In the above video, Charlie Eppes (David Krumholtz) is discussing what has become known in math circles as the Monty Hall Dilemma. The problem itself gained prominence when it was submitted as a question to Marilyn vos Savant's column, where it caused much debate. There is further discussion of the debate over the puzzle here.

What makes the solution so hard to accept is the counterintuitive nature of the answer. It seems like switching should have no effect, when, in fact, it doubles your chances. For some practical purposes, try this simulation (Java required). When you click a door, all 3 will open. Keeping in mind that, in the classic problem, you would have been shown a door that you didn't choose, and that had a goat behind it. With that in mind, all 3 doors opening will shown you the effects your choices would have. The simulation also keeps track of the results that both switching and not switching would have, so you can quickly see the improvement that switching offers.

Even with practical experience, it can still be hard to wrap your head around the “why”. On this page, in the Remark 2 section, there are several excellent descriptions which can help explain the conundrum.

Despite the current framing of the problem as relating to Monty Hall and the Let's Make a Deal game show, it is actually much older. It was originally known as the Three Prisoners Paradox. The interest provided by the game show renewed the interest in the problem, and the Marilyn Vos Savant controversy gave the problem wider publicity.

It's time for a little pure fun. Worth1000.com is a website that hosts regular photoshopping contests. The one that caught my eye recently is If Geniuses Ruled.

Among my personal favorites are Think Fast, Easy Open and Kid Genius. However, I don't want to rob you of the joy of discovery.

If you've tried Google Book Search before, there is now a vastly improved interface that is faster and far more manageable. If you've never tried Google Book Search, you're in for a treat.

For those who aren't familiar with it, Google Book Search allows you to browse, search and download PDFs of entire books. They even have a limited view of books that are currently available commercially. It's a great way to discover new books.

Not surprisingly, I've been looking to see what's available concerning mental feats. Among the completely free memory books are The Secret of a Good Memory, The Art of Memory: Exemplified Under the Two Leading Principles, Locality and Association and Dr. Grey's Memoria Technica.

Back in February, I wrote a review of the book Mind Performance Hacks, and I was even able to link to minor PDF excerpts of the book. Thanks to Google, I can now offer more excerpts from the book. Even these limited previews have value, and are akin to flipping through the book in the bookstore. Check out the limited previews of The Complete Idiot's Guide to Improving Your Memory, Your Memory: How It Works and How to Improve It and Memory: How to Develop, Train and Use It, too. This last book, written in 1912, can be hard to find. However, it's available here, and has been linked on my recommendations list for some time.

One of the great mathematical treasures I've discovered is the collection of Martin Gardner's books. This collection is fun to read through, so I won't rob you of the joy of discovery. I would like to bring special attention to The Colossal Book of Mathematics as one of that master's best works. I've treasured my copy ever since it was first given to me by Looy Simonoff.

The best thing about Google Book Search would have to be the feeling of having a library at your fingertips, all tailored to your specific interests. I'll probably be using this tool in future posts, and I'll definitely keep reading and sharing my discoveries from there.

There have been plenty of books on mathematically-based effects, but there are very few books available on the proper presentation of those same routines. Hidden Numerical Forces by Thomas Henry is a valuable and much-needed book on just that topic.

Thomas Henry breaks the process down piece by piece, so that not only do you know the techniques and proper presentation points, but also why other presentational avenues are not taken. Take a look at the PDF preview of Hidden Numerical Forces (opens in a new window) to see the first half of the first chapter, which discusses the 37/68 ploy.

He starts by talking about the basics of the technique in each chapter. One of the best parts about this book is that it often gives better explanations of the techniques than do many non-presentational math magic books. Also, when possible, credits to the originators are given in detail. Once the reader is on solid ground concerning the techniques, it's time to move onto presentational exploration.

I don't use the word “exploration” lightly, either. The author takes the time to lead the reader through less effective ways to present each force, and what makes each avenue more or less effective than it can be. In the process, you're not only learning about how to properly analyze presentation, but how to get inspired from the mistakes. It's not just one approach per force, either. Thomas Henry explores multiple presentations for each routine, as everyone is going to find ways that work better for their presentations and their audiences.

I'm amazed at the thoroughness of the included forces, as well. Especially interesting is the “Half 1089 Force”, which I first ran across in the October 2002 issue of MAGIC Magazine, in Jim Steinmeyer's “Two Dictionary Test”. Instead of using the full 1089 force, this is a way of effectively stopping in the middle to take advantage of a little-used property of the numbers generated after the first step.

Hidden Numerical Forces is valuable not only for the lessons it does provide, but also for the inspiration it gives you in learning how to explore presentations in your own routines. I highly recommend it!

The last time I discussed someone using mental training to win money on a game show, it concerned Michael Larson's appearance on “Press Your Luck”. This time, our hero is Ogi Ogas, who appeared on “Who Wants To Be A Millionaire?“ on November 7-8, 2006.

In his Seed Magazine article, “Who Wants To Be A Cognitive Neuroscientist Millionaire?”, Ogi discusses how his neuroscience training helped him advance through the game.

It's a fascinating inside look at the thought processes, as well as the drama, of a contestant on one of America's most popular game shows. It's especially interesting considering the level he achieved. How far did he get? You'll just have to read the full article!

For some time now, my book Terry LaGerould's Pasteboard Presentations II has been available at the Grey Matters Store, as well as numerous magic dealers.

If you wanted to read it, but wanted to get it quicker, or at a lower price, both requests have been answered! Over at Lybrary.com, I am now making the PDF version of Terry LaGerould's Pasteboard Presentations II available!

Many of you probably know the name Terry LaGerould from his recent DVD release, Sessions With Terry LaGerould #1, or the original Pasteboard Presentations book (currently out of print). For those unfamiliar with Terry LaGerould, as I mention in the blurb for the book, the hallmark of his magic is efficient, innovative use of standard moves combined with highly commercial and original presentations. All the material in Pasteboard Presentations II comes directly from Terry's repetoire, and has been perfected over years of performing at major casinos in Las Vegas, Lake Tahoe and Reno.

Here's a complete list and description of the effects in Pasteboard Presentations II, just to whet your appetite:

Unexpected - A psuedo-center deal demonstration with a four ace kicker

Royal Victory - A selected 5 card poker hand is changed into a Royal Flush

Ace Shuttle - The cardboard astronaut escapes from the shuttle

Up the Down Staircase - "Triumph" done with the four Queens

It's All in Your Mind - A mentally selected card repeatedly vanishes

Mental Photography - The black aces "burn" (turn red), printing a selected card

Tell-A-Pathic Gypsies - Four Queens change, and then are found by the spectator

Unforgettable - An impromptu "Triumph" effect that ends with blacks and red separated

Cardboard Keyboard - "Spectator Cuts to the Aces" with a musical presentation

Traveling Man - A King is sandwiched between to red Queens, and jumps back and forth

Cardboard Sobriety Test - Test the spectator's sobriety with the Jacks, Kings, Queens and Aces

Jewel Thief - Two cards change places in the spectator's hands

Instantane-E-Ace-Ly - Just as the magician gives up looking, the four aces are produced

Illusive Cocktail Gals - The Queens are each placed on one of four piles, and magically travel to one pile

Carboard Lie Detector - A small packet-size "Lie Detector" routine

Impromptu Invisible Deck - The Invisible Deck routine, done without gaffs

Incredible Cardboard Acrobat - Halves of the deck impossibly flip face-up and face down, with a "Triumph" finish

Magic squares have been a frequent topic here on Grey Matters, as a quick site search will show.

The classic presentation for magic squares is to ask for a number, quickly create the magic square, and then show the numerous ways that give the total.

This is not the only approach, however. Thanks to Stevens Magic Emporium and their Gemini Archives, you can learn two new and original approaches. In Mike Roger's magic square routine, a spectator chooses one of four business cards with playing card pips on them, and writes a two-digit number on the card, all without the performer's knowledge. The cards are then put away. The performer takes out another business card with a 4 by 4 grid on the back, gives a reading to the spectator, including naming the selected playing card pip, and then fills the 4 by 4 grid with numbers. Finally, it is shown that the grid totals their selected number in numerous directions.

Ted Lesley's magic square routine also employs a personal approach, but in a different way. In the Lesley routine, 5 cards and envelopes are handed out, and 4 of the 5 people are asked to give a sample of their handwriting on the back, while the other is asked to write a number from 34 to 100, and write their chosen numbers on each of their respective cards. They are then instructed to place their cards in their envelopes, without the performer seeing what each person wrote, and the envelopes are mixed by another spectator. The performer then divines to whom each card belongs, and finishes by creating a magic square that totals the number thought of by the 5th spectator!

Not only are these good routines in an of themselves, but they're also wonderful examples of taking classic presentations in new directions. They're well worth your time.

I enjoy hearing from those who are using my Train Your Brain and Entertain software (TYBE).

One TYBE user, Wallace Gluck, has been working on the 400 Digits of Pi section. He has come up with some improved mnemonics for some of the numbers, which he has graciously allowed me to include below. As with the original instructions, the capitalized letters are the phonetic equivalents of the numbers:


A7: ACHe - MoVe, MoaN
A9: APe - KNiFe Fur

C3: CoMa - NaiL MaRy
C7: CooK - haVe hiS FiSH

D1: DoT - SoaP MoVie
D2: DeN - ouR RoaCHeS
D5: DeaL - MaD CoN
D7: DoG - hoRSe FeD

E3: EMpty - By My FueL
E4: ER - NeeD DoSe
E5: EEL - yeLLow LiP

F5: FoiL - RaRe SHeeT
F6: FiSH - New FRoG

G4: GoRe - CHeeRFuL
G6: GuSHy - MaRRiaGeS
G9: GaP - RoMaN SHoe

H8: HooF - JuDGeS SHoe

J5: JaiL - JuDGe aLieN


If you wish, you can add these directly to the help section of TYBE. Open your “TYBE” folder, then open the “Help” folder, followed by the “100-Memory Techniques” folder. In there, you will find a file called “108-400 Digits of Pi.html”. Simply open this file in your favorite text editor, and copy and paste the various mnemonics into their corresponding places, and make sure you save the file with the same name in the same location!

Once you do that, the new mnemonics will show in the help section of the program each time you bring up the Pi Mnemonic technique help.

Thanks again, Wallace!

Have you ever opened up a new deck of Bicycle Playing Cards and seen the card featuring a Sudoku puzzle?

It's meant as an ad for the Bicycle Sudoku puzzle deck. Imagine, when someone opens a deck and finds such a card, that they hand you the Sudoku card, you take a brief look at it, and then hand it back, rattling off all the numbers from left to right and top to bottom!

One interesting thing is that the demo puzzle is always the exact same puzzle, the one pictured in the upper left corner of this article. With that little bit of knowledge, this pseudo-memory feat becomes much easier.

First, you need to learn the Link System and the Peg System. Once you're comfortable with those methods, you just need to learn the following paragraph by heart:

"Jay Leno, our Honda issue: My wheel may err. No good paved. Bike error? Bashed notch off Park Avenue, hit oil well here."

This sentence translates into the numbers from the puzzle! Here's how the phrase breaks down with the corresponding numbers in parentheses:

"J(6)ay L(5)en(2)o, our(4) Hon(2)d(1)a iss(6)ue: M(3)y wheel(5) m(3)ay err(4). N(2)o g(7)ood(1) p(9)av(8)ed(1). B(9)ik(7)e err(4)or(4)? B(9)ash(6)ed(1) n(2)otch(6) off(8) P(9)ar(4)k(7) Av(8)en(2)ue, hit(1) oil(5) well(5) her(4)e."

One you're practiced in both the mnemonic systems and the above phrase, you'll have a feat you can perform as either a psuedo-memory feat, or a divination feat!