I've added even more challenges to the Mental Gym!

First, there's Instant Insanity (Java required). You've probably seen this puzzle before, and maybe even tried it. This puzzle was originally released around 1900, and was the Rubik's Cube of its day.

The other puzzles are Flash-based, and are also true classics. Try Lights Out, Towers of Hanoi and Planarity.

The last two I've previously discussed on this site. Back in September 2006, I posted several Towers of Hanoi videos. I first mentioned Planarity back in this July 2005 post.

You don't need to worry about being driven completely mad. As with the other off-site tests, I've included links to solution strategies on each of their respective pages.

There have been a few changes being made to the Grey Matters site, so I thought I would keep you posted.

First, the video index is no longer in the rightmost column. Don't worry, it still exists! Under the Video section, you will now see a new link that says Full Video Index. Having the link in one place has already proven to make Grey Matters Videos far more manageable. As before, the Full Video List will constantly be updated as I come across new videos.

Also, there are now more challenges in the Mental Gym! Besides the classic challenges that are taught on this site, these new challenges each include links to off-site solutions. For example, the new 15 Puzzle section (Java required) links to these instructions, as well as my magic square variation.

Besides the 15 puzzle, I've also added Simon (Flash 8 or better required) and Triangular Peg Solitaire (Flash 8 or better required). As time goes on, more challenges will be added.

Finally, over in the Presentation section, I've added the Made To Stick Blog. This blog is run by Chip and Dan Heath, the author of the book of the same name. The basic idea behind the book and the blog is to show what qualities an idea must possess to become easily memorized and passed on. The authors use Malcom Gladwell's concept of "stickiness" to describe the effectiveness of a given idea.

Enjoy, look around, and explore these new sections!

Yes, Carnival of Mathematics fans, it's that time! The 5th Carnival of Mathematics is being hosted over at the Science and Reason blog.

To keep track of the dates and locations of future carnivals, check out the Carnival of Mathematics blog or Blog Carnival's page on the Carnival of Mathematics.

Note that the Carnival of Mathematics will be here on Grey Matters on June 29th!

I've just discovered a new product from Sega Toys, called Brain Trainer. It was originally released in Japan in October 2005, and is just now making its way to U.S. stores. It's so new to the U.S., Sega's Brain Trainer page is still available only in Japanese. However, viewing it with a web translation program can help clear things up (although the word maeno should be cortex).

The Brain Trainer itself looks like a small book. It does bear an unfortunate superficial resemblance to some joke electric shock books. When you open it up, you see basic instructions on the inside cover. On the other side, you see a screen with a 10-digit keypad, as well as buttons marked Menu/Stop, Select, Enter and the power symbol.

There are four activities which can train your brain. In the basic training mode, you're given 100 simple mathematical problems, all involving whole numbers, to solve as quickly as you can. The other three exercises are in the advanced training menu, and include counting verbally from 1 to 120 as fast as you can, focusing on 3 numbers and combining them in various ways, and the memorizing of a 30-digit number. As you exercise, the Brain Trainer keeps track of your progress, which you can view over a 30-day period, or a 1-year period, and both by time taken, and percentage of correct answers. This is a very handy feature for seeing your improvement.

It may sound like Sega is trying to cash in on the brain-training fad started by Nintendo's Brain Age, but the opposite is actually the case. The Brain Trainer was released in 2005, while Brain Age wasn't released until April 2006. However, both are based on the research of Dr. Ryuta Kawashima. While the games are well-known and used here in the U.S., apparently there is an absolute mania for brain-training games in Japan.

Whether or not the benefits are as claimed, I have found it to be fun and enjoyable. It's only $29.95, and is right down the alley of anyone who wants to train and strain their brain to entertain!

Check out the Binary Sensory Card Marking System. A PDF reveals instructional legerdemain for one original labeling system! This system is so ingenious it will let you idenitfy cards at a great distance or even in total darkness! Even better, magician Anders Moden, best known as the inventor of Healed and Sealed Soda, has released this ingenious system completely for free!

If you've read my reviews for Combo, Combo II or Leo Boudreau's books, you'll know how much I appreciate ingenious applications of binary math like this.

If you like this and are looking for other similar things to read, try reading this. If that post is too long, just read the first letter of every word in the second sentence in this post.

The Number 23 is currently in theaters, and as a result, has everyone wondering about the mysterious properties of the number 23.

Yes, there are many unique things about the number 23, but it is far from the only number with such interesting properties. As the Numbers Guy (Carl Bialik) shows, you can find just about as many interesting properties for the number 24, as well.

Are you still not convinced the number 23 is nothing special? Check out What's Special About This Number? and Number Gossip Search/Browse. It's not just whole numbers that have fantastic properties, either, as a trip to Notable Properties of Specific Numbers will prove.

Of course, these sites list numbers with many properties that are interesting mainly to mathematicians. What numbers are interesting to everyday people? You find out at The Secret Lives of Numbers (Java required). This site is the result of a unique project to find the search engine popularity of every number from 1 to 1,000,000. This project ran from December 1997 through January 2002, and provides an interesting view of our world of numbers. For example, you can't find any search engine terms containing 1039, and barely any searches. However, 1040, thanks to being the most prominent US tax form number, returns more terms and far more searches.

Next time, we'll focus on 300 (just kidding).

Philemon Vanderbeck has a new school show called Arithemagic. As you might guess from the name, the focus is on present AND teaching math-based effects.

To get an idea of the show, I suggest checking out the video (play along!) and photo sections.

When performing his school show, Philemon also gives teachers NINE, the lecture notes for the effects taught in the show. These lecture notes are also available for purchase, for $9, of course. As far as the effects themselves go, most of them are classics of mathematical magic, and I've discussed many of them on this site, such as extracting cube roots and fifth roots or the Fibonacci addition trick.

A quick look at the table of contents (PDF) might lead one to think that the notes aren't worth purchasing just because they're classics. However, there are some gems here, such as Werner Miller's Swindle Sudoku, as well as some impressive presentations. NINE has a great presentation for the old 1089 trick. As a matter of fact, NINE and Hidden Numerical Forces are the only two resources I've ever found with engaging presentations for the 1089 trick.

It's great to see math and magic being presented in such a positive and fun way to school students. Teachers and school administrators from Washington state should especially check this site out, but that shouldn't stop others. Anyone interested in mathematical magic should check out this site, as well.

I have good news for the fans of the Carnival of Mathematics! Yes, the 4th Carnival of Mathematics has been posted over at Jason Rosenhouse's EvolutionBlog.