tag:blogger.com,1999:blog-114399442022-01-22T07:29:59.085-08:00Grey Matters: BlogTrain and strain your brain to entertain!Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.comBlogger1022125tag:blogger.com,1999:blog-11439944.post-76319252003200682282017-09-17T09:00:00.000-07:002017-09-17T09:38:26.342-07:00Which is Greater: a^b or b^a?Here's an interesting mental math challenge. Given two different positive real numbers, which we'll call a and b, which is greater, ab or ba? If you're able to calculate both exponents mentally, such as 23 vs 32, then that's probably the simplest way to go. What happens if one or both exponential expressions are too hard to mentally calculate?
To solve this, we'll need to find a general rule. Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-30230406924603820142017-09-10T17:00:00.000-07:002017-09-12T18:05:39.896-07:00Estimating Square Roots: Improved AccuracyBack about 5 years ago, I taught a simple method for estimating the square roots of non-perfect squares. I recently learned an improvement that makes this far more accurate, and even a little more impressive.
The new approach works well with the original approach I taught. I'll start with a review of the original method I taught, and then I'll delve into the details of the improved method.
Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-61767705196757912412017-08-27T09:40:00.000-07:002017-08-27T09:40:05.998-07:00Yet Again Still More Quick SnippetsI 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 Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-75216573350178839342017-07-28T11:00:00.000-07:002017-07-28T11:03:49.183-07:00Solar Eclipse Mental Feat!On August 21, 2017, there will be a total solar eclipse visible in the United States, which hasn't happened since 2012, and won't happen again until 2024!
It's the perfect time to present an impressive knowledge of the moon, such as being able to estimate the moon phase for any date in 2017! Does learning this feat sound difficult? Surprisingly, it's much easier than you may think.
For 2017 Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-89919262258114553282017-07-09T09:45:00.000-07:002017-07-09T09:45:00.639-07:00Review: Perfectly PossibleMany 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 Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-22345323516228511882017-07-02T09:30:00.000-07:002017-07-02T09:30:35.841-07:00Squaring Numbers from 100-199Over in the Mental Gym, I have a tutorial on squaring numbers, starting with simpler techniques for multiples of 10 and 5, and working up to squaring numbers as large as 125.
Naturally, I always like to see how much farther I can go, especially when I can still keep things relatively simple. With the technique I'll be teaching in this post, if you're comfortable with squaring numbers up to 125, Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-46067156092955570082017-06-25T09:15:00.000-07:002017-06-30T19:03:04.002-07:00Magic, Math and Memory Videos!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 Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-17606671387978199862017-06-11T09:15:00.000-07:002017-06-30T19:04:05.680-07:00Yet Still More Quick SnippetsIt'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 Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-15007197359160411692017-05-28T08:45:00.000-07:002017-06-30T19:06:00.128-07:00Tour the U.S.!
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Starting in Delaware, you must tour the 48 contiguous United States, visiting each state exactly once. Where will you finish?
That's a puzzle from Futility Closet. I'll link directly to it later, so as not to get too far ahead. It's really a puzzle within a puzzle, however.
As anyone who has tried the Knight's Tour knows, moving around with the limitation of Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-1711801668769026002017-05-21T08:30:00.000-07:002017-06-30T19:07:37.905-07:00The Collective Coin CoincidenceThis 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 Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-81001629194891747682017-05-14T08:30:00.000-07:002017-06-30T19:08:43.041-07:00Chinese Remainder Theorem IIBack in January of 2012, I wrote about the Chinese Remainder Theorem. Also, Martin Gardner taught the basics well in his book Aha!: Insight, including a trick where you can determine someone's secretly chosen number between 1 and 100 just from hearing the remainders when divided by 3, 5 and 7. Going over that post again, I've developed a few improvements to this trick that make it seem much more Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-36253376372819887552017-04-30T08:00:00.000-07:002017-06-30T19:15:25.921-07:00Yin-Yang ChallengeFor this post, I'd like to turn to a variation of a classic Henry Dudeney puzzle, from his book Amusements in Mathematics. It can also be found in Martin Gardner's October 1960 Scientific American column, or his book, New Mathematical Diversions, as the 5th puzzle ,“Bisecting Yin and Yang”, in chapter 12, “Nine Problems”.
As you've no doubt guessed, this puzzle involved the yin (dark) yang (Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-79256460346431098122017-04-16T11:00:00.000-07:002017-06-30T19:17:23.959-07:00Monty Hall Dilemma SimulationBlame Marilyn vos Savant. Back in 1990, Craig F. Whitaker of Columbia, Maryland wrote to her with a probability puzzle, and found he'd kicked up a hornet's nest! He asked, “Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-13804848734106331042017-04-09T08:00:00.000-07:002017-06-30T19:19:32.239-07:00Out of ControlWould 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 Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-23043187937874613922017-04-02T08:00:00.000-07:002017-06-30T19:20:58.892-07:00Leapfrog Division V: I've Been Schooled!A little over 4 years ago, I wrote a post inspired by Alexander Craig Aitken's approach to dividing by numbers ending in 9, called Leapfrog Division. It's a remarkably fun and simple technique, so if you haven't already checked it out for yourself, give it a read.
I wrote 3 more posts in that series. Leapfrog Division II dealt with dividing by numbers ending in 1. My last 2 posts before this Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com1tag:blogger.com,1999:blog-11439944.post-29854692194465769972017-03-17T20:15:00.000-07:002017-06-30T19:21:40.096-07:003 Planets and a Rational WarDuels are a classic staple of westerns, but it took Sergio Leone's 1966 film “The Good, The Bad and The Ugly” to immortalize the truel (neologism for a three-way duel) in the popular mind!
Back in 1975, a high school teacher named Walter Koetke took the truel into outer space in a puzzle from the May/June 1975 issue of Creative Computing. I first ran across it in the 1980s, in The Best of Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-56026544875175060382017-03-14T08:45:00.000-07:002017-06-30T19:22:53.148-07:00Grey Matters is Back!Yes, I did take more than an extended break after my 10th blogiversary post, not posting at all in 2016, but with Pi Day coming around again, it seemed like a good time for a return! I probably won't have a regular posting schedule for sometime, as other commitments are keeping me busy, but I promise not to ignore this blog as I have been for about the past 1½ years.
While I've been thinking Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com3tag:blogger.com,1999:blog-11439944.post-41663987431245415162015-10-29T19:00:00.000-07:002017-06-30T19:29:22.542-07:00Leapfrog Division IVWhile I normally do my Leapfrog Division posts about a year apart, I though I'd wrap up this mental division series just 1 week after the previous entry.
In this post, you'll learn to mentally divide by numbers ending in 2!
STARTING POINTS: This is the most advanced technique of all of the Leapfrog Division posts, so you should be familiar with and practice the the previous techniques. Not onlyPi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-5298631841940138482015-10-23T16:00:00.000-07:002017-06-30T19:29:46.455-07:00Leapfrog Division IIIIn 2013, I posted about Leapfrog Division, which was A.C. Aitken's approach for mental division by numbers ending in 9. In 2014, I built on this method with Leapfrog Division II, an approach for mentally dividing by numbers ending in 1.
It's 2015, so it's time for another update to the Leapfrog Division technique. This time, you'll learn the method for mental division by numbers ending in 8!
Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com2tag:blogger.com,1999:blog-11439944.post-77531835596130345352015-05-10T21:15:00.000-07:002017-06-30T19:30:51.574-07:00Simple math? Not so simpleJust over a month ago, TheWeek.com posted an article titled The simple math problem that blows apart the NSA's surveillance justifications. It concerned the probability of detecting terrorists, when you have a near-perfect terrorist-detecting machine.
It turns out that the simple math isn't so simple.
Let's start with the question itself:Suppose one out of every million people is a terrorist (Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com1tag:blogger.com,1999:blog-11439944.post-3147352228386651542015-04-20T12:00:00.000-07:002017-06-30T19:31:53.482-07:00Cheryl's Birthday Round-UpThanks to a Singapore math exam, the internet is being driven crazy by the biggest problem in birthdays since the birthday paradox!
Here's the problem: Albert and Bernard want to know Cheryl's birthday, but Cheryl isn't willing to tell them directly. Instead, she gives them a list of 10 possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, and August Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com1tag:blogger.com,1999:blog-11439944.post-32054856110501321762015-03-29T12:00:00.000-07:002017-06-30T19:33:43.309-07:00Estimating Roots3 years ago, I posted a tutorial about estimating square roots of non-perfect squares, including tips and tricks.
Since then, I've wondered if there was a general formula for estimating other roots, such as cube roots, fourth roots, and so on. Reddit user InveighsiveAd informed me that there's a simple general formula very similar to the method I've taught for square roots! Once you pick up the Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com1tag:blogger.com,1999:blog-11439944.post-48087302881019803932015-03-14T09:26:00.000-07:002017-06-30T19:34:38.242-07:00Grey Matters' 10th Blogiversary!Ever since I started this blog, I've been waiting for this day. I started Grey Matters on 3/14/05, specifically with the goal of having its 10th blogiversary on the ultimate Pi Day: 3/14/15!
Yes, it's also Einstein's birthday, but since it's a special blogiversary for me, this post will be all about my favorite posts from over the past 10 years. Quick side note: This also happens to be my Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com3tag:blogger.com,1999:blog-11439944.post-8344518300738864882015-03-08T11:29:00.003-07:002017-07-02T09:35:28.318-07:00Estimating Compound Interest Without a Calculator
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Something about the challenging nature of calculating compound interest keeps drawing me back, as in my Mental Financial Wizard post and my recent Estimating Compound Interest post. Or, maybe I'm just greedy.
In either case, here's yet another way to get a good estimate of interest compounded over time. It's a little tricky to do in your head alone, so you'll Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com1tag:blogger.com,1999:blog-11439944.post-29089483994499297912015-02-22T12:15:00.000-08:002017-07-02T09:36:52.938-07:00Review: The Best Mental Math TricksTwo years ago, about this time, I reviewed Presh Talwalkar's previous Infinite Tower book.
Since then, not only has Presh not only been hard at work on his Mind Your Decisions blog, but also another book guaranteed to interest Grey Matters readers! This newest book is titled The Best Mental Math Tricks. Presh was kind enough to send me an advance copy, so I'll share my review in this post.
Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com1