these links for a discussion/explanation of it:

a short explanation: http://www.jimloy.com/number/prime6.htm

a longer explanation: http://tinyurl.com/77l94cc

Quickie Friday Puzzle

Just a quickie on this day of Festivus! ;-)

How many Santa's helpers must there be total in a group, if all but 2 are named Smith, all but 2 are named Jones, and all but 2 are named Wilson?
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answer: 3 total (1 Smith, 1 Jones, 1 Wilson)

Year-end Review...

For newer readers here, just a year-end list of some personal favorite posts from the last 12 months. Nothing particularly profound or deep about most of these; just touching on matters I happened to find interesting:

1) A Seemingly Impossible Task That Isn't
(a favorite paradox/puzzle coming from Raymond Smullyan)

2) Of Wheels and Circles and Points, Oh My
(another old mind-bending paradox)

3) Couple of Videos 
(couple of fun YouTube videos)

4) Fermat's Last Theorem
(a video on Andrew Wiles solving Fermat's Last Theorem)

5) Marilyn Rolls the Dice
(Marilyn vos Savant introduces another puzzle)

6) The Cantor Set
(the Cantor Set)

7) A Video Re-run
(A Bloggingheads/TV video with John Horgan and Jim Holt)

8) The Blind Spot
(Review of William Byers' book "The Blind Spot")

9) Kickin' Back With Cantor
(BBC documentary on Cantor)

10) Loser…
(just for fun)

Explaining the Riemann Hypothesis

For anyone who woke up this morning and muttered to themselves, "Hmmm, what is that there Riemann Hypothesis all about anyway?...":

http://www.askamathematician.com/2011/12/q-what-is-the-reimann-hypothesis-why-is-it-so-important/

Are These Folks Humans or Cyborgs!?

Some people's brains are definitely wired very differently from mine....

When I first read of autistic savant Daniel Tammet's recitation of pi to over 22,500 decimals back in 2004, it seemed like a stunt beyond human comprehension, likely not to be surpassed in my lifetime… BOY, WAS I WRONG!!
It was a couple years later that I learned that Tammet's effort merely set a British and European record for pi recitation, but wasn't even close to the world record. As far back as 1981, an Indian had already recited pi to almost 32,000 digits, and a couple of Japanese blokes later greatly surpassed that endeavor. Then in 2005, a Chinese fellow, Chao Lu, would more than TRIPLE Tammet's puny ;-) performance, by reciting from memory, a phenomenal 67,890 digits of pi, and is still listed as the official record-holder by some accounts. Here's one listing of the world's top pi record-holders:

http://pi-world-ranking-list.com/lists/memo/

I'm not sure how these "official" designations are established though, because the current proclaimed record-holder is a former Japanese engineer, named Akira Haraguchi, who recited pi to 100,000 digits in 2006 (breaking his own prior record of almost 84,000):

http://www.foxnews.com/story/0,2933,217765,00.html

Simply UNNNreal! (...Having said that though, pi has now been computed to 10 trillion digits, so HEY Akira, ya gotta ways to go yet!)

...Now, if only I could remember where I left my car keys last night.

A Little Bit On Randomness

h/t to Dan Meyer for this one:

The Depths and Intuition of Mathematics...

A long, interesting, insightful answer to a simple question posed on Quora.com:

http://www.quora.com/What-is-it-like-to-have-an-understanding-of-very-advanced-mathematics

Booklist

One blogger's list of 46 "interesting" math books from 2011 here:

http://tinyurl.com/8xmgf83

A variety of subject matter and material level is represented.

Friday Puzzle

A recent geometry puzzle from 'Futility Closet' here (with a possibly surprising answer):

http://www.futilitycloset.com/2011/11/28/rolling/

Carny Time!

Someone apparently submitted one of my year-old posts to the current Math Teachers At Play blog carnival (thank you to whoever you are!). The whole diverse Carnival is worth a look here:

http://letsplaymath.net/2011/02/18/math-teachers-at-play-35/

Infinite Trees Finitely Discussed

Keith Devlin takes on infinity via mathematical trees in this recent blog post:

http://devlinsangle.blogspot.com/2011/12/christmas-trees-from-land-of-santa.html

Of Higgs and Sigmas

What are the confidence intervals of confidence intervals, and other thoughts....

With a significant announcement from CERN on the Higgs boson presumed to be just hours away, KW Regan enters the fray with this interesting post about science, sigmas, and levels of significance:

http://rjlipton.wordpress.com/2011/12/13/the-higgs-confidence-game/

…an excerpt therefrom:

"The high rate of disappearing significance overall is still puzzling. Its extent in human sciences was detailed exactly one year ago in a disturbing article by Jonah Lehrer for The New Yorker. If 250 researchers try the same experiment, one would expect 2 or so of them to get  deviations (in either direction). The world will then see 2 or so published papers from them, but nary a peep from the 248 who failed and gave up quickly and forgot about it. Thus a significant result may appear independently confirmed when it was actually just by chance, and those failing to reproduce it will then peep up loudly. The effect is equally pernicious with 250 different experiments, especially given a fair chance of a lower-confidence positive from a test deemed related enough to corroborate the original."

Holiday Shopping For All Ye Merry Math Fans

Order early & order often ;-)

http://www.zazzle.com/sheckyr/gifts

Richard Elwes... Again

I've been aware of Brit Richard Elwes for barely over a year now, but he's already vaulted to one of my favorite math expounders. An interview with him here from Q Blog (and great to see that he has a new volume out, "The Maths Handbook," and yet another on the way! ....his first two books are two of my favorites):

http://www.quercusbooks.co.uk/blog/2011/12/07/the-quercus-couch-richard-elwes/

Another Friday Puzzle

Update: I had quickly adapted the original problem below from another site, only to realize it was far too easy as a problem of 2 equations with 2 unknowns, so have now re-stated it below in at least a slightly more challenging form:

"x" and "y" are two different 2-digit prime numbers composed of the same digits, but in reverse order. If it is true that x - y = 36, then what must the numbers x and y be:
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answer:  x=73 and y=37

Game Show Math

...or, why doing math in your head with a bazillion eyes upon you is no picnic!
(h/t to Presh Talwalkar for this)

Halting Problem In Verse

The Halting Problem, Dr. Seuss, poetry, and Geoffrey Pullum here... ohh my:

http://ebiquity.umbc.edu/blogger/2008/01/19/how-dr-suess-would-prove-the-halting-problem-undecidable/

quite cool!

Phi

The stream of popular books out on pi, the Fibonacci sequence, or the Golden Ratio seems unending… and, now we have another: Alfred Posamentier and Ingmar Lehmann are newly out with "The Glorious Golden Ratio" -- haven't read it, but for geometry fans, anything by these two is certainly worth some high anticipation!

Friday Puzzle

I adapted this problem directly from a recent NPR Car Talk puzzler, so if you heard that show you'll know the answer:

My brother Morty and I took a drive up to the mountains this weekend to see the Golden-breasted Flooglebird. Morty drove the first 40 miles and I drove the rest of the way. We saw the Flooglebird right away (or something closely resembling it) and immediately returned home on the exact same route.

On the return trip Morty again drove the first part of the trip, and I drove the final 50 miles this time.
In total who did the most driving, me or Morty, and how many more miles than the other brother did that driver do? (yes, there's enough information to reach an answer!)

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answer: I drove 20 more miles than Morty
(the Car Talk guys explain it their way here: http://www.cartalk.com/content/car-trip-trigonometry-0?answer )