tag:blogger.com,1999:blog-11439944Tue, 21 Mar 2023 00:24:25 +0000funmathmemoryvideosself improvementsoftwarememory featsmagicsite featuresproductspuzzlesbooksplaying cardspsychologydownloadscalendarMartin GardnerPimagic squaressnippetsTVmental mathinnumeracyScam SchoolreviewsKnight's TournimmoneypoetrycontroversyNumb3rsSudokuDVDsCarnival of Mathematicsworld recordsavantMath BitesGrey Matters: BlogTrain and strain your brain to entertain!https://headinside.blogspot.com/noreply@blogger.com (Pi Guy)Blogger1022125tag:blogger.com,1999:blog-11439944.post-7631925200320068228Sun, 17 Sep 2017 16:00:00 +00002017-09-17T09:38:26.342-07:00funmathmental mathPiself improvementWhich 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. https://headinside.blogspot.com/2017/09/which-is-greater-ab-or-ba.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-3023040692460382014Mon, 11 Sep 2017 00:00:00 +00002017-09-12T18:05:39.896-07:00funmathmental mathself improvementEstimating 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.
https://headinside.blogspot.com/2017/09/estimating-square-roots-improved.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-6176770519675791241Sun, 27 Aug 2017 16:40:00 +00002017-08-27T09:40:05.998-07:00funmagicMartin Gardnermathmental mathnimplaying cardsScam SchoolsnippetsvideosYet 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 https://headinside.blogspot.com/2017/08/yet-again-still-more-quick-snippets.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-7521657335017883934Fri, 28 Jul 2017 18:00:00 +00002017-07-28T11:03:49.183-07:00funmathmemorymental mathself improvementSolar 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 https://headinside.blogspot.com/2017/07/solar-eclipse-mental-feat.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-8991926225811455328Sun, 09 Jul 2017 16:45:00 +00002017-07-09T09:45:00.639-07:00booksfunmagicmagic squaresmathmental mathreviewsself improvementReview: 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 https://headinside.blogspot.com/2017/07/review-perfectly-possible.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-2234532351622851188Sun, 02 Jul 2017 16:30:00 +00002017-07-02T09:30:35.841-07:00funmathmental mathself improvementSquaring 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, https://headinside.blogspot.com/2017/07/squaring-numbers-from-100-199.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-4606715609295557008Sun, 25 Jun 2017 16:15:00 +00002017-06-30T19:03:04.002-07:00Knight's Tourmagicmathmemorymemory featsself improvementvideosMagic, 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 https://headinside.blogspot.com/2017/06/magic-math-and-memory-videos.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-1760667138797819986Sun, 11 Jun 2017 16:15:00 +00002017-06-30T19:04:05.680-07:00magic squaresmathsnippetsvideosYet 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 https://headinside.blogspot.com/2017/06/yet-still-more-quick-snippets.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-1500719735916041169Sun, 28 May 2017 15:45:00 +00002017-06-30T19:06:00.128-07:00funKnight's Tourpuzzlesself improvementTour 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 https://headinside.blogspot.com/2017/05/tour-us.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-171180166876902600Sun, 21 May 2017 15:30:00 +00002017-06-30T19:07:37.905-07:00funmagicmathmoneypsychologyScam SchoolvideosThe 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 https://headinside.blogspot.com/2017/05/the-collective-coin-coincidence.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-8100162919489174768Sun, 14 May 2017 15:30:00 +00002017-06-30T19:08:43.041-07:00funMartin Gardnermathmental mathChinese 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 https://headinside.blogspot.com/2017/05/chinese-remainder-theorem-ii.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-3625337637281988755Sun, 30 Apr 2017 15:00:00 +00002017-06-30T19:15:25.921-07:00Martin GardnermathPipuzzlesYin-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 (https://headinside.blogspot.com/2017/04/yin-yang-challenge.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-7925646034643109812Sun, 16 Apr 2017 18:00:00 +00002017-06-30T19:17:23.959-07:00funinnumeracymathpuzzlesself improvementsoftwarevideosMonty 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 #https://headinside.blogspot.com/2017/04/monty-hall-dilemma-simulation.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-1380484873410633104Sun, 09 Apr 2017 15:00:00 +00002017-06-30T19:19:32.239-07:00funmagicmathplaying cardsScam SchoolvideosOut 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 https://headinside.blogspot.com/2017/04/out-of-control.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-2304318793787461392Sun, 02 Apr 2017 15:00:00 +00002017-06-30T19:20:58.892-07:00mathmental mathself improvementLeapfrog 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 https://headinside.blogspot.com/2017/04/leapfrog-division-v-ive-been-schooled.htmlnoreply@blogger.com (Pi Guy)1tag:blogger.com,1999:blog-11439944.post-2985469219446576997Sat, 18 Mar 2017 03:15:00 +00002017-06-30T19:21:40.096-07:00funmathpuzzlesvideos3 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 https://headinside.blogspot.com/2017/03/3-planets-and-rational-war.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-5602654487517506038Tue, 14 Mar 2017 15:45:00 +00002017-06-30T19:22:53.148-07:00mathScam Schoolsite featuresvideosGrey 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 https://headinside.blogspot.com/2017/03/grey-matters-is-back.htmlnoreply@blogger.com (Pi Guy)3tag:blogger.com,1999:blog-11439944.post-4166398743124541516Fri, 30 Oct 2015 02:00:00 +00002017-06-30T19:29:22.542-07:00funmathmental mathself improvementLeapfrog 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 onlyhttps://headinside.blogspot.com/2015/10/leapfrog-division-iv.htmlnoreply@blogger.com (Pi Guy)0tag:blogger.com,1999:blog-11439944.post-529863184194013848Fri, 23 Oct 2015 23:00:00 +00002017-06-30T19:29:46.455-07:00funmathmental mathself improvementLeapfrog 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!
https://headinside.blogspot.com/2015/10/leapfrog-division-iii.htmlnoreply@blogger.com (Pi Guy)2tag:blogger.com,1999:blog-11439944.post-7753183559613034535Mon, 11 May 2015 04:15:00 +00002017-06-30T19:30:51.574-07:00controversymathself improvementSimple 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 (https://headinside.blogspot.com/2015/05/simple-math-not-so-simple.htmlnoreply@blogger.com (Pi Guy)1tag:blogger.com,1999:blog-11439944.post-314735222838665154Mon, 20 Apr 2015 19:00:00 +00002017-06-30T19:31:53.482-07:00controversyfunmathpuzzlesself improvementvideosCheryl'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 https://headinside.blogspot.com/2015/04/cheryls-birthday-round-up.htmlnoreply@blogger.com (Pi Guy)1tag:blogger.com,1999:blog-11439944.post-3205485611050132176Sun, 29 Mar 2015 19:00:00 +00002017-06-30T19:33:43.309-07:00funmathmental mathself improvementEstimating 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 https://headinside.blogspot.com/2015/03/estimating-roots.htmlnoreply@blogger.com (Pi Guy)1tag:blogger.com,1999:blog-11439944.post-4808730288101980393Sat, 14 Mar 2015 16:26:00 +00002017-06-30T19:34:38.242-07:00booksfunmagic squaresMartin Gardnermathmemorymemory featsmental mathnimPipuzzlesreviewsself improvementsite featuresGrey 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 https://headinside.blogspot.com/2015/03/grey-matters-10th-blogiversary.htmlnoreply@blogger.com (Pi Guy)3tag:blogger.com,1999:blog-11439944.post-834451830073886488Sun, 08 Mar 2015 18:29:00 +00002017-07-02T09:35:28.318-07:00mathmental mathmoneyself improvementEstimating 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 https://headinside.blogspot.com/2015/03/estimating-compound-interest-without.htmlnoreply@blogger.com (Pi Guy)1tag:blogger.com,1999:blog-11439944.post-2908948399449929791Sun, 22 Feb 2015 20:15:00 +00002017-07-02T09:36:52.938-07:00booksmathmental mathproductsreviewsself improvementReview: 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.
https://headinside.blogspot.com/2015/02/review-best-mental-math-tricks.htmlnoreply@blogger.com (Pi Guy)1