150 Digits of Pi Quiz

Published on Thursday, January 29, 2009 in , , , , , , ,

PiSporcle has gone and done it!

They've taken my well known love of timed quizzes and my love of all things Pi and combined them.

Just yesterday, they posted their 150 digits of Pi timed quiz. You have 5 minutes to type in those 150 digits after the decimal point. As an added challenge, you're only allowed to make 5 mistakes in your typing. Once you've made your 5th mistake, the quiz ends. This is also done to prevent people from quickly just typing the numbers 0-9 quickly to fill each post.

For anyone who has learned and practiced my 400 Digits of Pi feat, this should be no problem. To go through it, just think to yourself A1, then type the digits at A1, think A2, and so on. When you get to A10, start on the next row with B1, and continue from there. 150 digits will take you up to the first 2 digits of D8.

As of this writing, more than 14,300 people have taken the quiz, but fewer than 90 people have managed to get all 150 right, so you can be part of a very select group!

At first, try and push yourself to just get all 150 digits. The next time you take it, try and get all 150 digits with no mistakes. Finally, just for fun, if you do manage to type in 140 digits or so, and you find yourself with around 2 minutes left, try and finish with exactly 1 minute and 46 seconds left. That way, you'll honestly be able to say you completed the pi quiz in exactly 3:14!

In the comments section, they've already had requests for similar quizzes about e an i. While e could be interesting, an i quiz might prove too difficult to be fun (or to program, for that matter).


More Calendar Fun

Published on Sunday, January 25, 2009 in , , , , , , , ,

Dafne Cholet's Calendar* photoHave you been practicing the Day For Any Date in 2009 feat from last Sunday? This Sunday, we're going to push your mental skills with the calendar again, but in a different way!

Don't worry. We'll start slow. Our first project is an inexpensive calendar. How inexpensive? It's only 12 cents! This cheap perpetual calendar can be set up to show any calendar date. So where's the mental challenge? It's displayed in binary format! If you have Java installed, the web page will also show you how to properly display the current date.

Once you get the hang of reading binary dates, you can also try figuring out to read a free binary clock! If you need help, Wikipedia's Binary Clock page can help.

Moving to the next piece, we have a feat that will really help you come across as a calendar master! This is Walter Gibson's Magic Calendar (continues on another page). You hand someone a calendar page, and ask them to mark one day in each week of the calendar without you seeing their choices. You then ask how many Mondays were marked off, as well as how many Tuesdays, Wednesdays, and so on. When the spectator is done answering, you instantly give the total of the selected days!

We'll round this column out with some calendar puzzles courtesy of Ken Duisenberg:

1) Can you figure out a simple way to create magic squares starting from dates selected from a calendar?
2) Here's 3 puzzles in one, all of them concerning “calendar fractions”.
3) How is Ken's 6-block calendar constructed?

Those links should challenge you, and get you to look at the humble calendar in a whole new way. Of course, if you're interested in changing perspectives about the calendar, here's plenty of thought-provoking articles that will do just that.


Gilbreath Principle

Published on Thursday, January 22, 2009 in , , , , ,

A thing of terrifying beautyOne of my most embarrassing moments in my life concerns a time I was teaching a trick based on the Gilbreath Principles.

On one of my very first visits to Gary Darwin's Midnight Magic Club in Las Vegas, I joined a group of people who were performing and teaching tricks to each other, with each person taking a turn. When it got to be my turn, I performed and taught Terry LaGerould's Best Bet Yet from his book, A Magical Baker's Dozen. When it came time to teach it, I also tried to make sure everyone at the table understood the Gilbreath Principle behind it, as well. I finished, and stayed until others had taken their turn.

Later that same night, I had the honor of talking to Gary Darwin. I introduced myself, and mentioned my interests in mathematical effects. When Gary heard this, he asked one of the attendees to come over. I recognized this man as one of the people from the table where I had been earlier. Gary Darwin says to me, "You should get to know this gentleman, as he also likes mathematical card effects. Scott, meet Norman Gilbreath!"

Yep, I had actually spent part of one night teaching the Gilbreath Principle to Norman Gilbreath. I apologized for not recognizing him and knowing who he was, and he was very gracious. He replied, "That's OK. By the way, you taught the principle very well."

Moving on from my embarrassment, I'd like to work on just that - teaching the Gilbreath principle. When seen in action, the effects can be mind boggling, so it seems like it would be difficult to understand. Fortunately, Bitwise Magazine spends time not only explaining the Gilbreath Principle, but doing so in an extremely clear and understandable manner. In Martin Gardner's book, Aha! Insight/Gotcha, he teaches a simple trick that helps make clear the power of Gilbreath Principle when presented to an audience.

You'll often hear references to the First and Second Gilbreath Principles. The second, as it turned out, is actually a generalization of the first. To understand each of these versions, and the differences, Card Colm makes the differences clear in two magic effects, The First Norman Invasion and The Second Norman Invasion.

Colm Mulcahy has also written up a Gilbreath-based effect called An ESPeriment with Cards (PDF), applying the principle to Zener Cards.

These are some excellent resources for starting to explore this fascinating principle. This is one of those principles that, even when you know you're using it, it will still amaze you!


Day For Any Date in 2009

Published on Sunday, January 18, 2009 in , , , ,

May 1st on CalendarAs we get 2009 going, it seems like a good time to challenge your brain with the calendar.

What better way to begin the year by memorizing the entire 2009 calendar? Don't worry, it's easier than it sounds. You can easily figure out on which day of the week any 2009 date falls by using the Doomsday method. Briefly, the last day of February, regardless of whether it falls on the 28th or 29th, is considered to be the Doomsday for that year. 2009's Doomsday is Saturday.

Using that information, it's not hard to work out any day of the week for February (February 2nd? Feb. 28th is Saturday, and so is February 7th. 5 days before February 7th is the 2nd, and 5 days before Saturday is Monday, so Feb. 2nd will be a Monday), but what about the rest of the year? The other even months are easy to remember, as 4/4 (April 4th), 6/6 (June 6th), 8/8 (August 8th), 10/10 (October 10th), and 12/12 (December 12th) will also always fall on the same day of the week as the last day of February, the Doomsday.

How about the odd-numbered months? 5/9 (May 9th) and 9/5 (September 5th) will also always fall on the Doomsday, as will 7/11 (July 11th) and 11/7 (November 7th). So, if you can remember the phrase, "I'm working 9 to 5 at the 7-11", you can remember the odd months with ease.

For the first month, January 3rd will also fall on the doomsday, unless it's a leap year, in which case you use January 4th (2009 isn't a leap year, so it's January 3rd). If you think of the last day of February as the imaginary date March 0th (Hey, it does come just before March 1st!), then you have the month of March all set, as well.

So, using the knowledge that 2009's doomsday is Saturday, how do we work out the day of the week for a given date? Let's use the date from the icon in the upper left of this post, May 1st. On what day of the week does May 1st, 2009 fall? May is the 5th month, and we know (thanks to the mnemonic "working 9 to 5 at the 7-11") that 5/9 will be a Saturday (the Doomsday for 2009). One week before that is May 2nd, which will also be a Saturday. Obviously, then, May 1st, 2009 must be a Friday!

How about Christmas 2009? 12/12 is a Saturday, and therefore so is the 26th (exactly 2 weeks later). Dec, 25, 2009, then, must fall on a Friday! July 4th is even easier - 7/11 is a Saturday, and July 4th is exactly one week before that! Can you work out on what day of the week US federal and state income taxes must be filed (April 15, 2009)? Or, if you live in the US, on what day of the week does your state's Tax Freedom Day fall?

If you want to practice this, using the Day For Any Date (Mentalist Challenge) page is a great way to do this. Just click the Get Random Date button, change the year to 2009, and the figure out that date before clicking the Show button.

Another way to check your answers for any given date would be isotropic.org's date page, although you might learn too much about any given date for your comfort (Feel free to work out the Discordian Calendar for yourself, however!).

On the go with your iPhone? You can use the iPhone Perpetual Calendar to verify dates for yourself, or use it as proof of your perfect 2009 recall when you show off your newfound ability to someone else.

Granted, it may not be as impressive as learning the full Day of the Week For Any Date Feat, but this simple method can still impress your friends, family and neighbors.

Oh, and if you already do the full version of the feat, here's a bonus tip: When you get the key number for a given year, just add 3 to it, translate that number (mod 7) into a day of the week, and you'll have the Doomsday for that year! 1978? That year has a key number of 6, to which we add 3, giving us 9. 9 mod 7 is 2, and a 2 means Tuesday, so 1978's Doomsday is Tuesday! 1936? That's 3 (the key number for 1936) plus 3, resulting in 6, and since 6 mod 7 equals 6, that 6 means Saturday is the Doomsday for 1936 (Just remember that January 4th, 1936 is a Saturday in that leap year, not January 3rd).


Free Goodies From Made To Stick

Published on Thursday, January 15, 2009 in , , , , ,

Made To Stick by Chip and Dan HeathNot too long ago, I posted a series about applying the principles from the book Made To Stick in magic. If you missed it here are all the original posts:

Memorable Magic: Simplicity
Memorable Magic: The Unexpected
Memorable Magic: Concreteness
Memorable Magic: Credibility
Memorable Magic: Emotions
Memorable Magic: Stories
Memorable Magic: Wrap-Up

The authors, Chip and Dan Heath, have made several free goodies available that will help make just about anything more memorable, including 3 PDFs and 2 podcasts!

The PDFs include tips on making PowerPoint/KeyNote presentations memorable, making teaching lessons memorable, and a simple reminder of the principles mentioned above (simplicity, unexpectedness, concreteness, credibility, emotions and stories).

One of the podcasts concerns “branding yourself” in any field where you need to break out from the crowd and grab attention, and the other concerns urban legends, and the principles they use that can help you create your own ideas that spread on their own merits.

To obtain them, you do need to provide them with information such as your name, postal code and e-mail address, but the information is only used to send you a free newsletter, and is not provided to any other parties. The newsletter itself is only published 6-8 times a year, so it's not very intrusive.

In addition to the principles in the linked posts above, these free goodies are surprisingly valuable not only for improving your performances, but also marketing those same performances. Considering that you're getting these files in addition to a free newsletter that's also about making anything memorable, it's quite a good deal all around!


Online Visions New Issue

Published on Sunday, January 11, 2009 in , , , , ,

Symbol Pattern Square IIOnline Visions has just posted their newest issue, and the In Your Hands section is sure to interest Grey Matters this time around!

Werner Miller returns with ways to expand on Symbol Pattern Square I. The new variations include new ways of dealing, two person variations and patterns.

There's also Oliver Meech's new effect, Google Guessing. This is a pseudo-memory feat that makes it appear as if you had memorized the top site results for Google's 10,000 top searches! This uses an old approach to create the illusion. This routine is particularly effective if you pay attention to the suggestion at the end about developing progression in the effect by expanding the scope of the effect.

The regular columns are full of great routines and valuable advice, as always. The newest issue of Online Visions is definitely worth a look.


Mental Division With Decimal Precision

Published on Thursday, January 08, 2009 in , ,

Decimal PrecisionHere's a piece I wrote for curiousmath about 2-3 years ago, and I thought I'd post it here, since it would be of interest to Grey Matters readers.

This piece is all about dividing a 2-, 3- or 4-digit number by a 1 digit number, and doing so with decimal precision. When presented, it comes across as much harder than it really is. With a little practice, you can have a very impressive feat under your belt that's ready at a moment's notice.

First, you need to remember all the possible decimal equivalents for each single digit divisor. Most people will already know the first few decimal equivalents:




What are the rest? 5ths are easy, as you simply double the dividend, and place the decimal in front of that number:


With 6th, you already know 3 of the 5 decimals from above:


You simply need to learn just two more 6ths:


7ths have a very unique pattern! Let's start with 1/7:


All you have to do for 7ths is to remember the sequence 142857 (which repeats over and over again). Each 7th will always contain this same sequence, and only the starting point will change!

To find the appropriate starting point, take the dividend and multiply it by 14 (you should be able to do up to 14*6 in your head fairly quickly of course). Find the place in the 142857 sequence closest to this number, and you'll have the appropriate starting place!

Starting again with 1/7, we simply think (1*14=14, so 1/7 starts at the 14, and is thus equal to .142857142857...)

Here's how you figure the rest of the 7ths, with the thought process in parentheses:

2/7 (2*14=28)=.2857142857142857...
3/7 (3*14=42)=.42857142857142857...
4/7 (4*14=56)=.57142857142857...
5/7 (5*14=70)=.7142857142857...
6/7 (6*14=84)=.857142857142857...

Once you see the pattern and practice it, 7ths are very simple.

8ths are also very simple, as they are half-steps in-between the 4ths. Simply multiply the dividend by 125, and place the decimal in front of it:


9ths seem like they should be hard, but all you have to do is repeat the dividend over and over:


Just for reference, 10ths and 11ths aren't hard, and can be done in your head easily, as well.

For 10ths, simply place a decimal in front of the dividend:


For 11ths, you need to know your 9 times table up to 10:


With a little practice, these decimal equivalents will come to mind quickly.

Now for the full feat. To keep things simple, start working with 2 digit numbers.

Have someone choose any 2-digit number and any 1-digit number, and you can announce the result of dividing the larger number by the smaller one. For example, let's say they choose 59 divided by 6.

You should quickly realize that the closest multiple of 6 to 59, without going over, is 54 (6*9). So, the answer is 9 and 5/6ths. Instead of saying it that way, however, you remember 5/6 = 0.833, and so the answer is 9.833.

People see decimals as very complex, so this is very impressive, yet not hard to do.

For 3- and 4-digit numbers, you need to practice working through the division problem from left to right in your head.

Starting with a 3-digit example, let's try 698 divided by 7. Beginning with the leftmost digit, we quickly see that 7 won't go into 6, so we move to the next digit. 7 will go into 69 nine times, so our answer is 90-something. Taking away 63 (7*9), that leaves us with 68 to work with. 7 can go into 68 nine times, as well, so that gives us 99, with 5 as a remainder, or 99 and 5/7ths. Remember the decimal equivalent of 5/7ths? This means you can give the answer as 99.7142857 in short order.

4-digits work the same way, with one extra step, of course. 4732 divided by 6? Let's try it:

4/6=won't work
47/6=7, carrying the 5 (47-42=5), so it's 700 something
53/6=8, carrying the 5 (53-48=5), so it's 780 something
52/6=8, carrying the 4 (52-48=4), so it's 788 and 4/6, or 788 2/3

Translated into decimal form, you say "788.666".

Even if you never get comfortable with 4-digit numbers, dividing 3-digit numbers by 1-digit numbers is still impressive, especially when you can carry it out to many decimal places.

1) Regular practice will help increase your speed. You can get to the point where you can do it as quick as (or possibly even quicker than) a calculator!

2) Fractions seem a more "human" way of giving the answer, as they don't seem as precise (2/3 is much easier to understand than .666..., as 2/3 doesn't go on forever). Stating the answer in decimals is strongly associated with precision, the way a computer would give the answer, so the decimals give a stronger impression of a computer-like (or "Rain Man"-like) skills in math.

3) You'll find that people choose 7 more often than any other number for the 1-digit number, as it seems harder to most people. As you've seen above, not only are 7ths easier to deal with, but the ability to carry the decimal result out to 6, 7 or 8 decimal places with no decernable pattern makes it more impressive, as well!


Yet Again Still More Quick Snippets

Published on Sunday, January 04, 2009 in , , , ,

LinksIt's a new year, so I'm using this snippets entry to bring you up to date on various “Grey Matters”.

Mental Case has been updated to version 1.4.3 and now syncs with your iPhone! Among other new features, it now also supports FlashCard Exchange, as well.

• Speaking of the iPhone and memorizing, iCue Memory is a new piece of software that helps you improve your speed at memorization specifically in three tasks (links go to video explanations of each): Memorizing playing cards, memorizing numbers and memorizing binary numbers (long strings of 1s and 0s). It can be used for fun, as well as being helpful for anyone training to for a national or world memory championship. It's a sort of high-tech mobile version of the World Memory Challenge. At this writing, the full version is available for only $2.99 at the iTunes App Store, and there's also a free Lite version.

• Another free online flashcard site has been developed, and it's called Cramberry. It's relatively new, but there are already plenty of features, and more features are already in the works. It's free to use, so check it out and see what you think!

• The people who developed Agilix Backpack, software developed to download and study entire college and university courses offline, have posted a complete free memory course online. While it's only a one-page brief course, it is surprisingly thorough! There are even some unusual systems here, such as the Calendar Peg System, which gives you distinct images for remembering things by month.

• I've updated some old Grey Matters favorites myself. First, for Miro users, I've updated the Grey Matters Videos Miro Channel. A link to this channel will always be available over in the site feed widget in the rightmost column, as well. The new entries in include the full animated Disney cartoon Donald in Mathemagic Land, and Bob Miller's demonstration of a 25-card memory feat he teaches in his book, BAM! The Complete Course to the Borrowed and Memorized Deck.

• Also, my well-known Memory Effects document has also been updated for the new year, as well. There new entries are largely from the resources made accessible through Google's Magazine Archives, but other new resources have been added, as well.

That's all for now! As always, enjoy exploring these resources, and share any additional links in the comments of this post.


More Free Martin Gardner Goodies!

Published on Thursday, January 01, 2009 in , , , ,

Martin GardnerHappy New Year!

If you enjoyed my recent post about the Martin Gardner documentary, here's some more free Martin Gardner treats!

The first goodie was originally a giveaway at the Gathering For Garnder 3, back in 1998, and was inspired by the work of the late Jerry Andrus. Check out the video of these three dragons:

Believe it or not, these dragons are made entirely out of paper and glue (or tape) and have absolutely no moving parts! Thanks to the people at Thinkfun (originally known as Binary Arts) and Grand Illusions, you can get your own set of dragons free, and try out the illusion yourself! The Green Dragon, the Red Dragon and the Blue Dragon are all available as PDF files ready to download, print and construct. It's amazing how popular these 3 little dragons have become!

Illusions often bring to mind magic tricks, and Martin Gardner was no slouch in this area, either. Courtesy of Numericana.com, we have Martin Gardner's prediction effect, Paths To God, which employs the Kruskal Count. This is just 1 of 4 effects that were originally published by Martin Gardner in the May 1999 issue of GAMES Magazine.

Our final free goodie is a book titled The Mathemagician and Pied Puzzler: A Collection in Tribute to Martin Gardner. It was made available as a free PDF by the Gathering for Gardner Group back in 2000, even though they only first published it in 1999!

It's filled with not only interesting articles about Martin Gardner and his life, but about the topics he covered in his books and columns. It's one thing to read his original columns, and quite another to see the new directions in which they've been taken! If you love puzzles, science, math, magic, or any combination of the above, take some time to read and enjoy the many people who have been inspired by this amazing author.