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!

Many regular Grey Matters readers will be familiar with Michael Daniels' Mind Magician site, where he teaches numerous math and memory feats, such as calculating cube roots in your head instantly. He's recently written a new ebook on the 4-by-4 magic square, titled Perfectly Possible. I found it to be well worth the time and money invested, and wanted to share my thoughts with Grey Matters readers.

This is going to be a difficult review, as I can't give too much away, but I also want to share with you the quality of this method. I'll start with the qualities promoted by Michael Daniels himself:

• Completely impromptu. No set-up, gimmicks, or cribs.
  
• New, improved method - minimal memory and the simplest of calculations.
  
• Suitable for close-up or stage performances.
  
• Produces elegant magic squares.
  
• Can be immediately repeated for different totals.
  
• Includes a browser application that helps you to learn and practice (Internet connection not required).
  

I recently ran across a number of videos I figured would be interesting to regular Grey Matters readers, so I thought I would share them.

We'll start things off with a little math magic, courtesy of Tom London and his appearance on America's Got Talent earlier this week:



Yes, I could explain the method, but I don't want to ruin the fun and the mystery. Just enjoy the magic of the prediction for what it is, since that's how it's meant to be enjoyed.

If you want mathematical explanations, however, I highly recommend checking out PBS Digital Studios' Infinite Series. These are videos on assorted advanced mathematical topics, yet they're taught in a very accessible way. Back in March, I discussed a puzzle which required the understanding of Markov chains to solve. Compare that to their video Can a Chess Piece Explain Markov Chains?, which also happens to employ my favorite chess piece, the knight:



If you enjoy Grey Matters, you may also the work of 4-time USA memory champion Nelson Dellis, who focuses on both mental and physical fitness. He has a series of memory technique videos, as well as interviews with masters of mental skills. Both of these are available on his YouTube channel, as well. As a taste of his skilll, watch his video, Memorizing 28 names in less than 60 seconds!:



Curious how he's able to do that? He explains in the next video in the series, HOW TO // "Memorizing 28 names in less than 60 seconds!".

At this point, I'll wrap things up so you can get started on a potentially mind-expanding journey.

This week, Diamond Jim Tyler demonstrates a new take on an old trick. Regular Grey Matters readers won't be surprised to learn that I like it because it's based on math, and it's very counterintuitive. We'll start with the new video, and then take a closer look at the trick.

This week's Scam School episode is called The Collective Coin Coincidence, and features Diamond Jim Tyler giving not only a good performance, but also a good lesson in improving a routine properly:



Brian mentions that this was an update from a previous Scam School episode. What he doesn't mention is that you have to travel all the way back to 2009 to find it! The original version was called The Coin Trick That Fooled Einstein, and Brian performed it for U.S. Ski Team Olympic gold medalist Jonny Moseley. It's worth taking a look to see how the new version compares with the original.

Brian and Jim kind of rush through the math shortly after the 4:00 mark, but let's take a close look at the math step-by-step:

Start - The other person has an unknown amount of coins. As with any unknown in algebra, we'll assign a variable to it. To represent coins, change or cents, we'll use: c

1 - When you're saying you have as many coins (or cents) as they do, you're saying you have: c

2 - When you're saying you have 3 more coins than they do, the algebraic way to say that is: c + 3

3 - When you're saying you have enough left over to make their number of coins (c) equal 36, that amount is represented by 36 - c, so the total becomes: c + 3 + 36 - c

Take a close look at that final formula. The first c and the last c cancel out, leaving us with 3 + 36 which is 39. If you go through these same steps with the amount of coins (in cents, as it will make everything easier) as opposed to the number of coins, it works out the same way. This is what Diamond Jim Tyler means when he explains that all he's saying is that he has $4.25 (funnily enough, he says that just after the 4:25 mark).

As long as we're considering improvements, I have another unusual use for this routine. If you go back to my Scam School Meets Grey Matters...Still Yet Again! post, I feature the Purloined Objects/How to Catch a Thief! episode of Scam School, which I contributed to the show. It's not a bad routine as taught, but my post includes a tip which originated with magician Stewart James. This tip uses the Coin Coincidence/Trick That Fooled Einstein principle to take the Purloined Objects into the miracle class! I won't tip it here, so as not to ruin your joy of discovery.

Would you believe tha another of my contributions has made it on to Scam School again? It was 2 other recent Scam School submissions that spurred me to restart Grey Matters, so it's looking like that was the right move.

Even if you've seen this week's Scam School episode, you may want to take a look at this post, as I'm going to give a few tips that may make this routine easier to learn.

Let's get started right away with this week's Scam School episode with a trick I dubbed “Out of Control”!



Quick side note: On one hand, I love being promoted as "the genius". On the other hand, I can't help but think of “genius” in this context.

This trick is actually a combination of two idea from two men who have far more a right to be called genius than me. The dealing procedure comes straight from Jim Steinmeyer's routine Remote Control, as published in Invocation #43 and the May 1993 issue of MAGIC Magazine. If you check those sources out, you'll see that not much has changed, as the original involves spelling the word C-O-L-O-R, and using the 9th card.

I combined this trick with a technique from Simon Aronson's “Try The Impossible” called Simon's Flash Speller. It's this part that may help make it easier to work out what you need to do. First, you'll need to quickly work out how many letters are in the name of the turned-up card. Here's the starting point:

• For clubs, remember: 11 letters
• For hearts or spades, remember: 12 letters
• For diamonds, remember: 14 letters

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.

Presh Talwalkar, from the Mind Your Decisions blog, recently shared a fun magic trick.

It involves playing cards and dice. Because it's mathematically based, however, you might just fool yourself while performing it. You'll really only fool yourself if you don't analyze the math behind the trick, which is exactly what we're going to do in this post.

First, let's take a look at Presh's video, from this January 2015 post:



There's quite a bit going on here, so let's break this down piece by piece.

CARDS: Let's ignore the dice for the time being, and focus only on the playing cards. During the dealing process, cards fall into 1 of 2 categories: Either they're dealt individually, or they're in the remainder that is placed on top of the stack. Let's look at each of these categories separately.

DEALT CARDS: We'll start with the first example from the video, where 10 cards were used, 7 of which were dealt. What happens to those 7 cards. The card in position 1 is dealt first, and will obviously become card 10. The card at position 2 will wind up as the 9th card, and so on. Take a look at where these 7 cards end up in the final stack:

Starting position     Ending position
-----------------     ---------------
        1                  10
        2                   9
        3                   8
        4                   7
        5                   6
        6                   5
        7                   4

Starting position     Ending position
-----------------     ---------------
        8                   1
        9                   2
       10                   3

“Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.” - Ron Graham

100 years ago today, Martin Gardner was born. After that, the world would never again be the same.

His life and his legacy are both well represented in David Suzuki's documentary about Martin Gardner, which seems like a good place to start:



As mentioned in the snippets last week, celebrationofmind.org is offering 31 Tricks and Treats in honor of the Martin Gardner centennial! Today's entry features a number of remembrances of his work in the media:

Scientific American — “A Centennial Celebration of Martin Gardner”

Included in the above article is this quiz: “How Well Do You Know Martin Gardner?”

NYT — “Remembering Martin Gardner”

Plus — “Five Martin Gardner eye-openers involving squares and cubes”

BBC — “Martin Gardner, Puzzle Master Extraordinaire”

Guardian — “Can you solve Martin Gardner's best mathematical puzzles?”, Alex Bellos, 21 Oct 2014

Center for Inquiry — “Martin Gardner's 100th Birthday”, Tim Binga

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!

No, I'm not just putting random filler text in the title.

Ever hear the expression “the oldest trick in the book”? In this post, you'll learn about a card trick that certainly qualifies, as it's known to date back at least as far as 1769!

I'll start by letting Brian Brushwood perform and explain his version of this classic routine (YouTube link):



Now, you'll note that Brian teaches this with the words:

MUTUS
NOMEN
DETID
COCIS

BIBLE
ATLAS
GOOSE
THIGH

LIVELY
RHYTHM
MUFFIN
SUPPER
SAVANT

PILLAR
RHYTHM
MUFFIN
CACTUS
SNOOPY

MEACOCK
RODDING
GUFFAWS
TWIZZLE
RHYTHMS
KNUBBLY

Obviously, I'm a big fan of mixing math and fun. It's time to give a little credit to one group that's responsible.

27 years ago this month, Square One TV, a PBS show teaching math with the use of comedy skits, music videos, and guest stars, premiered!

2 years ago, on Square One's 25th anniversary, I posted a tribute to this show, including some of my favorite segments.

At the time I was unable to provide links to complete episodes. Since then, however, several complete episodes have been uploaded to YouTube! Not every episode is available (yet?), but the complete episode guide will give you an idea of what's missing.

I've arranged the full episodes I can find into YouTube playlists by season, with the individual episodes arranged in order of broadcast. The season 1 playlist begins with the original IBM show promo, and then moves on to the very first episode. Here are all the YouTube playlists:

• Season 1
• Season 2
• Season 3
• Season 4
• Season 5

If you watch at least 1 full episode, you'll note that roughly the last third of each episode is dedicated to continuing segment called Mathnet, a sort of mathematical Dragnet parody. Square One TV originally aired Monday throughly Friday each week, so these segments always started a new adventure on Monday, and continued through with the conclusion reached on Friday's episode.

One of the downsides of not having every episode of Square One available is that it's difficult to watch complete runs of the Mathnet adventures. Fortunately, fans have solved that problem by posting 26 of the 30 episodes on YouTube, which you can find in this playlist! The complete Mathnet episode guide, which includes spoilers, can help you catch up on the ones which still aren't available.

I hope you enjoyed this mathematical walk down memory lane. I'll leave you with my favorite segment of Square One TV, a video about how to solve almost any type of problem title “Change Your Point of View”:

It's time for some magic!

Don't worry, there's no complicated sleight-of-hand in these tricks. Not only does math make them easy, but you don't even have to do any math during the routines, since all the math involved has been worked out ahead of time.

I'll start with the simpler of the tricks. In this first one, you have someone think of any hour of the day, and you tap numbers on an analog watch while they silently count up to 20. When they reach 20, they say “Stop!”, and your finger is on the hour they secretly chose!

The method behind this simple trick is described in Futility Closet's On Time post.

At first, the workings may confuse you, but a little experimentation with different numbers will help you understand it. Obviously, this is also true for anyone for whom you perform it, so don't treat this as a big mystery, but rather as a simple and interesting experience.

The basic tapping presentation has a long history in magic. In Martin Gardner's book, Mathematics, Magic and Mystery, there's an entire section on tapping tricks. Thank to Google Books, you can read the entire section online for free, running from page 101 to page 107.

The next trick, courtesy of Card Colm, is a little more involved. You have someone name any card suit, have a regular deck of cards shuffled, and then the number cards (Ace through 9) are removed in the order in which they're found in the deck. You then make an unusual bet based on divisibility of various numbers formed by those cards.

This trick is called the $36 Gamble, and the method is found in Card Colm's post, The Sequence I Desire. Magic: When Divided, No Remainder. Beyond just the mathematical method, there's plenty to explore under the hood of this routine, including Arthur Benjamin's method for determining divisibility by 7, and a very deceptive shuffling method, which appears fair.

If you enjoy the deceptive shuffles discussed in the above post and its links, you also might enjoy Lew Brooks' book Stack Attack, which features the False False Shuffle. The false shuffle and the routines in Stack Attack mix well with the principles behind the $36 Gamble. In my 2006 review of the DVD of the same name by the same author, you can get a better idea of the contents.

Even though I've only linked to 2 tricks here, practicing them, understanding them, and digging in to the variations I've mentioned is more than enough to get your mental gears turning, so have fun exploring them!

I've been having a rough week this week, between being offline for most of Sunday, and dealing with a family emergency the rest of this week.

A little magic always cheers me up, so that's the focus of today's post.

Let's start with a quick opener that's a little different from most Grey Matters fare.

It's this week's episode of Scam School, and there's no math or memory involved. It's just pure, classic sleight-of-hand, developed by Marcus Eddie, who is teaching his SPLINTER! routine:



Now that you're awake and got your splinters removed, let's turn to a little more traditional magic. Not only are playing cards involved, but there is a mathematical basis, so it's probably a little more what you're used to on this site.

Our old friend Card Colm has been experimenting with the Gilbreath Principle. His latest results are in his most recent column, Rosette Shuffling Multiple Piles. It turns out that using a special adaption of the Riffle Shuffle, known as the Rosette Shuffle, it is possible to mix 3 piles of cards together, and still get startlingly predictable results!

I do have to keep this short, due to all I'm dealing with this week, but I hope you found these magical tidbits as enjoyable as I did!

Sometimes, you run across an old idea again and again, and you don't pay much attention to it. Then, someone comes along and shows you a new application of that old principle, and it seems like something completely new!

That's what happened to me recently, when a Magic Café user shared an idea I'm about to share with you.

The basic idea is to have someone choose a number from 1 to 100, then add that number together with the two numbers next to it. If the answer is a two- or three-digit number, then those digits are added together, and this prcoess is repeated until the answer is a one-digit number.

For example, if the total was 157, they would add 1 + 5 + 7 = 13. Since this resulted in a two-digit number, the digits in this answer would be added together again, 1 + 3 = 4. Since 4 is a one-digit number, they'd stop here.

While this seems fair, you can know, even before the number is chosen by the audience, that the total will be 6!

This idea was developed by a Magic Café user whose screen name is Pixelated. But how is this possible?

First, when you ask for a number from 1 to 100, you mention that it's going to be added together with the two numbers next to it. “Next to it” is a deliberately vague phrase that could apply to the two numbers immediately above and below their choice, the two numbers after their choice, or the two numbers before their choice. Until you know their number, you don't know which of these 3 groups you'll need to use.

Once they name a number, you have to ensure that the largest of the 3 is a multiple of 3 (naturally, you should be familiar with all the multiples of 3 from 1 to 100). Pixelated suggests having a row of 3 boxes on a board or piece of paper.

Let's say the person names the number 57. Since 57 is a multiple of 3, you would write it in the rightmost box, and then write the two previous numbers, 55 in the leftmost box, and 56 in the middle box.

What if they'd named 56? You will hopefully recognize that 56 is 1 less than a multiple of 3, so you'd write that in the middle box, so that 57 would naturally go in the rightmost box, and 55 would go in the leftmost box.

If they name 55, you should recognize it as a number that's 1 greater than a multiple of 3 (54, in this case), so you know to write it in the leftmost box, writing 56 in the middle box and 57 in the rightmost box.

Note that, even though the above represents 3 different cases, you always wound up with 55, 56, and 57 in that order. Also the reference to the “two numbers next to the chosen number” makes sense in all 3 cases.

Probably the easiest way to think about the process is to take the chosen number, and count up to the next multiple of 3, unless, of course, the chosen number is already a multiple of 3. Whatever the nearest multiple of 3 is, you think of that as a “ceiling” you cannot go beyond. If someone were to name 47 as their number, you can think: 47...48...Hey! 48 is a multiple of 3...48 has to go in the rightmost box, so 47 must go in the middle. That leaves 46 for the leftmost box.

In short, although you seem to specify how the three consecutive numbers will be chosen, it's your ability to specify the order which gives you control over the total.

Once you have the three numbers, have an audience member add them up as explained above. If the numbers are 55, 56, and 57, they'd add them together to get 168. Next, they'll add 1 + 6 + 8 to get 15, and then add 1 + 5 to get 6.

What about 46 + 47 + 48? That's 141, and 1 + 4 + 1 = 6. No matter which number is chosen, you can always make the resulting 1-digit total equal 6.

WHY DOES THIS WORK?: First, you'll need to be familiar with the concept of digital roots. Here's a quick introduction, or refresher course, on digital roots via video:



Since you're arranging the numbers so that the largest of the 3 numbers is a multiple of 3, that largest number can be written algebraically as 3x (in other words, 3 times some number). The two numbers immediately prior to it can then be described as 3x - 1 and 3x - 2. Add these three numbers together, you get 3x + 3x - 1 + 3x - 2 = 6x - 1 + 3x - 2 = 9x - 3.

As regular Grey Matters fans and mental math wizards already know, Any time you multiply a number by 9, the answer will have a digital root of 9. We can also be sure, then, that 9x - 3 means that the digital root will be equal to 9 - 3, or 6.

VARIATIONS: Using a similar approach, you could always make sure that the multiple of 3 winds up in the middle. In this case, the numbers would be 3x, 3x - 1, and 3x + 1. Added together, this comes out to simple 9x, so the total would have a digital root of 9.

You could also always ensure that the multiple of 3 is the leftmost number, making the numbers turn out to be 3x + 3x + 1 + 3x + 2 = 6x + 1 + 3x + 2 = 9x + 3. In this case, the number would have a digital root of 3.

Besides simply adding up the numbers themselves, you could also have the people add up the individual digits in each number. Going back to our previous example using 55, 56, and 57, you could have them add 5 + 5 + 5 + 6 + 5 + 7 = 15 + 6 + 5 + 7 = 21 + 5 + 7 = 26 + 7 = 33. Of course, 33 becomes 3 + 3 = 6, so it still works out to the same digital root.

THOUGHTS: The simplest presentation, of course, is to somehow show that you predicted the number 6 (or 3, or 9, depending on which approach you used). However, 6 could also mean something besides just a simple number. It might be a page, or a word on a page (the 6th word), or a time on a clock, or a month (6th month is June), or any of a million other possibilities.

As was once said about the laser, this is currently a solution looking for a problem. Somewhere out there is the perfect application for this numeric force. Try playing around with this idea, and let me know in the comments about any ideas you develop!

NOTE: This post originally appeared on Grey Matters back in July 2011. I'm reprinting it today because Werner Miller's mathematical magic really is worth a second look.

Grey Matters favorite Werner Miller is back, and he's brought more of his amazing mathematical wizardry with him!

If you're not already familiar with him, he's a retired mathematics teacher in Germany who has created some of the most original and compelling magic routines I've ever come across. He is the author of several magic books, including Ear-Marked, which is available in the Grey Matters store.

Starting off, we have a couple of good routines that are perfect as promotional tools, since you can print them on your business cards or brochures, and have people perform them for themselves or others without understanding how they work. There's Vive Le Roi!, which includes several variations of routines where you move your finger from card to card, eventually winding up on a predicted card. You can have two people do this together, as they'll be on different cards until the last card.

The other trick along this line is Magic Patchwork, a similar trick with a magic square. He mentions that it was inspired by Pedro Alegria’s El cuadro de colores, but the link given is no longer functioning. Fortunately, it was captured by the web archive. The original is here, with a translation to English via Google Translate available here.

Werner Miller also created a very sneaky calculator trick, called You Push the Button... that seems to be a mathematical trick, but isn't. The use of the calculator helps conceal the outright sneaky method.

Getting back to his specialty of mathematical magic, he offers a great routine with dice. It's called Lined Up, and has two different phases, both of which begin with different-colored dice arranged with the numbers 1 through 6 in numerical order. In Phase 1, you have someone choose a die and turn that number face down. After getting the new total of these dice, you announce which color die has been turned over. Phase 2 is similar, except that you have someone choose a die and turn over every die EXCEPT for the chosen one!

I've saved my favorite for last! It's called Ghost Rider, and uses a chess knight and some file cards. One of the file cards is signed, then mixed into the pile and dealt out into a 3 by 3 square. The spectator then uses the knight and their own free choices to find their own signed card! Part of the principle is taught here on Grey Matters in my Knight Shift post, as mentioned generously in Werner Miller's article. His added touches, however, make this a very impressive trick.

If you like Werner Miller's style and would like to see more, check out the rest of Werner Miller's work here on Grey Matters!

Ever try and solve a puzzle involving physical objects, such as cards, coins, or chips, with your eyes closed?

Despite the challenging conditions, this is just what you're going to learn in today's post! Even better, the solution is ingeniously simple.

Let's get right to the puzzle, shall we? It's presented in its basic puzzle form in this week's episode of Scam School. Before you play the video, grab 10 cards, and try and work out the puzzle before viewing the solution.



Did you solve it on your own? If so, congratulations! Even if you didn't, you should at least have viewed the solution before moving on from this point.

Now, let's try a similar puzzle, but we're going to throw a bit of a curve into it. Add another card to your group of 10, so you now have 11 cards. Just as before, mix them so that some are face-up and some are face-down. You challenge is to separate these 11 cards into 2 groups, so that both groups contain the same number of face-up cards. James Grime has a video puzzle version of this, using chips instead of cards.

Why is this version so much more challenging? There's no way to divide 11 into 2 piles of the same number of cards (or chips, coins, etc.), and that was such an important feature of the previous version.

Once again, try working it out for yourself with cards in hand, before peeking at the solution. When you're ready, here's James Grime with the solution to dealing with odd numbers of objects:



As you see, you need extra information to solve this latter version of the puzzle.

While this does make an interesting puzzle, it can also be turned into a magic trick quite easily. Bob Hummer and Jack Yates created a trick using this principle called Time Will Tell. That version uses 12 pennies, arranged in a clock formation, with some marker identifying one of the pennies as the 12 o'clock position. The performer turns away from the proceedings, and asks the volunteer to turn over any 6 pennies. Without looking at which coins were flipped and without asking any questions, the performer then separates the pennies into 2 groups, both with the same number of heads and tails in each group.

In the original version of the trick, you set up all 12 coins with heads up. As you've seen, however, this really doesn't matter. They can start with any number of heads and tails showing, and have them do several prescribed flips, and you can still separate the groups into 2 sets with equal amounts of heads and tails. Instead of simply having your back to the proceedings, you can even do this over the phone.

Whether you see it as a puzzle or a magic trick, this is a fun exercise to analyze and figure out why it works. If you develop any interesting versions of this routine, I'd love to hear about it in the comments!

It seems like Wener Miller just never stops creating!

He's just released E-Z Square 6, the latest in his series of magic square books!

E-Z Square 6 is a bit different from the previous works. Vols. 1-5 each focused on magic squares with a particular theme, such as birthdays, playing cards, and so on. What makes E-Z Square 6 different is that it goes back and updates and improves the methods and routines from past books.

The first routine is an update on the birthday magic square from E-Z Square 1. You start by putting the spectator's age in the center square of a 5 by 5 grid, and then you fill the remaining squares in a seemingly random way. When you're done, the magic total of every row, column, diangonal, and even several cross patterns, total the year the spectator was born! While the effect is the same, the method is greatly improved. Once you have the first few numbers, which is easy enough, the rest isn't much harder than counting.

The next routine is also an update on a bonus, this time on the magic square routine involving a measuring tape from E-Z Square 2. This one is a little sneakier than most of the routines, so it manages to pack an extra punch.

In E-Z Square 5, Werner Miller focused on magic squares with playing cards. The main problem with one of the feature routines, however, is that the resulting 4 by 4 squares usually featured duplicate numbers. In this volume, Werner Miller shows how to solve that problem once and for all, with a little inspiration from Richard Wiseman's The Grid, which also feature playing card magic squares.

Just when you think you've seen everything, the author goes on to teach other playing card magic square ideas with 3 by 3, 4 by 4, and 5 by 5 grids!

This ebook then rounds out with some fun magic square puzzles. One set of puzzles challenges you to cut an existing magic square into 2 smaller magic squares. The other set of puzzles require you to complete magic squares with only a few numbers with which to start. These very same puzzles, I'm proud to say, were first shared by Werner Miller to Grey Matters readers back in 2010 (puzzle 1, puzzle 2, puzzle 3, puzzle 4, answer to puzzle 4).

Technbically, you don't need the previous volumes to get use of E-Z Square 6, but reading this volume will certainly attract your curiosity about all the other routines.

If you're looking for a different take on magic squares, E-Z Square 6, which is also available in German, provides plenty of great routines and food for thought.

In today's post, we're going to look at a number trick presented by James Grime.

You predict the total of several 4-digit numbers, but don't worry. It's fun, simple, and straightforward.

The following routine is a quick video from the Numberphile series of videos:



The most commonly-used source for this routine is Martin Gardner's book, Mathematics, Magic & Mystery, in which it has the simple title of “Predicting A Sum”. Interestingly, the example number used in the book is 3,845, very close to James Grime's chosen example number, 3,485.

There are many ways to make this routine more impressive. You could employ a secret help, who provides the needed numbers at each step. This takes the heat off of your choices, and makes the whole routine seem fairer, and more impressive.

Another idea to consider is that you don't have to do this as a prediction. Instead, you can do it as a feat of mental arithmetic. Have two people, one of whom is your secret helper, write the numbers down out of your view, and then show the numbers to you briefly. You apparently quickly memorize and calculate the numbers in your head faster than they can do it with a calculator!

With a little creativity, you can think of numerous ways to perform this. Want to seem psychic? Divine the total without ever seeing the numbers (thanks to your secret helper again). You could also perform a routine similar to Scam School's first Pi Day Magic Trick, in which they circle a number, read off the remaining digits, and you can determine the digit or digits they didn't name. Since you know in advance what the total will be, it's all recall with no calculation!

There's a routine with a similar basis called “Alberti's Game”, in which you and two other people randomly choose 3-digit numbers to create 2 multiplication problems, and you're able to predict the sum of the answers to those multiplication problems. Because there's several steps involved, and the answers tend to be large 6-digit numbers, this version seems even more impressive.

How is it done? The answer is below, courtesy of Karl Fulves' Self-Working Number Magic (Amazon link):



Just as with the previous routine, a little creativity, and the possible secret helper, can yield some very amazing results.

Try these out, and if you like them,show your appreciation to Grey Matters by buying Martin Gardner's book, Mathematics, Magic & Mystery and/or Karl Fulves' Self-Working Number Magic. You'll find an amazing variety of number-based magic in both of these mathemagical classics!

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.