There are plenty of places you can find Pi easily on this blog, but you might be surprised as to where you can find Pi hidden, if you just look close enough. I'll start with a few of the easier places to find it.

Over on Twitter, user 3point141592653 is tweeting pi. As this writing, the tweets are only up to 290 digits, but there's more than enough material to suggest that many more entries are to come.

Back in September of 2007, I posted the following animation from Wikipedia where it seems Pi's presence would appear quite obvious. However, Pi was also ingeniously hidden in the picture itself in at least 2 ways. The ratio of the width to the length is equal to Pi to the first decimal place - 3.1 (if the picture was only 1 picture wider, it could've been accurate to 2 decimal places). Also, the final frame is held for exacty 3.14 seconds.

Ready to take your memory and mental math feats to the next level? I'll show you some excellent resources on how to do just this in this month's edition of snippets:

• GAMES Magazine's September 2009 issue is a must-buy for Grey Matters readers! First, it features a reprint of the late Mel Stover's Beadless Abacus routine (more on Mel Stover here), which is a great mental calculation feat! You display the diagram (included in the article) of a diamond-shaped arrangement of hexagons, in which each hexagon contains a simple arithmetic equation (6 + 4, 8 ÷ 2, etc.).

First, you ask your spectator to choose any 3 hexagons in a straight line, and you can perform and sum all 3 equations faster than they can with a calculator. Next, you ask them to choose any 4 hexagons in a straight line, and you sum up all 4 faster than their calculator. For a finish, you ask them to choose a group of 7 hexagons – any hexagon not on an edge, and the 6 hexagons surrounding it – and you can sum all 7 just as fast! If you somehow miss this issue (it's available until August 18, 2009), you can still find this routine at your local bookstore, in Games Magazine Big Book of Games II, as well (the amazon.com preview even shows part of the Beadless Abacus on the books back cover).

In this same issue, there's also an excellent article on Henry Dudeney's game Kayles. This seems to be a fair game, but can be played perfectly so that you win when you chose and lose when you chose. It's kind of like Nim taken to the next level. The September 2009 cover itself, in fact, is a Kayles puzzle themed with clowns (See the link above before August 18, 2009 to see the cover and the puzzle).

The last page of the issue is a Knight's Tour-base puzzle, where you have to discover the secret message using only legal knight moves.

• Ken Development has several iPhone and iPod Touch native apps available that are of interest to you. The first one I'd like to mention is Peg Solver (iTunes Link), which is available for free. If you've ever been frustrated by that Triangular Peg Solitaire game (Cracker Barrel customers know this game well), this app will finally teach you how to solve it (only how to solve it, as there's no instruction-free mode).

They also offer Math Tricks (iTunes Link), where you can learn a wide variety of fast multiplication-based and division-based mental math feats. The full version goes for 99¢, and there's also a lite version (iTunes Link) available that focuses on just 2 of the feats, so you can get the basic feel of the program.

• Remarkable Marbles is a memory techniques site that I hadn't run across before, which apparently began last year. They offer an excellent tool on their site called The Major Memory System Trainer, which helps you learn the peg/major system, including the phonetic alphabet. To use the trainer, you do have to log in, but registration is free, and gives you access to their forums, as well. It's highly customizable, and will help you quickly learn these systems.

• Ulrich Voigt has a manuscript in German available called Das Jahr im Kopf: Kalender und Mnemotechnik (in English: The Year in the Head: Calendars and Mnemonics), which is currently available for €35. Interestingly, it's available in English on the publisher's site as a PDF, absolutely free! Go to the Likanas site, click the Das Jahr im Kopf link on the left-hand side, and then click the How to compute Key Calendar Dates link (direct link to PDF here), which you can then save to your hard drive and view at your leisure.

For those who've learned and practiced the Day of the Week For Any Date feat, this manuscript goes to the next level. The method I teach is limited to the Gregorian calendar. Not only does Mr. Voigt teach how to handle dates in the Julian calendar, but much, MUCH more!

The How to compute Key Calendar Dates manuscript covers more abstract date requests, such as “Mondays in October 1948” or “Years in which June 14 fell on a Sunday”. From there, the author goes on to discuss how to mentally work out things like full moon dates, Easter dates in a given year, and even how to handle the Jewish calendar!

As the new look takes hold, new functionality starts taking hold, as well. In an effort to make the blog not only look better, but function better too, I've continued upgrading this site.

First, the Knight's Tour Game is working again. When I moved the blog over, I initially neglected to move the Knight's Tour graphics (the squares, the pieces and the other icons) over with them at the same time. That error has been corrected, and the game now looks and works as it should.

Also, the Timed Quiz Generator hasn't been functioning at all. I've not only fixed the problems so that the Timed Quiz Generator now works properly, but I've updated the video with the new address, and added a button to display the video tutorial on the site itself.

I apologize for these flubs, and any inconvenience they caused.

I've added a nice new feature to this blog's most popular post, How Many Xs Can You Name In Y Minutes?. It's called the droplist filter, and it allows you to narrow down the long categorical quiz lists to better suit your interests. To activate it, simply click on the magnifying glass icon () next to any category, type in a word relating to that category and your specific interests, and hit return. After you do that, the droplist will contain only items containing your search term.

For example, if you're looking for baseball-specific quizzes, you would click on the magnifying glass icon next to the SPORTS category, type baseball into the text field, and hit return. Let's say you decide that there's too few quizzes on baseball (only 8 at this writing), and that you want more. You could click the icon again, typing in MLB (short for Major League Baseball), and find many more!

Note that this isn't perfect. Neither of the above examples will include the quiz titled 1976 Cincinnati Reds Starting Players, as that doesn't include the terms baseball or MLB in it. The droplist filter looks only for the exact term you enter, so Cincinnati Reds would bring that quiz up, while Cincinnati Starting would not bring that quiz up (as the words Cincinnati Starting don't appear together in the name of any quiz).

The feature is nonetheless quite handy. Since each quiz lists the site that hosts it, this makes it easy to find, say, only MOVIES & TV quizzes that appear on Mental Floss. Click the magnifying glass icon next to MOVIES & TV, type in Mental Floss, hit return, and the droplist will now only contain quizzes from Mental Floss.

To return to the full list, click the icon again, then click the reset icon (), and the droplist will immediately return to its full contents. Keep in mind that visiting a quiz, and then returning to the timed quiz page will also reset the droplist to its full contents.

Besides the Knight's Tour I mentioned earlier, I've also reworked all the other challenges listed under Tests on the workout page of the Mental Gym. While the Knight's Tour itself still uses your browser's built-in dialog boxes, the others have all been reworked to use newer and more customizable dialog boxes.

One of the benefits of this can be immediately seen in the new version of the Mental Shopper Quiz. Since it's always going to be asking for a 4-digit price (2 digits for the dollar amount and 2 digits for the cent amount), it's a simple matter to have the input be pre-formatted in the form of a price (you'll also note that the input doesn't respond to any input other than numbers, as well). This feature is also used in the new Serial Number Quiz and the new Pi Digits Quiz, where it especially helps in answering the 40-digit challenges.

Since the Root Extraction Quiz and the Exponential Expression Quiz both require such a wide variety of input, their inputs aren't limited in this way. One good thing about using the new windows for these, though, is that when asking about exponential expressions, I can actually ask a question in a form such as, “What is 9⁸?”, instead of asking “What is 9^8?”, and subsequently having to explain that the ^ symbol is meant to represent “to the power of”.

In the updated version of the Day of the Week For Any Date Quiz, the custom dialogs also make it easier to use droplists for a response. Instead of worrying about whether you misspelled Wednesday in an input, or requiring that you enter it in all small letters or all caps, you simply select it from the droplist and get your response right after clicking the OK button!

The biggest change in all the quizzes is the new Playing Card Memorization Quiz. In the peg word quiz, it acts pretty much as before (although no longer requiring you to enter your answer in all small letters). However, when you click on any of the options to be quizzed on the card pair feat, you might be in for a surprise!

Originally, this quiz just gave you pairs of cards names in a shortened notation (5S for 5 of Spades, or KC for King of Clubs, for example). Now, you see detailed images of playing cards! As the window opens, you'll see 2 playing cards, and you can click View next pair of cards to see another pair (note that you cannot go back and see any previous pairs!). This continues until you've seen as many pairs as you selected, after which you'll briefly see two cards that say QUIZ TIME.

After about 3 seconds, the card window closes, and the quiz window opens automatically. Instead of having to enter the cards in a special notation, the input is now done in the form of a pair of droplists (one for the value and one for the suit), making the input far simpler, while decreasing the potential mistakes. Because this quiz continues until it's asked about every pair, there's also an option to discontinue the quiz at any time.

Most of these updates wouldn't be possible without the awesome power of jQuery and the work of numerous jQuery developers. The new modal windows are made possible via boxy, and the timed quiz droplist filter came from joshuachan.ca. The masked input in the quizzes was made possible by digitalBush.com's Masked Input Plugin. Juggergnost's Regular Cards Clip Art library is the source of the playing card images. All these developers deserve recognition for their help in making this blog simpler and easier to use.

Having recently covered the topic of gambling and math in Wanna Bet? and Scam School, I feel I should do the responsible thing, and cover the downside of gambling and math, as well. Even when the math is solidly behind you, the real world can often bring other factors into play.

Take the case of an anonymous couple from the south coast of England. They traveled to Owlerton Stadium to place bets on the greyhound races. Now, the jackpot for picking the 6 winners in all 6 races that day had reached a record-breaking £101,110.39 (Over US$165,000 at this writing!), so this English couple formulated an idea that would mathematically assure them the jackpot.

They gathered together £46,656, which was enough money to cover every possible placing of all six dogs in all six races, thereby both qualifying them for the jackpot, and assuring them of a win. As I mentioned, the real world often brings other factors into play. Since you have to bet in cash, the cash could have been stolen. Fortunately, that didn't happen.

However, it turns out there were other qualifying winners that day. Had there been only one other winner, the couple would've still made a modest profit of just under £3,900. However, there were 2 other jackpot winners, so it was divided evenly into prizes of just over £33,700 - resulting in a net loss of roughly £13,000 for the couple!

On the upside, at least the couple were aware they were gambling, as all the trappings are there, such as the betting window, the posting of odds, the daily specials, and so on. The math of gambling gets even more vicious when the fact that you're gambling is hidden.

Take a look at Swoopo.com. At first glance, it simply seems to be an auction site similar to eBay, with deals that are far more incredible. Looking at their front page right now, I see a Apple iPod touch 32 GB (new generation) getting ready to go for less than $15 (about $400 retail) and a Sony PSP 3000 that just sold for $38.28 (about $170 retail).

How can they do this? Take a closer look at the process. Most auctions start at 12¢, and each bid increases the price by 12¢ (There are also 2¢ and 6¢ auctions with similar rules). Even more interesting, if you're bidding in the final minutes of the auction, as has become so popular at sites like eBay, the time gets extended, as well! This enables more people to bid in the final minutes, especially there is more interest in a given auction.

What's the catch? The simple act of placing a bid costs you 60¢, whether or not you win. That's not 60¢ for the right to bid in an individual auction, that's 60¢ each time you place a bid.

Since I wrote about that Apple iPod Touch just a few minutes ago, it's now up to just under $20. Let's assume it closes at, say $24.60, and the winning bidder put in 20 bids before winning the iPod Touch. The person who won actually paid $36.60 for that iPod Touch ($24.60 for the item itself, plus $12 in bids), which is still a great deal for that person. However, if there are 40 other people who lost, each placing an average of 20 bids, that's $480 made by Swoopo.com in exchange for nothing more than the chance itself to get the item cheaply!

I'm more than willing to wager that my numerical estimates are far too low, in terms of both bids and bidders.

There's more detail on Slate's Big Money article The Crack Cocaine Of Auction Sites, by Mark Gimein. The best quote out of that article refers to Swoopo as, “the evil bastard child of game theory and behavioral economics.” If you want to get an idea of just how vicious game theory can be, you can read my Prisoner's Dilemma post from 2007.

To quote both Gimein and the computer from WarGames, it seems that, when it comes to gambling, the only winning move is not to play.

How about a nice game of Knight's Tour?

Yes, geeks and books go together. But for improving your geek cred, some books are better than others. Today, I'll share a few books that can help raise your status among your fellow geeks.

I've mentioned Garth Sundem several times in recent weeks, and rightly so. If you haven't explored beyond the links I've given you, then you need to check out his books Geek Logik and The Geeks' Guide to World Domination: Be Afraid, Beautiful People. About 2 years ago, I reviewed Geek Logik here, and even posted a video clip of the author answering tough life questions mathematically.

The Geeks' Guide to World Domination is the newest book by Garth Sundem. For an idea of what geekery you can get up to with this book, you can check out the teaser ad on the author's own site, but you can get an even better idea by going over the Geek's Guide columns, which are available online for free.

The next item for the geeked-out library comes from Mental Floss. True, that magazine should be required reading for such a library, but I'm going to be a bit more specific. Their new book Be Amazing, has a good mix of geeky lessons, as well as tidbits that can often come in handy. For example, take the Be Amazing approach to quitting smoking. Do you use a patch? No. Will-power? No. Try chain-smoking until you get sick, drinking a mild hallucinogen, and then living under violent threat should you go back! Before you pick up the book, take a look through the free Be Amazing online columns.

So far, none of these books stand out with an extremely geek title. Our next book solves that problem, with its title of The Chrysalis of a Polymath (Confused? Look up chrysalis and polymath). Unlike the other books on this list, this one isn't intended for a general audience. It's written by performing magician Paul Brook, and includes full performances and unique angles on things like the Day of the Week For Any Date feat, the Knight's Tour, memory feats and more (sound familiar?). These are not just the techniques, but tested approaches for entertaining an audience with these feats!

One older book on this list, which still deserves an honored place in it, is Mind Performance Hacks, which I reviewed more than 3 years ago. The author is Ron Hale-Evans, who also hosts the Mentat Wiki site, which is a Wiki dedicated to learning and performing assorted mental feats. The book was written in the same spirit as the site, but goes far beyond it. A quick look at the sample hacks and the very generous book preview show exactly how far.

If you think you're even halfway to a decently geek library, ThinkGeek's Techie Non-Fiction book section will give you an idea of just how far you still have to go (as will the Mental Floss book section and the Mind Performance Hacks related-book section). They're all worth perusing, but one group that especially stands out here are the Sneaky series: Sneaky Uses for Everyday Things, Sneakier Uses for Everyday Things, Sneakiest Uses for Everyday Things, The Sneaky Book for Boys and The Sneaky Book for Girls. While their name pretty much explains it, these book contain the type of obscure but useful information that comes in handy at times, often when you least expect it. Fans of MacGyver will love these books.

I've tried to cover my favorite books, but I might've missed your favorites. Let me know about any of your best recommendations in the comments!

Just because I've finally finished the external redesign, as described in Grey Matters' New Look! Part I, Part IIa and Part IIb, doesn't mean this blog is going to stop changing!

The outside is done, now it's time to work on the inside.

Some of the pages on this site were used as far back as 1998, and could really be made to function better. When I originally posted the serial number feat quiz, for example, the random numbers used to create a serial number were based on the computer's clock. That worked great when computers were slower, but as computers sped up, the numbers generated became all the same. Instead of getting serial numbers such as 93486407, you'd get 55555555 or 22222222. I've now re-written the algorithm that generates the random serial number, so that it gives you more realistic numbers.

I've already had several comments from people who landed on one of Grey Matters' quiz pages that they were confused as to what the quizzes related, and that it was difficult to understand the context of the quizzes. In response, I've added links to each of the quiz pages that take you directly to their corresponding lessons. For example, one reader e-mailed me to mention that he found the Mental Shopper Quiz via Google, but didn't understand why prices were being asked about. Now there's a link to Doug Canning's Mental Shopper Quiz feat, and everything is immediately much clearer.

Probably the biggest visible change on the site already would have to be how the Questions For Better Magic page works. Originally, this was just a long list of questions, based on the book Strong Magic, written in outline form. As a matter of fact, if you have Javascript turned off in your browser, that's still how it will appear.

However, if you have Javascript turned on, this outline of questions is now interactive! When you first bring up the page, all you see are the four main sections, Effect, Character, The Act and The Audience. Whenever you click on any blue text in the outline that has an arrow next to it, all the subsections under it expand and become visible. Click on any open section will collapse it, and any subsections underneath it. In this way, you can now see only the questions in which you're interested, and the outline as a whole becomes less imposing and far more readable.

As I predicted in Part IIa of my site update report, Google has already started covering the new Mental Gym site in its searches. Just 10 days ago, the new Mental Gym searches were always empty. Now, when you search for Pi, the new Mental Gym results are far better, as you can see.

From time to time, you'll see other improvements in this site. Most I'll bring to your attention, and others I just may leave you to discover on your own. If you have any suggestions for improvements, please let me know in the comments!

Back in April, when I wrote about scams in relation to math, I only scratched the surface. It seems I'm not the only one who turns a mathematical eye towards bar bets.

Over at allmagic.com, they've rediscovered the joys of a trick they call Encounter, but which you may remember as The Trick That Fooled Einstein, from the Scam School video I posted back in April. There are some excellent touches here to which anyone should pay attention, whether you're performing it as magic or a bar bet.

(BTW, allmagic.com reuses their magic URLs, so if you like Encounter, save it now! In a few weeks, there will be a completely different routine at that exact same address.)

Grey Matters favorite mathematical blogger, Garth Sundem, has also recently posted on the mathematics of bar bets, as seen in installment I and installment II. These aren't all subtle mathematical principles, as discussed in the previous column. They are great examples of lateral thinking of a mathematical nature, however.

Many of the ones Garth Sundem posted reminded me of Bob Farmer's Flim-Flam column, which appeared in both MAGIC and Genii. He's rumored to be working on a book that would be a collection of these columns. Should that book ever appear, it will be a must buy! Until then, I suggest doing your best to track down his past columns on scams. They're pure gold!

In the second part of their How To: Be Popular In Bars series, AskMen.com has even more suprising mathematically-based bets. The very first one is my favorite, as it starts by putting the focus on math, and at the end the math seems to be completely irrelevant, even though it is more important at the end!

Don't forget - while you're pouring over these bar bets, Scam School itself has been posting more creative ways to win free drinks. Have fun with these, and let me here of any good stories you have about bar bets, as well!

While many of my snippet columns have a theme, sometimes it's fun just to bring out a mixed bag of goodies.

• Over at UC Irvine, Professors Jim Arvo and Dennis Eichhorn teach a computer class in game theory, mainly using LISP. Fans of this site, as well as the TV show Numb3rs, will enjoy the resource page for this course. 4 Monopoly playing pieces are used as a key for the links, with the top hat indicating a playable online version of a game, the iron indicating a PDF paper on a game, the dog indicating a Wikipedia article, and the thimble to link to other information. Just clicking the top hats alone on this site will keep your brain busy for some time.

• One puzzle that has long eluded cryptographers is a coded message contained in a letter sent to President Thomas Jefferson in 1801 by Robert Patterson. Not only is there no evidence that Jefferson himself solved the mysterious cipher, but he considered it so inscrutable, he considered having the State Dept. use it for secret communications. However, after 208 years, the code has finally been cracked by a 36-year-old mathematician by the name of Dr. Lawren Smithline. The story about how it was cracked is interesting, and the final message is also somewhat amusing. The interactive look at the code-solving process gives you a good sense of the ingenuity it must've taken to originally develop this code.

• For those of you who have been patiently following the redesign of Grey Matters (as discussed here and here), the redesign is now complete! As promised, the Presentation section, the Online Store, and even the iPhone/iPod Touch Mental Gym have all been updated. I guess you could call this Grey Matters New Look! (Part IIb).

The online store now has its own search engine, which has also been integrated into the Grey Matters search engine. When you click the Store tab, it takes you over to the store's search engine to give you the results. Speaking of the search engine, you will now get results under the Mental Gym tab, as it now searches both the old mentalgym.freehostia.com site, as well as the updated version of the Mental Gym. Until Google starts indexing the new site, you'll mostly see results from the freehostia version of the site, which will redirect to the new site automatically.

The new iPhone/iPod Touch Mental Gym has been redesigned in Dashcode so that it appears properly on those devices. Originally, the selections needed to be zoomed in. Now, however, they are immediately readable. Also, some of the older, non-functioning links have been removed.

One last interesting note: This post marks the first time that the front page of the Grey Matters blog has been populated entirely with posts shortened with the Read More... feature. Since the narrower space has been put into play, this greatly helps in keeping the front page more organized and readable.

No, Grey Matters' new look is not just for the blog and the video blog. The rest of the site is going to be resdesigned in accordance with the new look, as well. The Mental Gym has already been redesigned!

If you take a look at the opening Mental Gym page, you might think, “It doesn't look all that different.”

That's true, but part of the the redesign includes moving the Mental Gym back to its original address. The new Mental Gym is now located here, where it resided before my ISP removed the site, roughly 1 year ago.

Besides a new look, there's better functionality, too. In the old version, many of the feats were taught over several different pages, such as the Day of the Week For Any Date feat. Now, all the multi-page lessons have been shrunk onto one page, and the content sections have been tabbed. The new version of the Day of the Week For Any Date feat looks feels, and operates much better. It's even possible to bookmark the individual tabs, if you want to save a page to return to later.

All the original memory basics, feats and tests are still there. In some cases, there were some minor changes, such as replacement of dead links. Probably the most noticeable change to the tests would be the replacement of the old Javascript version of Sudoku with an updated Flash version. Oh, I should mentioned that the WKRP Contest Song Timed Quiz has been fixed, and is now working perfectly.

Note that the Mental Gym already has a Site Navigation section similar to the one in the rightmost column of this blog. Click any of the arrows present, and you can navigate more deeply into the Mental Gym.

The move is not only affecting the Mental Gym itself, but the site as a whole. If you go up to the drop-down menu at the top and select Mental Gym, or any of the pages in it, it no longer goes to the old freehostia site, but rather the new updated version. As I finish redesigning the other sections of the site, the old freehostia site will soon become little more than a collection of pages redirecting to the new site.

There is one last additional change I want to mention. The search engine at the upper right originally would only search the section you were in, such as just this blog or just the videos. It has now been re-written so that it searches the whole site! If you type, for example, for “Pi” into the search engine, here are the results you'll get.

Yes, the search results have been tabbed so that you can look at results from just the section you want. For example, here's all the places Pi is mentioned in the video section. As with any of the other new tabbed sections, you can bookmark individual searches and tabs. Also, note the three small icons above the results. Clicking on them will let you see 1, 4 or 8 results per page, depending on which of the three icons you click.

At this writing, you won't get many search results for anything in the Mental Gym tab, as the new location hasn't been thoroughly searched by Google yet, but you should see good Mental Gym search results before July ends.

Next up, I'll be redesigning the Presentation section, the Grey Matters Store and the iPhone/iPod Touch page, so keep your eyes open!