I apologize for the irregular posting over the past few months. I've had to deal with some personal issues (don't worry, everything is fine!). The good news is that, with this entry, everything should start returning to normal.

Having said that, let's dive into August's snippets!

• James Grime and Katie Steckles made a video about a seemingly simple game:



First, if it's on Grey Matters, you know all is not always what it seems. Long-time fans of Grey Matters may remember this when I described it under the name Wythoff's Nim. It winds up having some very interesting math behind it. James went on to make a solo video explaining the mathematics behind it in more detail:



• We can't ignore Katie Steckles' game video after all that! Katie teaches 2 games (or does she?). The first one involves numbered fishes, and the second one involves cards with stars and moons on them:



It's a little bit surprising that these are actually the same game! Back in June's snippets, there was a multiplication version of this. Like this and Scam School's game of 15, they all go back to Tic-Tac-Toe. If you want to see some other interesting variations of this same idea, read Martin Gardner's Jam, Hot, and Other Games column.

• There's usually more than one way to use your knowledge. In my tutorial about mental division, I teach a simple method for mentally dividing the numbers 1 through 6 by 7. Presenting it as an exacting feat of mental division is one thing. How else could you present it? Take a look at how Scam School presents the same feat:



If you watch the full explanation, you'll notice another difference between the way I teach it and the way Brian teaches it. He puts emphasis on the last digit, which works well for performing the feat this way. In my version, I teach how to work out the first few digits, as you'll need those first when giving the answer verbally. This is a good lesson in the benefits of changing your point of view!

It's now been a few months since Grey Matters was back, so now it's time to bring Quick Snippets back!

This time around, we have plenty of mathy goodness, so it's best to just jump right in!

• Besides the Clay Institute's famous selection of Millennium Problems, which will make you a millionaire if you prove or disprove any one of them, there's a lesser known set, known as John Conway's $1,000 problems. Not long ago, the 5th conjecture, which claims that working through a certain procedure (described in the link an video below) will always end in a prime, was disproven by physicist James Davis. The Numberphile video below details the problem and James Davis' counterexample:



For more about the million-dollar Millennium Problems, watch the BBC's Horizon documentary, "A Mathematical Mystery Tour of Unsolved Mathematical Problems."

• Speaking of fun discoveries in recreational mathematics, check out Allan William Johnson's "Magic Square of Squares", discovered back in 1990, and just recently posted over at Futility Closet.

• James Grimes introduces us to a different sort of "Square of Squares", in his latest Numberphile video, "Squared Squares". The challenge here is to make a perfect square shape from a set of smaller square shapes:



• Presh Talwalkar, of Mind Your Decisions, posted an interesting puzzle recently. It's titled, "The Race To 32,768. Game Theory Puzzle". Read the article up to the point where you're challenged to work it out yourself, or watch the video below up to the 2:12 mark, and try and figure it out for yourself. If you get stuck, try going over my Scam School Teaches the Game of 15 post for inspiration.



• Late last month, mathematical video maker 3Blue1Brown posted a must-watch video on the visualization of all possible Pythagorean triples. Even if you remember everything from you math classes about Pythagorean triples, this video is both eye-popping and an eye opener:



• We'll wrap this set of Quick Snippets up with help from Mathologer. His videos are always interesting, but his latest one is one of those unusual approaches to math that makes you appreciate its beauty. This video is titled, "Gauss's magic shoelace area formula and its calculus companion", and it teaches an simple but unusual method for working out the area of any polygon that doesn't intersect itself. The host even goes on to show how this approach can be adapted in calculus to work out the area contained by curves!

February's snippets are here. Thanks to some old favorites, and some new favorites, we have a good selection to share with you this month.

• Just 2 days ago was Friday the 13th, so MindYourDecision.com's Presh Talwalkar decided it was a good time to teach how to divide by 13 in your head:



This is a handy technique, and you really only need to learn how to do this up to 12, which isn't too difficult.

If you'd like to learn similar tricks for dividing by 2 through 15, check out the Instant Decimalization of Common Fractions video.

• Like me, Presh seems to have plenty of fun with mental math techniques. Here's a mathematical magic trick of sorts, in which you apparently divine a crossed out digit:



Are you curious as to why this works? Presh has a detailed proof on his blog.

For those who are worried that just multiplying by 9 may seem too obvious, scroll down to the end of my Age Guessing: Looking at the Roots post. The section entitled “Sneakier ways of getting to a multiple of 9” has several useful and clever ways to disguise the method.

• IFLScience just posted 21 GIFs That Explain Mathematical Concepts. More than a few of these will be familiar to regular Grey Matters readers. Many are from LucasVB's tumblr gallery, and others are from videos I've shared over the years. Nevertheless, it's nice having all these in one place.

• Steve Sobek, who has a wide variety of videos on his YouTube channel, has recently made several mental math-related videos that are worth checking out. For example, here's his video teaching a trick for mentally subtracting large numbers:



You can find more of his mental math tricks at AmysFlashcards.com.

The first snippets of 2015 are ready!

This time around, I have some clever and fun approaches to math to share. I think you'll be surprised by them, even (or especially) if you don't usually like math.

• This January marks the 28th anniversary of Square One TV, an educational program that taught math with the use of skits, songs, and other fun approaches. While it's not on TV anymore, YouTube user Anton Spivack has been making full episodes available. I've been gathering them together in playlists by season if you want to experience this show for yourself:

Square One TV: Season 1
Square One TV: Season 2
Square One TV: Season 3
Square One TV: Season 4
Square One TV: Season 5
Square One TV: Mathnet

• While I'm thinking about YouTube channels, check out Funza Academy's site, as well as their YouTube channel. Being interested in math shortcuts, I especially enjoy their Math Concepts and Tricks playlist, as it teaches some impressive math shortcuts, including rapidly multiplying any 2-digit numbers together!

• Magic Cafe user RedDevil, author of the RedDevil Mentalism blog, recently shared a great tip for my Day One routine. Day One is my approach to minimizing the work required for the classic Day of the Week For Any Date feat.

RedDevil took this one step further by pointing out that you don't need to remember all the year information I teach in there. Instead, you can only memorize just the leap years, and move 1, 2, or 3 days forward as you go 1, 2, or 3 years ahead respectively.

If you have Day One, you'll understand this. If you don't have Day One, it's still available for only $9.99! If you're a member of the Magic Cafe with at least 50 qualifying posts, you can read his tip in more detail in RedDevil's original thread.

Yes, the snippets are short and sweet this month, but there's still plenty to explore in these links if you take the time to learn and enjoy them!

Since I've changed my posting schedule, I seem to have neglected my monthly snippet posts!

Not to worry, however, as we're kicking off September with a good round-up of different takes on some of my favorite mental feats.

• One of the longest-standing tutorials on Grey Matters is the classic Knight's Tour. The traditional version usually happens on an 8 by 8 chessboard. What about other irregular, non-rectangular shapes?

Over at the Wolfram Blog, Jon McLoone explored that question using Mathematica in his post Solving the Knight’s Tour on and off the Chess Board. If you're interested in the programming and the math, there's plenty in this article. Even if you don't care for all the math and programming, the variety of boards with successful Knight's Tours is amazing and amusing. Who knew Pac-Man could play the Knight's Tour so well?

• Over in the Mental Gym, I have a full tutorial on squaring 2-digit numbers in your head. I've often wanted to move on to squaring 3-digit numbers, but never really found a method that suited me. However, I recently ran across a video tutorial from Mind Math called Mental Math Trick to Square 3-digit Numbers for Faster Calculation. It breaks the problem up into 2 steps, working with the hundreds digit followed by the remaining 2 digits as a group. If you're used to squaring 2-digit numbers, this method isn't difficult to learn and adapt:



• Back in March, I wrote a post about calculating powers of e in your head. At the time, I was unaware of Colin Beveridge's post, Secrets of the Mathematical Ninja: Estimating Powers of e, which featured a quicker, yet less accurate estimate.

After seeing my post, Colin took it upon himself to develop an improved method, which he posted as Powers of e Revisited: Secrets of the Mathematical Ninja. When you're done exploring those posts, check out the rest of Colin's Blog!

• Another favorite blog topic of mine is calendars. Beyond the standard day of the week for any date feat, there's plenty of interesting mathematical patterns and shortcuts waiting to be discovered in the calendar. One of the best round-ups I've found on the internet is P.K. Srinivasan's Number Fun with A Calendar (PDF version). Besides the PDF version, there's a zipped .DOC version and even a video demonstration of some of the topics from the book:



That's all for this month. I hope you found these enjoyable and useful!

June's snippets are ready!

This month, we're going back to some favorite topics, and provide some updates and new approaches.

• Let's start the snippets with our old friend Nim. The Puzzles.com site features a few Nim-based challenges. The Classic Nim challenge shouldn't pose any difficulty for regular Grey Matters readers.

Square Nim is a bit different. At first glance, it might seem to be identical to Chocolate Nim, but there are important differences to which you need to pay attention.

Circle Nim is a bit of a double challenge. First, you may need to try and figure it out. Second, the solution is images-only. Once you realize that different pairs of images are referring to games involving odd or even number starting points, it shouldn't be too hard to understand.

• Check out the Vanishing Leprechaun trick in the following video:



These are what are known as geometric vanishes, and can be explored further in places such as Archimedes' Laboratory and the Games column in the June 1989 issue of OMNI Magazine.

Mathematician Donald Knuth put his own spin on these by using the format to compose a poem called Disappearances. If you'd like to see just how challenging it is to compose a poem in geometric vanish form, you can try making your own in Mariano Tomatis' Magic Poems Editor.

• Back in July 2011, I wrote a post about hyperthymesia, a condition in which details about every day of one's life are remembered vividly. That post included a 60 Minutes report about several people with hyperthymesia, including Taxi star Marilu Henner. Earlier this year, 60 Minutes returned to the topic with a new story dubbed Memory Wizards. This updated report is definitely worth a look!

• If you're comfortable squaring 2-digit numbers, as taught in the Mental Gym, and you think you're ready to move on to squaring 3-digit numbers, try this startlingly simple technique from Mind Math:



That's all for June's snippets. I hope you have fun exploring them!

March's snippets are ready!

This time around, we've got a round up of math designed to amaze and surprise you!

• @LucasVB is the designer behind some of the most amazing math-related graphics I've ever seen. You can see some of his amazing work at his tumblr site, and even more at his Wikimedia Commons gallery. Even if you don't understand the mathematics or physics behind any given diagram, they're still enjoyable, and may even prompt your curiosity.

• Just recently, @preshtalwalkar of the Mind Your Decisions blog posted an examination of the classic four knights puzzle. Read the post up to the answer, and then try playing it yourself in my 2011 post on the same puzzle. It's a challenging puzzle, until the simple principle behind it becomes clear. Once you understand the principle behind the four knights puzzle, see if you can use it to work out the method for the Penny Star Puzzle.

• Our old friend @CardColm is back with more math-based playing-card sneakiness! In his newest Postage Stamp Issue post, he presents a sneaky puzzle that you can almost always win. After shuffling cards, the challenge is to cut off a portion of cards, and see how many of the numbers from 1 to 30 you can make using just the values of those cards. It seems very fair and above-board, but the math behind it allows you to win almost every time!

• About a year ago, @Lifehacker had a post about measuring your feet and hands to measure distances accurately without needing a ruler, which was based on this quota.com reply. To take this a step farther, I recently learned you can even judge far-off distances and even angles using just your fist and thumb! This is one of those tricks that can be handy and even impressive at the right moment.

That's all for this month's snippets, but it's plenty to explore and discover, so have fun with these links!

For January's snippets, I'm featuring an unusual mix.

This time around, I've got 3 different things for you: Math, memory...and Macs?!?

• Numberphile took a breather from their usual number videos to do something a bit different. They interviewed UC Berkeley professor Edward Frenkel with the question, “Why do people hate mathematics?” It's an interesting topic and well worth your time:



• In the video above, they talk about the important roles of math teachers. Longtime Grey Matters readers know that I'm not just a big proponent of memorizing, but rather memorizing along with understanding. Above and beyond great sites that aid in mathematical understanding, such as BetterExplained and Plus magazine, there's also an excellent free ebook called Nix The Trix. It's aimed at students who are great with shortcuts, but never took the time to understand the foundations of what those tricks are actually doing. It can help teachers undo the damage by showing how to teach the actual mathematical basis, which is also a great help in understanding when to use the math tricks.

• Almost just in time for this month's snippets, Reddit featured an interesting and popular thread asking, “What are some things worth memorizing?” Yes, of course, there are the usual array of sarcastic and silly answers, but if you take the time to wade through some of the roughly 12,000 comments (at this writing), there are some great ideas. I won't rob you of the joy of discovery, especially as the reply you most enjoy may not even exist yet as I write this!

• If you've ever memorized something with the help of spaced learning, where the concept you're trying to memorize is reinforced 3 times at spaced intervals, you know how powerful it can be. There's now an online web service called MemStash which help you do this almost automatically. You save things you wish to remember by highlighting them in an online page, and then clicking a special MemStash bookmarklet. After that, they'll send you 3 reminders at spaced intervals, which can help you recall what you saved!

• OK, this last snippet isn't really along the usual Grey Matters topics, but I thought it would be fun to sneak it in. 30 years ago this week, the Apple Macintosh computer first came on the market. During Super Bowl XVIII on January 22, 1984, they aired their now-classic 1984 ad, announcing the upcoming release of the Macintosh on January 24th. The lesser-known January 24, 1984 introduction of the Macintosh has also been preserved on video:



That's all for this month's snippets. I hope you enjoy them!

It's time for December's snippets.

I've noticed the simpler, more direct skills prove popular, so this month will feature more skills you can learn, use, and demonstrate quickly.

• We'll start off with a simple skill: figuring out your longitude by looking at the night sky, assuming you're in the northern hemisphere. First, you need to find the star Polaris, which is why you need to be in the northern hemisphere for this to work. If you don't know how to do that, my post from September about learning to find various stars will be of help here.

The next step is to determine how many degrees above the horizon Polaris is located. This post from One Minute Astronomer shows how to measure the approximate angle using only your hands! This is a fun skill to demonstrate and teach, as well.

• From arrangements of stars, we come down to earth to arrangements of numbers. Michael Daniels, over at mindmagician.org, has posted a new magic square generator which can handle any integer from 34 through 9999. If you're curious about the method used to create these, you can learn more about it in his ebook, Mostly Perfect. You can even download free excerpts from the book for free!

• One of my favorite feats, the calendar feat, is taught in a very simple and direct version in the following video from Mister Numbers:



If you're not already familiar with Mister Numbers' work on YouTube, check out his channel, and see some of his other work in number patterns. He details more about this calendar procedure in his Kindle ebook, Amazing Calendar Math Magic.

This method has it roots in John Conway's Doomsday Method, and I show how to build on this basis in a simple way to handle almost any year in my ebook, Day One.

• Also from Mister Numbers, here's an impressive video that quickly teaches kids, or anyone really, to be able to handle multiplying the numbers from 1 to 40, and beyond, by themselves in a simple way:



I take advantage of this same basic pattern in my lessons on extracting the roots of perfect squares over in the Mental Gym, so this is a very useful pattern to know!

I hope you've found something quick an interesting. Have any quick and interesting math tips or patterns of your own? I'd love to hear about them in the comments!

November's snippets are ready, and they're chock full of some amazing and fun ways to get involved with math!

• If you enjoyed the recent Arthur Benjamin posts from MAA, It's All About The Benjamin and Fibonacci Meets Dr. Benjamin, you should know they have plenty more!

This includes Dr. Benjamin on how to square 2- and 3-digit numbers in your head (below) and an interesting little side story about how he discovered this principle on his own, even before learning algebra!



Among the other interesting goodies on their YouTube channel is James Tanton's Curriculum Inspirations, which feature challenging math puzzles. James Tanton helps you get started on these puzzles, and then encourages you to solve them on your own.

• Vi Hart, a longtime Grey Matteras favorite, has released a new video titled How I Feel About Logarithms. It's an intuitive and holistic look at logarithms that is probably quite different from any approach to the topic that you've seen before. Compare it to, say, the more linear (but still intuitive) approach used in BetterExplained.com's Using Logs In The Real World post, or Steve Kelly's Logarithms, explained.



• A while back, there was a company which produced a DVD series titled Total Breeze Mathematics. Their videos on memory and math shortcuts, which they made available for free on YouTube, were visual and very clear. Their company website and videos quickly disappeared, but fortunately there were those who managed to save the videos and have since reposted them. I've gathered them in their original order, and put them in a YouTube playlist, so you can enjoy them once again.



There are some parts missing, though. There was a 3-minute section on multiplying vertically and crosswise in one video. This can be replaced by viewing the Math Tutor videos on multiplying any 2 digit numbers, multiplying 3 digits by 1 digit, multiplying 3 digits by 2 digits, and multiplying 3 digits by 3 digits.

There's also a section on memorizing numbers that isn't included on the playlist. This free video by Dr. Benjamin on memorizing numbers covers the same technique.

• From 2007-2010, there used to be a magazine called iSquared, which focused on the interesting ways in which mathematics applied to the real world. Originally, it required a subscription, but the entire run of 12 issues has now been made available online for free! This is not only a fun read, but can also help you answer questions such as when you're going to use a particular math technique in the real world!

Last month's snippets focused on the simple and straightforward side of math.

I thought it might be fun to dabble in the other end of the spectrum, so this month's snippets focus on taming the seemingly complex side of math.

• One interesting mental challenge is what are known as Fermi estimates. These are estimates which are seemingly done with little or no information, yet give an accurate estimate to the nearest power of 10. The folks at TED-Ed produced the following video which explains the concept in more detail:



Learning how to do this can be a little tricky, as you really have to learn as you go. One of the best online tutorials I've run across as of this writing is this FermiQuestions.com tutorial. The more you learn, the better equipped you'll be to answer the sample questions they give at their website.

There's also a great book titled How Many Licks? that focuses on teaching you how to develop your Fermi estimation skills clearly and simply.

• If you enjoyed Vi Hart's video on dragons from August, you'll be glad to know she's produced two more videos in the same series. The second one in the series is called “Dragon Dungeons”:



...and the third in the series is called “Dragon Scales”:



• Speaking of dragons and other mathematical monsters, the Data Genetics blog has just posted an interesting tutorial on how to escape a monster (using calculus). Ideally, you'll have a basic understanding of calculus to understand what is going on in this fun article. Even if you don't, the article is still readable, and you get a good understanding of how the real world relates to the needed calculus.

September's snippets are ready!

These mathematical snippets are all designed in intrigue your curiosity while being simple and straightforward.

• Although it seems to be an unusual source for math information, Business Insider recently published an article titled 7 Animated GIFs That Will Make You Instantly Understand Trigonometry. It's a great article, because it doesn't claim to be any more or less than what it is - just clear, informative animations. If you like these, imgur.com has a more complete gallery you may enjoy, as well.

• If you've enjoyed my discussions of the Monty Hall problem in 2006, in 2010, and in 2012, you might enjoy the BBC's article and video on the Monty Hall problem, which they know as the Deal Or No Deal problem.

• I bet that, if I let you choose 5 random integers, I'll be able to find 3 of them that sum to a total which is evenly divisible by 3. What are the odds of me being able to win this bet? The Mind Your Decisions blog takes a look at the surprising answer to this riddle.

• NumberPhile's latest video is oddly amusing. Both James Grime and Brady were sent packages simply labeled Warning: Contains Numbers. The surprise in the package was, well, interesting...

August's snippets are here!

This month, our snippets return to their original roots, and are just a mixed bag of goodies I thought might be of interest to Grey Matters readers.

• While reading Numericana, I learned about a trick dubbed Enigma. The video for the performance is shown below:



The explanation video can be found here. However, Grey Matters readers can use their knowledge of quick binary conversion to speed up the needed calculations!

• Speaking of base conversions, here's an unusual fact. For any integers x and y, x^y in base x will always be 1 followed by y zeros! For example, 6⁸ in base 6 is 1 followed by 8 zeros. Here are the number 2 through 6 raised to the second through the tenth power in Wolfram|Alpha, as an example.

• Futility Closet features a simple way to calculate the probability of any number from 2 to 12, when rolling 2 six-sided dice.

• While playing around with memorizing the speed of light in meters per second (299,792,458 m/s), I was originally using the method of using words of a given length to represent a given number (3-letter word to represent 3, etc.). I noticed that it was taking longer to count the longer words, and thought it might be better to combine that technique with words that rhyme.

In other words, use 9-letter words that rhyme with the word NINE, 8-letter words that rhyme with the word EIGHT, and so on. Using sites like WordHippo and RhymeZone, here's what I came up with for the speed of light: “To recombine, valentine, shorten storyline. Do more alive, soulmate!”

That's all for this month's snippets. I hope you enjoyed them!

July's snippets are ready!

Instead of trying to pick a theme this month, I decided to return to the original purpose of snippets, and just grab random items of interest to Grey Matters readers:

• For those who enjoyed my post on temperature conversion, and the added trick to make it easier, there are simple tricks for other metric conversions, as well.

Nurse Debra Mallory teaches this simple trick for converting pounds to kilograms. Need to work out a metric distance? Here's a quick trick for converting kilometers to miles.

• Last month's snippets focused on hexadecimal numbers. If you want to learn more about those, check out this introduction to hexadecimal numbers. The approach taught on that page is taught quite clearly, so it's easy to grasp.

• Many of the feats I teach on this site require mental arithmetic. If you want to take your mental math to the next level, check out Aaron Maxwell's online book Inner Algebra: How To Do Algebra In Your Head. The whole book is available at that link, and you can also buy a paperback copy on Amazon.

• Just for fun, and completely unrelated to just about anything else I've ever posted on this site, check out this fun and amazing toy, known as Tumble Rings. You can build them yourself, using several sets of key rings. If you're familiar with the toy known as a Jacob's Ladder, you'll recognize the same principle at work here:



That's it for July's snippets. If you have anything you'd like to add, let me hear about it in the comments below!

June's snippets are ready!

This month, we're going to look at computers, and especially the use of hexadecimal notation. It seems scary at first, but with a little understanding, it's easily tamed.

• Regular Grey Matters readers are very familiar with the videos from Numberphile. Here's their excellent introduction to hexadecimal, a system used with computers that help makes software and hardware engineering simpler:



• Speaking of computers and Numberphile, the makers of that channel have a newer video series, dubbed Computerphile. Not surprisingly, it's about all aspects of computers. Below is their newest release, about the early BBC B Microcomputer:



• One thing that often confuses people about hexadecimal is how to quickly recall which letters A through F go with which numbers 10-15. As long as you know that A, B, C, D, E, and F are the 1st, 2nd, 3rd, 4th, 5th, and 6th letters respectively it's actually pretty easy.

For example, what is the equivalent of 13? Simply add the two digits, 1 + 3 = 4, so it must be the 4th letter, which is D! This works for all the digits:

10 = 1 + 0 = 1 = A
11 = 1 + 1 = 2 = B
12 = 1 + 2 = 3 = C
13 = 1 + 3 = 4 = D
14 = 1 + 4 = 5 = E
15 = 1 + 5 = 6 = F.

Those of you in the US are probably spending Mother's Day honoring your mom, so I'll just sneak a wide variety of snippets in today, and you can check them out later.

• Jan Van Koningsveld, along with Robert Fountain, has released a new book that will be of interest to Grey Matters readers, titled, The Mental Calculator's Handbook (Amazon link). If you're not familiar with Jan Van Koningsveld, he was able to identify the day of the week for 78 dates in 1 minute at the World Memoriad. I haven't had a chance to read this book myself yet, but his reputation does suggest the book is worthwhile.

• Starting back in 2008, I kept track of assorted online timed quizzes, the type of quizzes that ask you how many Xs you can name in Y minutes. I found these so fun, useful, and challenging, I even developed my own timed quiz generator, and even posted several original timed quizzes created with it. However, sporcle.com, home to numerous timed quizzes (despite starting out as a sports forecasting site) has gone and outdone this. Not only can you create your own timed quizzes, you can also embed them on your own site now! Find a quiz you like, for example, this landlocked states quiz, go down to the info box below the quiz, and click on Embed Quiz. A pop-up will ask whether you want a wide or narrow window (minimum width is 580 pixels), and you will be given the proper embed code, which can be used in a manner similar to YouTube embed codes.

• For those of you who do the Fitch-Cheney card trick, as taught on Scam School or YouTube, Larry Franklin has posted a simple tutorial on using Excel to practice this routine. As long as you understand your favorite spreadsheet program well enough, it's also not hard to adapt. It will take a while to create in the first place, but once it's ready, it's fairly easy to use.

• One of the most useful card memory feats to learn is memorizing basic blackjack strategy. Over in reddit's LearnUselessTalents section, user Tommy_TSW posted an interesting approach for memorizing this using your favorite video game, movie, or TV characters. Basically, you create a battle scenario for every possible situation, and when the various cards come up, you simply recall the corresponding battle (and result). Depending on the particular variation of blackjack you're playing, basic strategy can change, so you might want to calculate the right moves using basic strategy calculators at places like Wizard of Odds or Online-Casinos.

• Fans of the game Nim will enjoy this online version, playable even on all mobile devices. It's standard Nim, meaning that the last person to remove a card is the winner. It's simple, straightforward, and a good way to practice solo.

Is it time for April's snippets so soon? It only seems soon because March's were so late.

This month, the focus is on resources which help you remember more effectively!

• Just today, Forbes.com posted a wonderful article titled 6 Easy Ways to Remember Someone's Name. In addition to the standard advice, I especially like the tip of asking them a question, so you can take some time to mentally link their name with their face.

If you want to examine this in more detail, I've prepared a YouTube playlist focusing on memorizing names and faces. There's also an excellent book titled How to Remember Names and Faces: How to Develop a Good Memory (originally published in 1943, but the advice is still very sound!). I've also covered various mobile apps that help you practice these techniques.

• Speaking of apps, there's a new free iOS app called Brain Athlete (iTunes link). This focuses on memory-competition feats, including memorizing numbers, word lists, and playing cards. If you've read Joshua Foer's Moonwalking With Einstein and/or read my PAO system post, you should have a good understanding of the basics.

If you get stuck finding a certain person for your PAO system, here are links to lists totaling 10,000 famous people to help. No actions are objects are included, as these need to be developed based on how you imagine each of these famous people.

• Every so often, I run across free memory web apps that I find useful, such as these. The newest one I've found is the Major System Database. It's very simple and direct. You can find words for a given number, the numeric equivalent of a given word, or even break up numbers into small groups and give you mnemonics for each group!

• For Windows users, there's a new free program available, simply titled Memorization Software. It's designed to help you remember various types of texts, such as lyrics, poems, and speeches word for word. The tutorial video below (no audio) gives you an idea of the various approaches used here.



If you like this approach, but don't have a Windows machine (or even if you do!), my web app Verbatim 2 (Video Tutorial link) is also free, works in a similar manner, and runs in any modern browser.

March's snippets may be a little late, but they are here!

This month, I present several classic geometry puzzles. Not all of them are solvable, but they are all interesting.

• Let's start this with one of the longest-running, and apparently most maddening, geometry puzzles in history! James Grime discusses “squaring the circle,” the challenge of constructing a square and a circle with the same area, using only a straight edge and a compass, in a finite number of steps:



Despite the impossibility, you can find many interesting approaches which have been tried over the years.

• One geometry puzzle that recently gained plenty of attention over at Gizmodo is the Winston Freer Tile Puzzle. You can purchase your own here, or a smaller version here, but ponder the seeming impossibility of it first:



• James Tanton posted an interesting geometric challenge which can be presented in stages. The first challenge is just to determine the size of an arc without a protractor. This is usually solved by finding the center first, but can you do it without finding the center?



• Sometimes geometry itself is the puzzle! Jeff Dekofsky, via TedEd, discusses Euclid's puzzling parallel postulate. This is another part of geometry in which the answer will be forever closed off to us, but will remain interesting to ponder:



• I'll wrap March's snippets with Emma Rounds' poem, “Plane Geometry,” a parody of Lewis Carroll's classic “Jabberwocky”:

‘Twas Euclid, and the theorem pi
Did plane and solid in the text,
All parallel were the radii,
And the ang-gulls convex’d.

“Beware the Wentworth-Smith, my son,
And the Loci that vacillate;
Beware the Axiom, and shun
The faithless Postulate.”

He took his Waterman in hand;
Long time the proper proof he sought;
Then rested he by the XYZ
And sat awhile in thought.

And as in inverse thought he sat
A brilliant proof, in lines of flame,
All neat and trim, it came to him,
Tangenting as it came.

“AB, CD,” reflected he–
The Waterman went snicker-snack–
He Q.E.D.-ed, and, proud indeed,
He trapezoided back.

“And hast thou proved the 29th?
Come to my arms, my radius boy!
O good for you! O one point two!”
He rhombused in his joy.

‘Twas Euclid, and the theorem pi
Did plane and solid in the text;
All parallel were the radii,
And the ang-gulls convex’d.

February's snippets are ready!

This month, we're going to delve into math and memory techniques you may have thought were too dificult to develop. With sufficient practice, however, they become powerful additions to your mental toolkit!

• One of the main reasons people want to improve their memory is so they can recall names and faces. This appears difficult to many people, because of the social pressure involved, and the apparent difficulty of connecting a name with the face. As USA Memory Champion Nelson Dellis will show you, it's not as difficult as you may think:



• Another memory skill that comes across as impressive is memorizing the order of a shuffled deck of cards, especially when you can do it in under 60 seconds. Over at the Four-Hour Work Week blog, they have a wonderfully vivid tutorial on memorizing the order of a shuffled deck. They use the easy-to-understand analogy of a software purchase. They start your new brain software off will a trial version they call “Bicycleshop Lite,” where you get the basic process down of memorizing shuffled cards. Once you've done that, you're ready for “Bicycleshop Pro,” which improves your speed. Need some incentive to learn this feat? They're offering $10,000 to the first person who masters it from their tutorial!

• For those who have mastered squaring 2-digit numbers, you might have wondered about taking numbers to higher powers in your head. To do that, you'll need to develop a few other skills. First, you should know the binary equivalents of the numbers 2 through 10 from memory, as well as getting comfortable squaring 3-digit numbers (Video tutorial: Part 1, Part 2, Part 3). Being able to multiply 3-digit numbers by 1-digit numbers is also helpful.

Once you develop those skills, the following video will teach how to bring them together to take any small number to any small power in your head:



• Multiplying numbers by themslves repeatedly is one thing, but how about multiplying any 2 numbers together in your head, up to, say, 7 digits? YouTube user Joesph Alexander has a series of tutorials on how to develop your mental multiplication skills to this level. He starts by teaching how to handle 2- to 4-digit numbers (presentation, explanation), then moves you up to 5-digit numbers (presentation, explanation).

When you're comfortable with doing those type of problems in your head, you're ready to move up to 7-digit numbers (presentation - shown below, explanation):



Try picking just one of these skills to develop, and you just may amaze yourself at how far you can go!

It's time to introduce 2013 to our tradition of snippets!

This month, we'll explore a wide variety of unusual mathematical treats,

• My post about making math visual with Wolfram|Alpha may have been slightly ahead of its time. Wolfram|Alpha's latest blog posts cover the use of equations to draw pictures and the visualization of basic arithmetic problems.

• James Grime is back, and he's covering a topic that is near and dear to his heart. In the video below, he talks about the Enigma machines that the Germans used to code messages during World War II, and the race to break this allegedly unbreakable code:



If you enjoyed this, there is another video detailing the flaw that allowed the Enigma codes to be broken, as well as some tidbits and outtakes.

• I've always encouraged people to learn at least a few amazing feats. Cracked.com is now doing the same thing, albeit with a harsher title, "5 So-Called Signs of Genius That Any Idiot Can Learn." Grey Matters readers will be familiar with many of these, if not all of them. Looking around the web, you can find many examples of such feats, including quickly multiplying by 9, dividing by 9, squaring numbers, and more!

* I'll wind up these snippets with some offbeat links. First, here's a very unusual magic square, featuring resistors that form a magic square if wired in parallel. If your resistor math is a little rusty, here's a short video to get you up to speed.

And because I'm a fan of iOS apps that help you train your brain, check out becomeananny.com's list of 10 iPhone apps that boost brain function.