All this week, the news has been sent around the world about a 16-year-old Iraqi-born teen, currently living in Sweden, who solved a 300-year-old math puzzle.

Most of the write-ups are variations of the AFP story originally published with the headline, Iraq-born teen cracks maths puzzle:

A 16-year-old Iraqi immigrant living in Sweden has cracked a maths puzzle that has stumped experts for more than 300 years, Swedish media reported on Thursday.

In just four months, Mohamed Altoumaimi has found a formula to explain and simplify the so-called Bernoulli numbers, a sequence of calculations named after the 17th century Swiss mathematician Jacob Bernoulli, the Dagens Nyheter daily said.

Altoumaimi, who came to Sweden six years ago, said teachers at his high school in Falun, central Sweden were not convinced about his work at first.

"When I first showed it to my teachers, none of them thought the formula I had written down really worked," Altoumaimi told the Falu Kuriren newspaper.

He then got in touch with professors at Uppsala University, one of Sweden's top institutions, to ask them to check his work.

After going through his notebooks, the professors found his work was indeed correct and offered him a place in Uppsala.

But for now, Altoumaimi is focusing on his school studies and plans to take summer classes in advanced mathematics and physics this year.

"I wanted to be a researcher in physics or mathematics; I really like those subjects. But I have to improve in English and social sciences," he told the Falu Kuriren.

More details about this story can be found at the Personal Money Store write-up of the story, Amazing 16-Year-Old Finds Bernoulli Numbers Relationship.

If you're not familiar with Bernoulli numbers, the clearest explanation I've found of them is over at The Straight Dope, where the concept of Bernoulli numbers is discussed in detail.

“Although it's difficult for us ‘math guys’ to appreciate, the vast majority of the population (here and elsewhere) has neither heard of a ‘magic square’ nor is aware of its properties. So the entertainment aspect of presenting same is inherent in its surprise value, as the audience is brought to realize the truly amazing number of ways in which this hastily constructed set of numbers can be summed to create the ‘magic number’.”
-Doug Dyment

It seems like too long to me since I last discussed magic squares, and it seems like magic square resources have been jumping out at me recently, so it seems to be the right time.

First, there's the classic W. S. Andews book, Magic Squares and Cubes (PDF), which is now available in the public domain. If you've ever wanted to study the magic square (and/or the magic cube) in depth, you'll find this work very satisfying.

On a briefer level, Curious Math offers several excellent, and easily-digestible, magic square lessons. I especially enjoy the look at the thought process behind the creation of the standard 3-by-3 magic square.

For those of you who've tried learning the magic square here on Grey Matters, there are some further help on helping memorize the required numbers. There are even some alternative approaches here that you may find quicker, depending on your particular approach to learning. I've included a permanent link to this discussion in my tutorial itself, as well.

Even when you get a magic square method down, there still remains the question of presentation. Traditionally, there have been 2 standard approaches to the square. In the first, you openly ask for the number, and quickly generate a magic square for that number. This option gives a Rain Man-type feel, and it can be tough for the performer to overcome the “show-off” perception by the audience.

The other standard magic square presentation is that of having a spectator choose a number and keep it secret, and then creating a square, after somehow secretly obtaining the number. The nice thing about this is that the magic square doesn't really communicate what relationship it has to the chosen number until you reveal the patterns. It has good potential for comedy, drama and or mysticism, and when done well, seems much less like a stunt.

These aren't the only possible presentations, however. In Subliminal Squares, for example, you create a magic square, and then demonstrate that a an audience member's mind has been invaded subconsciously by the magic total!

One way to make the magic square more meaningful to an audience is to use a meaningful number or total, such as someone's birthday. Professor Arthur Benjamin, back in 2006, published a means of generating what he calls the Double Birthday Magic Square (PDF), which has recently been made available on his site. The magic square that's created features the spectator's birthday both across the top and in the 4 corners! As it happens, this method works very well with the presentation I first discussed in my Plots For Memory Routines post.

To wind up this magic square post, enjoy Benji Bruce's take on the magic square. He grabs interest by performing it as if it were being done at a poetry slam:

A little less than a year ago, my quest to see flashcard development on the iPhone was sated for the first time, when I found iFlipr. The idea is already starting to spread, and now you have a wider choice of iPhone flashcard programs!

While there are many responses in the iPhone App Store when you search for Flashcards, most of them are dedicated to a pre-set topic, such as beginning Spanish or medical terminology. For this list, I'm going to focus on customizable flashcard programs. This also is not intended as a review of each program, but rather an overview of what's available and what features are offered.

Many of these programs use a version of Leitner System, so that you can learn more efficiently by studying more difficult material more frequently.

Here's what I've found so far, in alphabetical order by App name:

Name: Elephant
Web Link
iTunes Link (Full Version)
Features:
• Pre-made flashcards installed
• Cards can be created and shared on developer's website
• Account on developer's website is free
Price: US$4.99

Name: Flash Your Mind
Web Link
iTunes Link (Free Version)
Features:
• Cards can be shared on developer's website
• Cards can be created by any app that exports an XML file (most text editors programs do this - see site for required XML structure)
Price: Free

Name: FlashCards
Web Link
iTunes Link (Full Version)
Features:
• Cards can use graphics or text
• Cards can be shared on developer's website
• Cards can be created by any app that exports to CSV format (most database and spreadsheet programs do this)
Price: US$2.99

Name: Flashcards Deluxe
Web Link
iTunes Link (Full Version)
iTunes Link (Free Version)
Features:
• Cards can use graphics or text
• Cards can be shared on developer's website
• Cards can be created by any app that exports to a tab-separated format (many text editors do this)
Price: US$1.99

Name: gFlash
Web Link
iTunes Link (Full Version)
iTunes Link (Free Version)
Features:
• Cards can use graphics, text, sounds, YouTube clips, HTML formatting
• Cards can be imported from StudyStack
• Cards can be created in Google Docs
• Cards can be shared on developer's website
Price: US$4.99

Name: iFlipr
Web Link
iTunes Link (Full Version)
iTunes Link (Free Version)
Features:
• Cards can use graphics, text, sounds, HTML formatting
• Cards can be created and shared on developer's website
• Cards can be created by any app that exports to CSV format (most database and spreadsheet programs do this)
Price: US$4.99

Name: iMemento
Web Link
iTunes Link (Full Version)
iTunes Link (Free Version)
Features:
• Pre-made flashcards installed
• Cards can use customized backgrounds
• Cards can be created on your offline computer
Price: US$2.99

Name: Mental Case for iPhone
Web Link
iTunes Link (Full Version)
iTunes Link (Free Version)
Features:
* Syncs with offline app
• Cards can use graphics or text
• Cards can be shared on developer's website
• Cards can be imported from Flashcard Exchange
Price: US$7.99

Name: Touchcards
Web Link
iTunes Link (Full Version)
Features:
• Cards can be imported from StudyStack or Quizlet
• Cards can be created in Google Docs
Price: US$1.99

Ever since I first ran across Leo Boudreau's books, I've been a big fan of his innovative use of binary principles in magic. In fact, my first mention of his work on this blog was in my 2nd post!

Over at the Magic Cafe, Leo has recently posted some more of his incredible work, and for free! Well, they're free assuming you're a member of the Magic Cafe, and have written 50 relevant posts, as determined by their standards.

The first routine really should have been included in my original Free tricks from Leo Boudreau post, but was unfortunately overlooked. It's called Total Audience Participation and, appropriately for our first Boudreau effect, it's an opener for a mentalism show.

You introduce a box, sealed with rubber bands, and propose a test of the entire audience's intuition. You have everyone in the audience stand up, and ask everyone to think of an object. Gradually, you describe which qualities the item in the box lacks, and ask people who are thinking of things with those qualities to sit down. After these various qualities are eliminated, there will still probably be several people standing. You take a quick poll of the items of which they're thinking, and walk up to one of the people, asking them their name and finding why they chose the particular object they did. They are asked to open the box, where they find not only the thought-of object, but a slip of paper with their name on it, as well!

Routines that involve the whole audience, especially openers, can prove very powerful, as performers who use Lior's Mobile Opener can attest. Nobody feels left out, and you can easily set your theme and a your standards of audience control immediately.

Moving up to more recent work, we find the routine Intuition: My Favorite Card Trick. In this routine, a spectator cuts and shuffles a deck of cards. They are then asked to name any card in the deck as the focus of an experiment of intuition. Groups of cards are eliminated in various random ways (no equivoque!), and then individual cards, as the deck gets smaller. Finally, one card remains, and it proves to be the very same card named earlier by the spectator!

My favorite of the new effects, however, I've saved for last. As it happens, it intersects perfectly with the recent uptick in the number of poetry-related posts here on Grey Matters. The post itself is titled The Raven & The Beatle Decoded, but I've nicknamed it Poems II, relating it to his earlier poem-related routine.

In the new routine, you have 4 spectator each choose consecutive words from a poem or song lyric. You then walk them through mentally spelling their chosen words. The spelling is done mentally, so that they don't communicate how many letters their chosen word has. Once they're done mentally spelling their chosen words, you can immediately name all 4 chosen words!

This is a very clean mentalism routine, as the only prop required is a business card with the line from the poem or song lyric on it. This trick employs unaltered poems or unaltered song lyrics, similar to the way Max Maven's Autome uses unaltered books. Also like Autome, there's some work employed in finding pieces with the particular required qualities, but the result of the effort will definitely be worth it when you receive your audience reaction.

Because so many people find Leo Boudreau's tricks via my Free tricks from Leo Boudreau post, I will be updating that post each time I find new routines of his. You'll probably want to keep that post bookmarked for future reference. If you're able to access these posts, I hope you enjoy these amazing routines!

If it's true that many classic poems are treasures, then I've just discovered an entire treasure trove about which I formerly knew nothing!

Back in 1996 and 1997, UBS made an entire series of ads that, due to their opening text, became known as the Thoughts That Transcend Time series.

The ad series was the idea of marketing guru Neil French, who gives a behind-the-scenes look at this series on his site.

The concept was simple: Notable actors would recite classic poetry, with the ultimate goal of not only being entertaining and educational, but to give a timeless image to UBS and it's reputation for security and longevity, as well.

The poems featured were from William Ernest Henley, Frost, Shakespeare, Alfred, Lord Tennyson, R. L. Sharpe, Matthew Arnold, Ella Wheeler-Wilcox, Edgar Albert Guest, Shelley, Arthur Hugh Clough, Longfellow, Lao Tzu, Wang Zihuan, Walter D. Wintle, Yeats and Kipling. The actors who recited these works were Sir Alan Bates, Sir John Gielgud, Maggie Smith, Ben Kingsley, Paul Scofield, Ying Ruocheng and Harvey Keitel.

If you're trying to memorize poetry, this is a wonderful series in which to find pieces you may not have considered. Even better, if you're eventually going to perform them, this is a great way to find inspiration for presenting a piece, as well.

Remember some old favorite poems and maybe even discover some new ones by either watching them all below, or by viewing the playlist itself at YouTube. Enjoy!

In this edition of snippets, we're going to fold, spindle and mutilate your brains in as many fun ways as possible!

• This first puzzle is usually done as a magic effect, or some sort of Rain Man-type feat. It's called the Three Dice Sum. The page does give the specific solution, but can you work out a generalized solution that would work if more dice were used?

• I ran across Sandy Wood's puzzle, 2010 is Coming!, yesterday over at Mental Floss, I was a little amused. Anyone who does the Day of the Week For Any Date feat can simply ignore the clue altogether and give the answer! Actually, the process of working out the answer from the clues given is still an interesting one, so you may still want to work that out even if you can do the Date feat!

* It wasn't that long ago I linked to the Schoolhouse Rock videos (among others) as a good source of learning. I hope you've been watching them! Because before we leave Mental Floss, they have the Schoolhouse Rock Anti-Trivia Quiz ready for you. Afterwards, you can relax with some more educational programming from Mental Floss, although (as I note in the comments), they somehow missed Tom Lehrer completely. That's OK, however, since the Tom Lehrer Wisdom Channel can remedy that immediately.

• Ok, that's enough puzzles for now. For some strange fun, let's turn to Sternest Meanings. This is a web-bot that will reply to anything you type in, and the response you get will always be an anagram of what you just typed! It's simple, strange and fun.

• Even with all the mentions I've made of poetry on Grey Matters, I'm discovering newer poetry sites all the time. Among the most notable ones I've found are Kenn Nesbitt's hilarious Poetry 4 Kids site, the well-thought-out Black Cat Poems and the rather unusual Poetry Visualized site, where users submit videos of classic or original poetry. If any discoveries you make inspire you to memorize a poem, the hubpages article How To Memorize A Poem has a great technique for doing so. I even used this approach to quickly memorize Washington Crossing The Delaware before work one day!

• Before I wind up this entry, let's start your brain juices flowing again with some brain training sites. The first site is BrainTrain, which offer plenty of challenges from Lipton Iced Tea's Australian site. Apparently, it's part of their Australian ad campaign which also includes puzzles in their magazine ads. The Matica Brain Training Gym offers 4 games, which can be played without registering, unless you wish to keep track of your progress. I like the games here because they're number-based, which is my strong point, and you get your rating as a percentile. Queendom's Mind Stretchers is another good source of a wide variety of puzzles, as well.

• Now that you've fried your own brain, I'll wind up this entry with a way you can fry other people's brains. You can do this with an iPhone magic effect called iSensor (iTunes link. Here's a web link for iSensor), which sells for US$1.99. This was developed by Lior Manor, who also developed the 21st century Knight's Tour. Below is a video of the performance of this rather ingenious bit of iPhone magic (Warning: Some foul language included):

Today being Mother's Day, I've spent more time making my mom's day special, but I would like to share with Grey Matters readers one of the things I did for her.

My mom used to have a VHS video that she enjoyed, titled Andrew Lloyd Webber's Premiere Collection Encore. It featured original music videos to many of Andrew Lloyd Webber's best-known songs. That video has long since disappeared, and we haven't been able to find a DVD of it anywhere. It's one of those things she enjoyed, but figured she'd never see again.

As it turns out, though, all of the videos from the Premiere Collection Encore video are available on YouTube! It took a little digging to find the original list, their order and all the videos on YouTube, but I managed to do it! She thought it was one of the best things I could've done for her on Mother's Day.

If you want to pick and choose the individual videos, you can click the link above. If you want to watch them in their original order, however, here they are (click side arrows to jump to the next or previous video):

You've probably heard plenty about Apple's iLife and iWork software suites, so this won't be another review of those products. Instead, I'm going to talk about a different use for them, that of memorization tools.

Regardless of the particular memory techniques you're going to be using for a given task, it's a safe bet it's going to involve some sort of visualization. Traditionally, you're supposed to just imagine these images. However, actually creating the unusual images you need on your computer will help make the images more vivid to you. In addition, the process itself of putting the images together will also help lock the images into your mind better.

Since you'll probably be working a wide variety of images, a good clip art library, such as those sold in stores, or online sources such as Wikimedia Commons, will prove very useful. The clip art can be easily organized with iPhoto, especially if you set up your individual memory task as an “event”. This will make it more accessible later on.

Granted, you could just use iPhoto's slideshows to put your imagery together, but there's not really enough freedom to put the images together as you may like. Pages certainly offers more freedom in combining and laying out images, but I've found that it can be too static for memorizing images.

The way to go, I believe, is to combine the images in Keynote. Keynote has all the image manipulation power of Pages, but putting the images together as presentation will help bring the needed imagery more alive. Plus, if you're doing the sort of memorizing where one image needs to lead to another, slide transitions such as Magic Move can help lock in the associations. The animated nature of slide transitions is an oddly beneficial in a way that no other traditional memory techniques have been able to capture.

Remember that you're not making a presentation for someone else, so as long as the associations and images make sense to you, that's all that is needed. If there's a possibility that you may need to go over these images later on, you may want to add presenter notes that detail what the images mean. This will not only remind you later, but add another layer to help you remember your task.

With a little creativity and thought, there are many other ways that iWork and iLife can help you memorize information. Numbers, for example, is very helpful in organizing information such as the number and mnemonics for the 400 Digits of Pi feat. Need a calendar so that people can verify your Day of the Week For Any Date feat? Many at the iWork community have solutions all ready for you! All the documents I've posted over at scribd.com, as a matter of fact, are right out of iWork.

I discovered an unexpected use for iLife while working on memorizing poetry. While going over the tips and tools at How to Memorize Verbatim Text, About.com and Poetry X, it occurred to me that GarageBand's podcast-creating features would come in very handy.

What I do when learning a poem now is enter the poem itself into a podcast document, and use the above tips and tools to memorize it as best I can. At that point, I hide the poem from view, and I record my recitation of it in GarageBand as if I were creating a podcast. Once I've recorded it, I bring the written poem back into view, and read the poem as I play back the recording. I go through and highlight any words on the written version that I incorrectly stated in the recorded version. In this way, I can see my errors visually, and learn the poem verbatim quicker and more effectively.

Do you have any favorite programs you've used in unexpected ways that you think other Grey Matters readers would enjoy? Let me hear about them in the comments!

7,636 Missing Persons, 2,260 Murders, 6 Unsolved Serial Killings, 100 Episodes - that's the tag that opened Numb3rs' 100th episode, which just aired this past Friday.

This episode picks up from the previous episode of Numb3rs, Fifth Man, in which Charlie's math leads to an FBI stakeout in which Don is injured by a man Charlie didn't expect via his pattern analysis. This leads Charlie to question whether he can really see beyond the math.

In Disturbed, the 100th episode, Charlie begins analyzing numerous (num3rous?) previous unsolved cases. This makes the FBI team wonder whether he's still grasping at straws after feeling responsible for Don's life, or whether he's really on to something.

If you haven't already seen the episode, here it is in full:

Need to catch up? Between Fancast's Numb3rs page and CBS' own Numb3rs videos, you should become well versed on at least the current season.

Naturally, CBS threw a 100th episode party for the stars.

Personally, I'm thrilled to see a show with such a strong math background make it this far. The nice thing is, you can delve into the mathematics of any show as deeply as you want. Redhawke's Running the Numb3rs site and Wolfram's The Math Behind Numb3rs site (and it's featured interactive demonstrations) are probably the two highest respected sites when it comes into delving into the principles discussed in the show. CBS' main Numb3rs page has even more links for Numb3rs fan, including their weekly math puzzle.

Congratulations to the Numb3rs team for making it to your 100th episode! Here's hoping that the show goes on and makes 100 more!