tag:blogger.com,1999:blog-114399442017-04-22T05:17:27.694-07:00Grey Matters: BlogTrain and strain your brain to entertain!Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.comBlogger1010125tag:blogger.com,1999:blog-11439944.post-79256460346431098122017-04-16T11:00:00.000-07:002017-04-16T11:09:13.708-07:00Monty 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-13804848734106331042017-04-09T08:00:00.000-07:002017-04-09T09:33:21.479-07:00Out 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-23043187937874613922017-04-02T08:00:00.000-07:002017-04-02T08:03:13.248-07:00Leapfrog 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.com0tag:blogger.com,1999:blog-11439944.post-29854692194465769972017-03-17T20:15:00.000-07:002017-03-17T20:18:43.827-07:003 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-56026544875175060382017-03-14T08:45:00.000-07:002017-03-14T08:45:04.280-07:00Grey 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.com1tag:blogger.com,1999:blog-11439944.post-41663987431245415162015-10-29T19:00:00.000-07:002015-10-29T19:00:03.510-07:00Leapfrog 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-5298631841940138482015-10-23T16:00:00.000-07:002015-10-24T09:24:57.870-07:00Leapfrog 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-77531835596130345352015-05-10T21:15:00.000-07:002015-05-10T21:15:00.446-07:00Simple 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-3147352228386651542015-04-20T12:00:00.000-07:002015-04-20T12:00:05.268-07:00Cheryl'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-32054856110501321762015-03-29T12:00:00.000-07:002015-03-29T12:00:07.926-07:00Estimating 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-48087302881019803932015-03-14T09:26:00.000-07:002015-03-14T09:30:08.585-07:00Grey 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-8344518300738864882015-03-08T11:29:00.003-07:002015-03-09T20:27:21.696-07:00Estimating 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.com0tag:blogger.com,1999:blog-11439944.post-29089483994499297912015-02-22T12:15:00.000-08:002015-02-25T22:11:30.231-08:00Review: 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.com0tag:blogger.com,1999:blog-11439944.post-18157253463276643122015-02-15T20:00:00.000-08:002015-02-15T20:00:03.314-08:00Still More Quick SnippetsFebruary'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 Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-49168203401018724512015-02-08T20:35:00.000-08:002015-02-08T20:35:00.501-08:00Estimating Compound InterestA recent question on the Mathematics StackExchange about mentally the compound interest formula caught my attention.
It got me thinking about good ways to work out a good mental estimate of compound interest.
Part of what makes it so tricky, is that compound interest doesn't work in a straight line, like much of the math with which we're familiar. Compound interest builds on itself Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-7774587387465216092015-02-01T10:30:00.000-08:002015-02-01T10:34:28.843-08:00Cards and DicePresh 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, Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com1tag:blogger.com,1999:blog-11439944.post-88820405764463016942015-01-18T20:45:00.000-08:002015-01-18T20:45:00.775-08:00Even More Quick SnippetsThe first snippets of 2015 are ready!
This time around, I have some clever and fun approaches to math to share. I think you'll be surprised by them, even (or especially) if you don't usually like math.
• This January marks the 28th anniversary of Square One TV, an educational program that taught math with the use of skits, songs, and other fun approaches. While it's not on TV anymore, YouTube Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-53768890657692268072015-01-04T09:45:00.000-08:002015-01-04T16:29:02.762-08:00Day & Moon Phase For Any Date in 2015Happy New Year!
With a new calendar year, you deserve a couple of new calendar feats to go with it. In this post, you'll learn how to quickly give the day of the week AND the moon phase for any date in 2015.
Even better, both of these feats are much easier than they sound!
DAY OF THE WEEK FOR ANY DATE IN 2015: The method to do this is quite simple, and is known as the Doomsday method, Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com2tag:blogger.com,1999:blog-11439944.post-12174690046868001962014-12-28T08:15:00.000-08:002014-12-28T08:15:00.872-08:00Calendar Calculation Made SimpleAs we wrap up the year, it's natural for thoughts to turn to the calendar.
Yes, I've talked about calendar calculation many times before, but I'm always on the lookout for better methods and better teaching. MindYourDecision.com's Presh Talwalkar, whom you may remember from last week's post, is back this week with some great calendar calculation lessons!
Let's face it, calendar calculation can Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-92049136396878235832014-12-21T12:00:00.000-08:002014-12-21T12:00:01.847-08:0012 Days of ChristmasNote: This post first appeared on Grey Matters in 2007. Since then, I've made it a sort of annual tradition to post it every December, with the occasional update. Enjoy!
Since the focus of this blog is largely math and memory feats, it probably won't be a surprise to learn that my favorite Christmas carol is The 12 Days of Christmas. After all, it's got a long list and it's full of numbers!
On Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-19248675705892257392014-12-14T12:00:00.001-08:002014-12-14T12:00:06.334-08:00Calculate Cube Roots of Perfect Cubes In Your Head!Imagine having someone think of a number from 1 to 100, having them cube the number using a calculator, telling you only the result, and you're able to calculate the cube root of their result (the original number they put in the calculator)!
Learning to work out cube roots of perfect cube is an impressive feat, but it's far less difficult than it appears.
We'll get right to the method, taught Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-66146045836275635342014-12-07T12:00:00.000-08:002014-12-07T12:00:02.040-08:00Numbers GameI apologize for not posting the past 2 Sundays, but my internet connection was down.
Grey Matters is back this week, however, with some Sunday afternoon football...postgame conference, anyway. How does this relate to math or memory? Read on!
In the November 30 Texans vs. Titans game, Texan player Ryan Fitzpatrick threw 358 yards for 6 touchdowns, setting a record for the franchise.
You'd thinkPi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-89173349494975740422014-11-16T20:00:00.000-08:002014-11-16T20:00:04.131-08:00Even More Quick SnippetsSorry about missing a post last week. It turned out to be a busier weekend for me than I originally planned.
I'm back this week, and I've brought plenty of snippets with me to make up for the missing post!
• Back in September, in DataGenetics' Grid Puzzle post, an intriguing puzzle was posed: Imagine there is a grid of squares. You draw a line connecting one intersection to another intersectionPi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-57376795068361969482014-11-02T21:00:00.000-08:002014-11-02T21:00:37.908-08:00Prime MatesI've wanted to write about factoring numbers in your head for a while, but never really had a good approach to analyze and discuss.
Recently, I've come across some strategies that mesh well with what I've discussed before on this site. Learning to factor a number in your head can be tricky, but it can be done.
BASICS: Starting from a given number between 1 and 10,000, you're only going to testPi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com0tag:blogger.com,1999:blog-11439944.post-72206889323846639622014-10-26T20:30:00.000-07:002014-10-26T20:30:01.012-07:00Calculate Powers of 2 In Your Head!Earlier this year, I posted about calculating powers of e in your head, as well as powers of Pi.
This time around, I thought I'd pass on a method for calculating powers of a much more humble number: 2. It sounds difficult, but it's much easier than you may think!
BASICS: For 20 up to 210, you'll memorize precise answers. For answers to 211 and higher integer powers, you'll be estimating the Pi Guyhttp://www.blogger.com/profile/09760001560356969164noreply@blogger.com2