Have you been practicing the states since I discussed it in my posts titled The States and The States Mis-Stated? I hope so, because today we're going to put you to the test!

In the 50 States of Mind site, they not only teach you the names of the US states and capitals, but also on many of its pages, it also teaches an ingenious way to remember the locations of the capitals within the states. To help reinforce the knowledge, check out the 50 State Capital Quiz. All you get is the name of a state capital, which you have to place in the correct location on a US map. You need to figure out which state's capital it is, where that state is on the map, and where the capital is located within the state! As long as you're reasonably close, this game is somewhat forgiving. Also, due to the scale, some states are easier that others. If you're given the capital of Rhode Island (quick, what is it?), the star for that capital is actually larger than the entire state, so as long as you can locate the state on the map, you can't help but get it right!

If you really want to push yourself, Mental Floss blogger Sandy Wood has a fondness for state puzzles. I suggest having a good knowledge of the state names, the state capitals names, and their respective locations on a map before trying these without any sort of cheating.

I like the following challenges, because they make you think about the states and their capitals in different ways. By the way, in some of the following puzzles, there are cities other than state capitals mentioned. Among the stately challenges posed by Sandy Wood:

• The Tri-State Brain Game
• Why Wyoming?
• The Elite Eight
• I Lettered at State
• East, West, North and South
• A Capital Idea
• Three of a Perfect Pair
• Actually Take This
• Lune Latérale
• Ottoman Winch Saga
• Weekend Genius Challenge: Win a T-shirt at ‘State’ College (OK, you can longer win the T-Shirt, but the challenge is still fun!)

It's time to wake up your brain with a little math! Don't worry, in this task that must be done, there is an element of fun.

I'll even start off easy with Quick Math. This is a test of speed in identifying the proper mathematical symbol that correctly completes the equation. You've probably played games similar to this in one or more of the various brain-training games that have become so popular.

OK, now that your brain is warmed up, let's try some math with a little more real-world feel. Try FunBrain's Change Maker, in which a purchase is described with the item cost and the amount given to you, and you have to figure out the correct change in your head! You can play the game in American, Canadian, Australian or Mexican dollars, as well as British pounds, and choose the range of money problems you'll be dealing with. I'm sure we've all been in situations where, were this game used in training cashiers, there would have been much less hassle.

Get ready, because we're moving from basic mathematical operations into algebra, with Algebraic Reasoning. Too often, algebra is presented in dry terms like 3p + 2d = 35 and 4p = 36, which can make the task seem mind-numbingly dull and much harder than it really is.

In the Algebraic Reasoning game, it's presented as a task using several scales, and various items in a toy store. For example, you might be shown one scale with 4 presents that reads “36”, and another scale that contains 3 presents and 2 drums that reads “35”, with your task being to find the value of 1 drum. Once you work out that the value of each present is “9” (36/4=9), you can then see that the 3 presents on the second scale must account for 27 of the 35 read on the second scale, and that the 2 drums must have a value of “8”. 8 divided by 2 is 4, so each drum must have a value of “4”! Even though the dry equations I mentioned earlier are exactly the same as the ones described with the scales and toy store items, the latter gets the understanding across quicker.

As you may know from my posts on visualizing math, visualizing Pi and visualizing scale, I'm a big fan of anything that can foster understanding quickly and effectively.

We'll conclude with geometry, but without any direct work with numbers. Instead, the Eyeballing Game challenges you to estimate the answers to various geometric tasks using only your eyes! The challenges include adjusting a graphic to make a parallelogram, find the mid-point of a line segment, bisecting an angle, marking a point inside a triangle that is equidistant from each of the triangle's edges, finding the center of a circle, drawing a right angle, and finding the point where three straight lines will meet.

Each task is scored by how close you were in “units”, with a lower score (fewer units off) being better. You perform each task 3 times, and your overall score is the average score of all 21 attempts. The last 10 best recorded scores of the last 500 games are constantly displayed, so you can see how well you measure up to the best players.

Do you have any favorite online mathematical games? Let me know about them in the comments!

Did you ever wonder about the source of my conviction that learning should be fun? I've been surrounded by the concept since I was very young. I'd like to share many of the books and programs that are responsible for this. Maybe you'll understand me better, or maybe you'll discover something you didn't know before, or a new way of looking at things.

Whatever the result, below are some of my favorite fun learning resources (in no particular order), all available for free for you to enjoy.

VIDEOS:

• James Burke's Documentaries – Yes, I've written about James Burke's work before, here and here, but his work seems to have finally found an official home at JamesBurkeWeb's YouTube Channel. Instead of teaching history in the same straight lines, as most dry textbooks do, James Burke's documentaries are famous for showing how history zigged and zagged, creating a more understandable feel for how history really happened.

Not only are all the episodes of Connections, Connections², Connections³ and The Day The Universe Changed available, but they've been broken down into convenient playlists, so that each episode plays the next part automatically.

• Schoolhouse Rock – From 1973 to 1986, these 3 minute shorts played on ABC every Saturday Morning. Thanks to these shorts, just about everyone who grew up on them could recite the Preamble to the US Constitution, or tell you the basics of how a bill becomes a law with little trouble.

There were many “divisions” of Schoolhouse Rock, and each Saturday morning would be dedicated solely to one of these divisions. They included America Rock, Grammar Rock, Multiplication Rock, Science Rock and more.

• Eureka! - While Schoolhouse Rock did cover basic science, it never really delved into physics. Eureka! (no, not the SyFy show), an animated series from TVOntario, picked up the slack here. They had multi-show segments on force and energy, simple machines, heat and temperature, convection, conduction, and even radiation! Even without the catchy tunes of Schoolhouse Rock, Eureka! was a very effective educational series.

• For All Practical Purposes - This is a great series from PBS back in 1987 that teaches all about modern mathematical concepts, and how they apply to today's real-world challenges. While some of the examples used seem out of date, the principles taught are still valid. The teaching is clear, and the examples are brought to life so that they're easier to understand and absorb.

• The Phantom Tollbooth – This 1970 movie, based on the 1961 book of the same name, is about a boy who is frustrated with school and life, until a journey through a phantom tollbooth to lands like Dictionopolis and Digitopolis help drive home the point about how important the thing you learn can be in life. Many consider this movie to be at least part of the inspiration for the Schoolhouse Rock videos. Part 2 is available here.

• Mr. Wizard – Don Herbert, better known as Mr. Wizard, taught science on TV in a fun, hands-on style. Instead of lecturing about heat, he might challenge you to figure out why a candle isn't burning up a piece of paper. His original show in the 1950s was called Watch Mr. Wizard, and you can even see a rare full episode of it on YouTube (Part 1, Part 2, Part 3). In the 1980s, Nickelodeon revived his popularity with a new version of the series, this time called Mr. Wizard's World.

The Mr. Wizard shows inspired numerous other fun science TV shows, including Beakman's World (The Penguins doing the introduction are even named Don and Herb in honor of Don Herbert/Mr. Wizard!), Bill Nye The Science Guy (More episodes here) and Newton's Apple (How cool is Ted Nugent describing the physics of audio feeback?).

• Square One TV – What Sesame Street was to letters, and The Electric Company was to words, Square One TV was to mathematics. The original format was a half-hour show, which consisted of 20 minutes of skits and music videos, all teaching various math concepts, and then close with Mathnet, a Dragnet parody in which detectives solved crimes with math.

• Hulu's News and Information Section – Hulu has some great classic documentary series available, including the recently-added Cosmos, NOVA and Scientific American Frontiers. Fancast's Documentary Section has a few choice series, as well, but Hulu seems to have the edge here.

• Science Documentaries and More Science Documentaries! – Those two links comprise an amazing history of educational science television, from The Ascent of Man and Cosmos, all the way up to more modern series like The Universe and Evolve. You can lose whole days in these playlists alone!


BOOKS AND MAGAZINES:

• 1970s and 1980s Computer Magazines – Ever since my dad first bought an old Commodore PET 2001 home from the office for the weekend (this was back in 1978), I've been hooked on computers. At the time, the only real resource I could understand and learn from was Creative Computing Magazine, but by the early 1980s, I turned to COMPUTE! and COMPUTE!'s Gazette as my computer magazines of choice.

Most of the magazines in this archive walked you through even the most difficult computing concepts in an easy-to-understand manner, so these are great resources for learning about the basics of programming (regardless of your programming language of choice), as are . . .

• 1970s and 1980s Computer Books – If you've ever wanted a glimpse of what the early days of home computer culture were like, you won't find a better place than this site! Besides the often-excellent lessons in programming, resources like the Best of Creative Computing volume 1, volume 2 and volume 3 provided news, made predictions about the future of computers (sometimes accurate, sometimes humorously inaccurate), and just plain provided fun.

Even if you learned BASIC, but have moved on to another programming language (or even a web development language), translating something from books like the popular BASIC Computer Games, More BASIC Computer Games and Big Computer Games can prove to be an interesting and enlightening personal challenge.

• How To Develop A Super-Power Memory – Do you think this site would even exist if I had never read this book? Along with Harry Lorayne's more recent memory books, this is a must-read for anyone who wants to begin training their memory for work, school or fun!

• The Richest Man in Babylon – This is a classic work on how to handle money. What has made it such a classic? The lessons in handling money are written as a series of parable that take place in Ancient Babylon. It's a fun read, and drives home its point without ever becoming tiresome. I still do my best to live up to all its rules, and can honestly say it's changed my financial outlook and prospects.

This general philosophy of this older book on personal finance meshes well with a more recent work (originally written in 1981 and revised in 1996), called . . .

• The Ultimate Resource II: People, Materials, and Environment – It would be easy to say that this is simply a book on economics, but it examines economics with a philosophy that gives one a sense of hope for the future. It examines many commonly-held economic myths, destroys them, and replaces them with a sense of optimism.

Before the author passed away in 1998, the PRC Forum taped an interview with Julian Simon that can give you a brief overview of his economic philosophies. While you're checking that interview out, you may want to examine several other economic documentaries with a similar philosophy that are posted in the same YouTube channel.

Those are some of my favorite learning resources from days past that I still keep close to me. How about you? What books, videos or other resources strongly influenced your education and that you still treasure? Let me know about them in the comments!

If you have more than 50 posts on the Magic Cafe, and you enjoyed last year's Free tricks from Leo Boudreau post, you'll be glad to know that Leo Boudreau has just posted another great original free effect!

This new one is called Lie To Me. The effect is that one of four objects is chosen by a spectator, who also decides whether to be a truth-teller or a liar. You then ask them yes-or-no questions about various combinations of the objects. Not only can you divine the object after these questions, but also whether the person was lying or telling the truth!

Beyond the trick itself, the thinking behind the method and the care put into the presentation make this a great effect. The ensuing Cafe discussion about other presentational angles are also worth a read.

While there are calculations involved in the method, they can be eliminated with the use of standard memory techniques, complimented with the use of binary mnemonics. They will also come in handy for many of Leo Boudreau's effects in last year's post, as well.

For those who don't have enough posts to get in and see Lie To Me, there is a similar effect in the book Puzzler's Tribute: A Feast For The Mind (a published tribute to Martin Gardner), called Cubist Magic. As it happens the full effect can be found online for free in Google Books' limited preview of Puzzler's Tribute. Here's the first page, the second page, the third page and the accompanying graphic needed for the routine.

If you like these effects, I definitely recommend going through this post, last year's post (if possible) and purchasing Mr. Boudreau's books to see the wide variety of amazing and clean effects he's created.

This post is a day earlier than usual. Why? It's Pi Day, which also means it's Grey Matters Blogiversary! It was 4 years ago today that I started Grey Matters.

Here's the very first post. Take a look at the first, second and third blogiversary posts, and you'll get a good idea of just how much this site has grown since the beginning.

In the past year alone, I've added the constantly-updated How Many Xs Can You Name in Y Minutes list, which is far and away the most popular feature of this site. There was also this blogs' Pi-versary (posted when the blog was exactly 3.14159265 years old). The most unusual thing that happened this year, though, would have to be the temporary disappearance of my MemoryEffects list, which was due to a misunderstanding (details available at the link).

Among the new features added in the past year were the Grey Matters Miro Channel, and Werner Miller's Age Square. As a matter of fact, Age Square and my iPhone Knight's Tour proved to be popular entries as iPhone features.

Let's not forget that today is Pi Day, as well. How should you celebrate? Well, you could have a drink with Pi-ice cubes, make a Pi necklace, and even watch the giant Pi drop.

Just earlier this week, House Resolution 224 officially passed the US House of Representatives by a vote of 391 to 10, with 30 abstaining, which officially supported the designation of Pi Day (More details on this act here).

However you celebrate, and, indeed, whatever you celebrate today, make it a great day!

Yes, it's time for the March edition of Quick Snippets!

• Do you need to memorize a speech? Whether you have a month, a day or only a minute, Speech-Time's How to Memorize Speeches can show you how to do so effectively. I like the discussion of the principles involved, which makes this article much more useful.

• Closely related to memorizing speeches is Memorizing Shakespeare. This is a brief blog, largely to promote the author's products that help memorize their lines in various Shakespeare plays. However, the tips offered are good techniques for memorizing lines for any production, and are worth reading.

• Last November, I posted an article about learning Japanese. To aid you in a similar challenge, Skritter has been created to help you to read Chinese. Even better, it's also set up to help you learn how to write in Chinese, as well! Instead of flashcards, you learn through writing them in the interface. It's still in Beta, so it's free for now. I wouldn't mind seeing a site like this for Japanese.

• Earlier this year, I taught the Dommsday method as a way of memorizing the 2009 calendar. Back in 2005, Ricky Spears posted another simple method for memorizing the calendar. The article itself covers the 2006 calendar, but it can be easily adapted for 2009. Looking at the 2009 calendar provided by CalendarLabs.com (which has proven a good source for free calendar-related items), you can quickly see the numbers you need to remember for 2009 are: 41, 15, 37, 52, 64, 16. As mentioned in the original blog post, good images for these numbers can be found by looking through Wikipedia's integer category.

In January 2008, I offered several links to mental math tricks. I've gathered a few more over the past months, and I thought it was time to share them with you.

I'll start with an original mental math feat I've never seen anywhere before. You have someone name a repeating decimal, for example, 0.5757575757, and you can instantly name a fraction, like 19/33 for our example, which will give that repeating decimal. Blake O'Hare's Nerd Paradise teaches this feat in his Math Funbox: Decimal to Fraction post. The rest of his posts should interest most regular Grey Matters readers, as well.

I've mentioned Wild About Math! before, and the site is still worth checking out. They offer 4 great mental math feats, each taught in a “mathcast”, which are videos done in a sort of whiteboard style. Most of them involve the quick multiplication of 2- and 3-digit numbers, yet are suprisingly easy.

While I'm thinking about Wild About Math!, they also have one post that contains 9 different mental math tricks which should be in any math geek's arsenal. This post, for obvious reasons, has been copied and posted on several different blogs, but I think the originator should be given the proper due.

I'll round out this post with gummy stuff's Vedic Math page. There are plenty of links containing the 16 principles of “Vedic Math”, but these have the clearest examples and explanations I've seen for how and why these principles work. Only 10 of the 16 tutorials on this page were completed, however, so the rest you'll have to find out about for yourself.

Does anyone else besides me think it's curious that all of these pages use lists of lengths that are square numbers?

In keeping with the theme of money from my previous post, and the overall theme of this blog of having fun while learning, I'm going to post some fun educational cartoons from the 1950s that are about money and capitalism, which have only recently become available on YouTube (since my previous post, as a matter of fact).

First, I'd like to try and get you into the mindset of the 1950s as it related to money, investing and capitalism. Anyone who was in their 30s in the 1950s still had the Great Depression fresh in their minds, due to growing up with its effects for most of their life. Although there were other factors involved, the stock market's role in the Great Depression meant that the market was seen as scary, frightening and complicated thing.

In the 1920s, though, the stock market was largely unregulated and there was little transparency of any company's financial situation. During the Great Depression itself, Roosevelt had created the Securities and Exchange Commission (SEC), so government oversight and requirements about financial closures had come into being. Confidence rose in the market after these acts (and trials of several SEC rule violators), but many who had been in the market before had decided that investing wasn't worth it anymore. Through the 1930s and 40s, investing was at a sort of standstill.

After World War II, when American GIs were returning home (interestingly, to ticker tape parades), there was a new optimism about the country's future. The soldiers were coming home, marrying their sweethearts, buying homes, and raising children.

Brokers saw an opportunity to bring many new investors in the market. Having learned their lesson in the depression, and with the help of the new market regulations, they put forth an effort to educate the public, as well, so as to have not only more investors, but better educated investors, as well. Charles Merill, of Merill-Lynch, began an own your share of America attitude, which included such actions as opening brokerage houses in the suburbs, offering investment classes for women, and even setting up a display in Grand Central Station to give the average person a closer look at the stock market.

The three cartoons below were part of a similar effort by the Alfred P. Sloan Foundation, which focuses largely on encouraging education in science, technology and economics. The Sloan Foundation set up an agreement with Warner Bros., in which they would underwrite cartoons that would educate the general public about business, investing and the market place. The three cartoons that produced as part of this effort are posted below. Fortunately, Warner Bros. was able to keep their style and humor and place while still teaching these economic concepts.

By Word of Mouse: The first of these cartoons, made in 1954, tells the story of a European mouse who visits America, and is astounded by the sheer volume of economic activity there. This mouse and his American cousin then consult a mouse professor at a university to learn more about it.


Heir-Conditioned: The second cartoon of this project, made in 1955, focused on Sylvester the Cat (the only regular Warner Bros. character to appear in all 3 cartoon shorts), and his inheritance of a fortune from his late owner. As Elmer Fudd tries to educate Sylvester on the benefits of investing, Sylvester and his alley cat friends try to get the money so they can go have fun spending it on themselves.



Yankee Dood It: The third and final cartoon from 1956 is probably the most recognizable of the 3. It's a take off of the classic Elves and the Shoemaker story, with elf king Elmer Fudd trying to get his shoemaking elves back home by teaching the shoemaker how a modern business should be run.

With the economy in the condition it's in, knowing about money will come in handy more and more. Here are a few quick mental math tricks that can help you get a better overall idea of some financial questions.

First, let's look a pay. It's common to know how much you make per hour, but when you try to figure it with hours per week, and account for vacations, it all seems to complicated to work out. The shortcut, however, is startlingly simple. Double your hourly pay, and then just multiply by 1,000 (just adding 3 zeroes will work in many cases), and you'll get your yearly pay! Do you make $9/hour? $9 doubled is $18, and multiplying by 1,000 gives us $18,000/year! $21.75 per hour? That's $43,500/year.

It's not hard to do this mentally, with a little practice. That same calculation also works backwards, as long as you work it backwards. If someone is making $250,000/year, get rid of the 3 zeroes at the end first, giving us $250, and the divide by 2, giving us $125/hour as the equivalent. These calculations assume that you work 40 hours a week, and take 2 weeks for vacation.

If you want to take these calculations to extreme, just for fun, Salary Money can take this all the way down to how much you make per second!

There is a similar quick mental math trick you can do for weekly expenditures. In this case, you simply halve your weekly amount, and then multiply by 100. $20/week? Half of $20 is $10, and multiplying by 100 gives $1,000/year. I usually spend about $75 on groceries each week, so I can easily see that $3,750 is what I can expect spend on groceries this year. As above, this assumes that normal expenditures don't apply during a two-week vacation period.

Probably one of the toughest things to calculate is interest. First, you have to determine if the interest involved is simple, continuous or compound, and you must understand the differences.

However, there is one well-known rule that makes it easy to calculate how long it will take you to double your money at a given interest rate. It's called the Rule of 72 (although there are those who believe it should be updated to the Rule of 76). All you have to do is divide 72 by the interest rate in question, and you'll get the approximate time required to double your money. Since 72 is so easily divisible by so many numbers (such as 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36), this calculation usually isn't difficult.

Dividing 72 by 5 might seem hard, but you consider that all you have to do is double the number and then divide by 10. 72 doubled is 144, and dividing by 10 gives us about 14.4 years to double at 5% annual interest. So, at 4% interest, your money would take roughly 18 years (72/4) to double. At 3%, though, it would take roughly 24 years (72/3) to double! If you've ever wondered why there's so much talk over seemingly small interest rate changes, now you know.

Note that, due to the complex nature of money, these calculations are all approximate. However, they're also time tested, so you can quickly get a general picture of your economic situations with these handy monetary mental math tricks.