Ever played the electronic game 20Q? You think of any tangible object, and then it asks you questions. After 20 questions, often less, it guesses the object of which you're thinking.

If you've never tried the game, or even if you have, try the free online version a few times before continuing with this article.

20Q's popularity owes much to the way the game builds. You start by wondering if it will get your item correctly. As you see the questions, you sometimes wonder what it is thinking. Often, the tension builds as you get closer and closer to the 20-question limit. Finally, it either misses your object, in which case you're happy that you could beat it, or it guessed your object, and you're left wondering how it could have possibly guessed that object.

How exactly does it work? By your questions, you're basically helping the 20Q work through a search tree. Even if the device only asked 20 questions and only had YES or NO buttons, then it would be able to distinguish 2²⁰ things, for a total of 1,048,576.

When most people understand that, even just over 1 million items doesn't seem enough to cover every possible object. Consider this, however: Your average standard reference dictionary contains almost every object that is going to be thought of for this game, and most dictionaries only contain 50,000 to 100,000 entries. Even the 2nd edition of the Oxford English Dictionary, which took up 20 volumes, contained “only” 615,000 entries, which is far less than 20Q's capacity.

There are a few other tricks used, as well. First, the limitation to tangible objects: not every word in a dictionary is a tangible object. You can eliminate words like a, an, the, adjectives like blue, hard, shiny, and so on.

Also, note that 20Q doesn't absolutely limit itself to YES or NO choices. Some versions include the choices: Yes, No, Unknown, Irrelevant, Sometimes, Probably, and Doubtful. This array of choices both narrows down the available choices and helps obscure the method.

While the popular versions of 20Q have only become available within the last decade, the basic idea is much older than that. The first popular computer game to guess what you're thinking of was already making the rounds in 1976!

The game was known as “Animal”, and one of the original BASIC listings is available here: Page 1, Page 2. Notice how short the listing is, as it only starts with 2 animals and 2 questions in mind. Even the capability to learn new things isn't that difficult to program.

An early computer magazine, Creative Computing (who also published the book containing the Animal listing above), published a detailed and thought-provoking article on the exact process of the Animal program, which became the basis for 20Q. The article is called Learning, Innovation and Animals, and is available online for free here: Page 1, Page 2, Page 3, Page 4, Page 5, Page 6.

The 20Q project itself in 1988, and was even admittedly inspired by animal. The database was developed by years of testing the program with people, and allowing them to add their own questions. Also, the idea of more human-seeming answers, such as Irrelevant, Doubtful, etc., were developed during this testing.

This is one of those rare times where the way the game was developed is almost as fun to explore as the game itself!

It's Thanksgiving here in Grey Matters central, so this is going to be a quick post. I thought I'd share some quick card tricks with which you can entertain your family over the holiday weekend.

Garth Sundem starts us off with a simple card trick in which people determine how many cards you deal in each of several piles. When the final cards are revealed, they prove to be all Aces! It isn't intended to be the most amazing trick, as you might guess by the title of the article, Math Card Trick: Amaze And Astound Your (Idiotic) Friends And Family!, but it's still good fun.

If you know someone else who enjoys mathematical card tricks, and would like to help you pull one over (as long as you agree to do the same for them), check out Poker-Faced Over the Phone. In this trick, you mention that there's a prediction that's been placed in the card case. You ask someone to get out a good, but not perfect, poker hand out for a game of draw poker. You then ask them to replace any card of their choice with another one from the deck.

When they replace the card, you tell them to open up the card case. Inside the card case is a name and a phone number. Your participant calls the phone number, reads off the cards in the new hand, and the person on the other end of the phone identifies which card was not in the original hand! This is an interesting take on the Fitch Cheney Card Trick. I won't go into the exact method, but I will say that fans of Leo Boudreau's work will probably enjoy this.

While doing research for my posts on Game Theory and Game Theory in Popular Culture, I ran across a game theory documentary I'd never heard of.

It's called Nice Guys Finish First, by Richard Dawkins. It's a 1986 BBC Horizons documentary all about the prisoner's dilemma. The full documentary is available below the fold.

This is one of largest editions of snippets yet, so let's get right to it!

• If you liked the native app iSensor (iTunes Link), which was mentioned in my iPhone and iPod Amazement post, there's a new program that take the routine to the next level. It's called iForce (iTunes Link), and it uses the same basic idea as iSensor, but allows you to customize it to any sort of routine you want!

iForce comes disguised as a simple drawing program, but has hidden features that allow you to perform impressive mind-reading that limited only by your imagination. Even more ingenious, the drawing program as which it is disguised is available separately in the iTunes store, so if anyone tries to discover your secret, they'll be looking for the wrong program. The drawing program isn't even posted under the same company name, so it's all the more difficult to accidentally run across the real program. Ordinarily, I'd mention the name of this program, but I'm doing my part to keep it out of search engines to avoid exposure.

• Alan Rorrison has another trick out called Google App. You ask the spectator to name any playing card, and then type “what is my card?” into Google, and hit the Google search button. The Google search results then displays results containing the name of their card! This may sound similar to boondoggle (method here), but the difference is that your spectator is the one who types in the search question, not you.

• So many magic iPhone/iPod Touch apps are now available, that the Magic Café has decided to give them their own forums! They now offer APPS-alutely (for general discussion of apps), APPealing or APPalling? (for app reviews), and APPearing Soon... (for discusing app announcements, rumors, and marketing).

• Over at the Magic Café, user MemDeck329 has posted a great five-part approach to learning a memorized deck effectively. It's called Memorized Deck Made Easy, and is posted in 5 parts:

Part 1
Part 2
Part 3
Part 4
Part 5

The approach does use Nick Pudar's Stackview program, which is a Windows-only program, but Intel-based Mac users can run it by using either Darwine or WineBottler (I prefer the latter, but both are good).

• Ever had a great idea for a trick involving specially-designed cards, but couldn't perform it because it wasn't available? While there are places that will make custom cards for you, such as Make-A-Deck.com and Card-Shark, Lybrary.com offers up a different approach: the ability to make them at home! The best place to start is with their article, How To Make Your Own Playing Cards. You'll need:

• A color laserjet or inkjet printer with a straight paper path (the article recommends the Brother HL-4070CDW)
• The right cardboard, which you can find at Lybrary.com in sets of 10 sheets, 20 sheets or 40 sheets
• A poker-size card cutter
• A corner rounder
• Vector playing card images and software for your system that can load, save and edit vector files (free software is available to do this).

Starting last Thursday (November 12) and ending yesterday (November 14), the World Memory Championships have been taking place. Defending champion Ben Pridmore has won the overall competition, making this his 3rd win.

There's more detail, including video reports, about the World Memory Championships below the fold.

CBS covered the award ceremony in this report, and briefly explained what the competition detailed. The video version of their report is here:

I first discussed Dr. Frank Wang's educational DVD, Beauty and Mathematics, back in 2006, when I linked to 2 videos from the DVD's product page.

Dr. Wang has recently been generous enough to send me a copy of this course, so I thought I would share my thoughts on it with Grey Matters readers.

Disclaimer: I was provided with the complete course by Dr. Wang himself and was not charged for it. I do not make any money off the purchase of the course. The thoughts below are purely mine as a result of going over the course on my own time for the purposed of informing Grey Matters readers.

The course itself, whose full name is Beauty and Mathematics: Mathematician's Search for Order and Pattern, comes as a DVD set and handouts related to the various sections of the course. There are also a few advertising and promotional items included, such as a pocket protector and a sample board for an arithmetic challenge called Witzzle Pro.

The DVD case contains 2 DVDs and a CD-ROM. The first DVD contains the presentations, and the 2nd DVD contains the explanations. The CD-ROM contains handouts related to the each section in the form of PDFs. Pre-printed copies of these PDFs are also included with the course.

Dr. Wang currently teaches at the Oklahoma School of Science and Mathematics, and much of the presentation footage is shot at an assembly there, with some footage from a teacher's meeting where he lectured. The presentation talks are the basics, and even include some amazing demonstrations, including the "The Birthday Paradox" and "The Death-Defying Feat" (free videos and worksheets available at link).

Each segment of the lecture follows the theme of finding order and patterns from some sort of random mix. The segments included focus on the Rubik's Cube, Ramsey Theory, the small-world and birthday paradoxes, random walks, crumpled paper, Pi from random numbers and the Death-Defying Feat (as linked above). These sections are designed to grab you, and draw you in, and are presented with humor, fun, and even surprise and mystery in some cases.

The explanation DVD, by contrast, is shot in a studio, and explains each section in more detail. The focus here is on clarity, as it should be. The explanations often go deeper into each topic than you'd expect, which pleasantly surprised me. Even when discussing how the number of Rubik's Cube configurations, for example, he delves into decimal point vs. decimal comma and short scale vs. long scale. Even on topics where I was fairly sure I understood them, such as estimating Pi from random numbers, I learned more than I expected.

I'll sum up this review in 2 different ways, as I'm really writing for 2 different audiences in this review. First, for this set's intended audience of teachers and students, I definitely recommend this set. Math can often be hard to teach, and even harder when trying to grab your student's interest. The approach in the Beauty and Mathematics set, of demonstrating order coming out of apparent chaos, and making the demonstration of that fun and engaging, is a great way to help your students truly learn. Much of the material you may have thought of as too advanced for some students becomes clear, intuitive and understandable with Dr. Wang's approach.

Second, Grey Matters readers should already be interested in this, and fun and math have long been a focus of this blog. Unlike many education products, the $49.95 price it's affordable, and not priced for only schools. If you've enjoyed the mathematics approach used in places like this blog and BetterExplained, where intuition and clarity are paramount, you'll enjoy Beauty and Mathematics.

I recently came across a site that featured a copy of an 8th grade US Constitution test, to which I'll link later in this post. I thought it would be interesting to link to some online quizzes concerning the modern-day equivalents, to see how you would do today.

Here are your challenges:
• Can you name all 15 US Presidential Cabinet positions?
• Can you name the people who currently hold the US Presidential Cabinet positions?
• Identify all 27 US Constitutional Amendments.
• Legislative branch of the US Federal Government questions
• Executive and Judicial branches of the US Federal Government questions
• Complete the Preamble of the US Constitution.

How did you do? You should have at least breezed through the Preamble and Constitutional Amendment sections if you practiced the mnemonics from my US Constitutional Amendment Mnemonics posts (Part I, Part II, Part III).

Here's the post that inspired this post, with the quiz from 1954. The student who took this quiz got a score of 98.5%. How did you do on your test?

In my prior Game Theory post, I briefly mentioned the classic bar scene from A Beautiful Mind as one example, but there are far more examples of just about every aspect of game theory to be found in popular culture.

One common game theory scenario is known as “The Pirate Puzzle”. Here's the description, courtesy of the Mind Your Decisions blog:

Three pirates (A, B, and C) arrive from a lucrative voyage with 100 pieces of gold. They will split up the money according to an ancient code dependent on their leadership rules. The pirates are organized with a strict leadership structure—pirate A is stronger than pirate B who is stronger than pirate C.

The voting process is a series of proposals with a lethal twist. Here are the rules:

• The strongest pirate offers a split of the gold. An example would be: “0 to me, 10 to B, and 90 to C.”
• All of the pirates, including the proposer, vote on whether to accept the split. The proposer holds the casting vote in the case of a tie.
• If the pirates agree to the split, it happens.
• Otherwise, the pirate who proposed the plan gets thrown overboard from the ship and perishes.
• The next strongest pirate takes over and then offers a split of the money. The process is repeated until a proposal is accepted.

Pirates care first and foremost about living, then about getting gold. How does the game play out?

A couple of years ago, I wrote about the prisoner's dilemma, a challenge in making choices without perfect knowledge. That's only one aspect of what is known as game theory, the branch of mathematics that studies strategic situations where the players choice's conflict with each other. Game theory covers strategic games, of course, but also covers many common social, political and economic situations, as well.

Probably the most famous example of game theory is this bar scene from the movie A Beautiful Mind, where it's applied to men trying to get dates in a bar. If you enjoyed that article, Plus Magazine has many more clear articles on game theory that you may enjoy.

A good introduction to game theory can be found in two of the episodes of the program I mentioned in my previous post, Zero Sum Games and Prisoner's Dilemma. You can find a good variety of introductions to game theory on the web, ranging from the basic introductory videos I just mentioned, all the way up to full free game theory courses from Yale!

Once you have an understanding of the basics of game theory, you might want to take another look at the Beautiful Mind scene, and take a deeper look at the game theory analysis of that scene.

Learning about game theory is one thing, though, while applying it is quite another. The whole point of game theory is to learning to make the most effective choices you can for your situation, and I know that Grey Matters readers are people who enjoy learning by doing.

Over at Game Theory .net, they not only offer excellent references for students, but quizzes and tests, too. More importantly four our purposes, for both students and geeks, there is an excellent selection of interactive demonstrations and games to try out!

Even as new situations arise, you can usually find ways to apply classic game theory principles to them. There is an excellent blog, focused on game theory applications to current events, called Mind Your Decisions. Readers of this blog who are interested in game theory will definitely enjoy this blog, as the explanations are clear, and presented in an understandable, often fun, manner. You can find just about everything relating to game theory, ranging from jokes to questions on current events, and even links to other blog posts. I won't rob you of the joy of discovery by linking to specific parts.

As you can see, learning about game theory is just about learning math, it's about evaluation your choices more effectively so that you can make better decisions. If you go through these resources, and thinking about how each type of challenge applies to your own life, you'll be amazed at what you can learn.