Pages from Mathematical Mizardry

How to Perform Feats of

MATHEMATICAL WIZARDRY

(They’ll Marvel At Your Amazing Number Tricks.

Games, Lightning Calculation, Your Magical Knowledge!

They’ll Think You’re A Genius!)

Books by Harry Lorayne Close-Up Card Magic • Personal Secrets • My Favorite Card Tricks Deck-Sterity • Best of Bill-Fooled The Hundred Dollar Book • Dingle’s Deceptions Reputation-Makers • The Great Divide • Tarbell #7 Rim Shots • Afterthoughts • The Epitome Location The Magic Book • Finger Fantasies • Card Animations The Card Classics of Ken Krenzel • Quantum Leaps Best of Friends, Volume I • Best of Friends, Volume II Star Quality • Trend Setters • Doug Edwards Packs A Wallop The Himber Wallet Book • Personal Collection Lorayne: The Classic Collection • Mathematical Wizardry Apocalypse: Volumes 1 to 4 How To Develop A Super-Power Memory Secrets of Mind Power • Instant Mind Power Miracle Math • Memory Isometrics Course Mental Magnetism Course • Good Memory—Good Student!

Good Memory—Successful Student! • The Memory Book Remembering People (The Key to Success) The Page-A-Minute Memory Book • Memory Makes Money Super Memory—Super Student The MEMORY POWER Package (sold on national television) Audios by Harry Lorayne How To Improve Your Memory • How To Remember Names & Faces Public Speaking Without Fear • The Busy Executive’s Memory Guide Videos by Harry Lorayne Stars of Magic • Magic Video #2 L & L Publishing Video Series

How to Perform Feats of

MATHEMATICAL WIZARDRY (They’ll Marvel At Your Amazing Number Tricks.

Games, Lightning Calculation, Your Magical Knowledge!

They’ll Think You’re A Genius!)

Harry Lorayne Design & Composition by Andrew J. Pinard

Harry Lorayne, Inc. 62 Jane Street New York, NY 10014 U.S.A. www.harrylorayne.com

“How in the world did you know that there are 314 sheep in that flock?”

“Easy. I just counted all the legs and divided by four.”

Copyright © 2006 by Harry Lorayne, Inc. All rights reserved. No part of this publication may be reproduced in any form or by any means, which are now known or to be invented, without the written permission of the author.

For RenĂŠe and Robert . . . Let me count the ways.

CONTENTS

Foreword ................................................................................................. xi

CHAPTER I Ten Eighty Nine ....................................................................................... 3 Lightning Calculation ............................................................................... 6 It All Adds Up .......................................................................................... 9 Roots ......................................................................................................15 The “Missing Digit”.................................................................................18 Pascal’s Triangle & The Card Pyramid ......................................................23 The Fibonacci Series, And More ...............................................................29

CHAPTER II Total The Series, Plus ...............................................................................37 Pleasing Combination ...............................................................................45 Nim ........................................................................................................ 51 The Chicken Or The Egg ..........................................................................54 More Moving Matches .............................................................................57 Ageless ...................................................................................................60 Yellow!....................................................................................................64

CHAPTER III CalendARithmetic ...................................................................................69 CalendARithmetic, Cont’d. .......................................................................73 Stolen From The Calendar ........................................................................76 Matrix ....................................................................................................80 vii

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A Unique Number “Property”..................................................................85 More “Unique” Numbers .........................................................................88 “Unique” Finale ...................................................................................... 91

CHAPTER IV Wanna See A Card Trick? ........................................................................95 Pocket Change .........................................................................................98 Magic Squares ....................................................................................... 100 Magic Squares, Cont’d ........................................................................... 104 4×4 Magic Square Breakthrough?? ......................................................... 109 The To-And-Fro Magic Square ............................................................... 120

CHAPTER V Divided We Fall ..................................................................................... 125 Division Phenomenon ............................................................................ 128 Lucky Number ...................................................................................... 131 Another “Combination” ......................................................................... 134 Additional Adding................................................................................. 139 “Real” Adding ...................................................................................... 142 The Elevator Method ............................................................................. 146

CHAPTER VI Perpetual Calendar ................................................................................ 151 Count On Your Fingers ........................................................................... 154 Money Talks ......................................................................................... 158 Mark On My Boot ................................................................................. 161 Heads Or Tails ....................................................................................... 163 Prove It! ................................................................................................ 165 The Heaviest Digit ................................................................................. 169 Times Nines .......................................................................................... 171

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Contents CHAPTER VII

The Memory Magic Square .................................................................... 175 Taelbpah (Alphabet?) ............................................................................. 180 Odds And Ends ..................................................................................... 182 Is A Puzzlement .................................................................................... 187 To Square.............................................................................................. 192 Square—and Piecemeal ......................................................................... 195 Finally, All’s Square............................................................................... 198 Last Word ............................................................................................. 201

FOREWORD

W

hen I was very young I dreamed of being in show business; I desperately wanted to be an entertainer. Unfortunately, as I grew older, I realized that I couldn’t sing, dance or tell jokes! Still, I craved that attention, wanted to entertain. It was difficult for me since I also happened to be extremely shy. I mean, shy to the point of illness. I never made eye contact, never spoke unless I was spoken to. I was like that for a variety of reasons. But that’s another story . . .

Two things helped me spread the bars of that shyness cage and escape; helped me to get some of that attention I craved. One was my interest in card tricks. In order to do a card trick I had to speak, had to make eye contact. Had to say at least three words—“Pick a card.” I got to be pretty good at it at quite an early age. It was a “look what I can do and you can’t” concept. And that led me into a “partial” career, and a life-long avocation. That’s another long story . . .

The other thing that forced me to speak to people, and that garnered some of that attention, was my interest in (entertaining with) numbers. Again, I was forced to speak—”Think of any number, double it” or, “Write any four 3-digit numbers, I’ll write some more, and then add them all in five seconds,” or, “I’ll instantly square any 2-digit number,” and so forth.

I did start to entertain using a combination of these two ideas—card magic and “miraculous number manipulations.” I started to realize that I could be funny, get laughs, as I was demonstrating these abilities. That, too, changed my life. Again—another story . . .

Years sped by, I was in my early teens. An adult watched me doing some of these things for friends. He asked if I could do some of “that stuff” for a group of about 75 people, at an organization he belonged to. I did it, trembling and sweating (I wasn’t yet sophisticated enough to perspire!) but I did it. The nervousness must have been very apparent, but I did the “lightning calculation,” the mental arithmetic, the number manipulation, and it went over extremely well.

I had realized that card tricks wouldn’t work for a larger group. The card magic I liked and performed (to this day) was strictly close-up, right underxi

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the-nose kind of magic. I told this man that I’d need a blackboard, chalk and an eraser. And I did it. I think the fact that I wasn’t much more than four feet tall at the time had something to do with the standing ovation I received!

And this one, this first, “appearance” started a bit of a chain reaction. I started doing a lightning-calculation act. I had to learn more stuff so that I could do longer “on stage,” and I had to routine the things I knew and wanted to perform.

Through those early years I searched out every book on the subject I could find in libraries; I certainly couldn’t afford to buy them. There weren’t many.

I found books on mathematics, of course (I wrote one myself on shortcut methods many years later), but none that stressed or even touched on “tricks, stunts, feats” with numbers, that included, or even thought of or recognized entertainment value. And that’s the only area I was interested in at the time.

Well, of course, I found some things that I could use—with a bit of a twist or change here and there. In the four years that I did the “act,” I collected more entertaining “number manipulations” than anyone I knew at the time, and probably up to this time.

Please understand that I’m not a mathematician—hell, I have only two years of high school. I’m not bragging, I’m complaining. I couldn’t finish High School because . . . well, that too is another story.

My interest in card magic has lasted all my life (I’ve written over twenty books on the subject—best sellers within the “milieu”). So has my interest in lightning calculation. And that’s the raison d’être for this book.

I’ve been asked, so many times—“Can you teach me how to do that?” Well, sure I can, and could, but didn’t really want to. Why shouldn’t I be the only one who could do this kind of thing? Why shouldn’t I be the only one considered to be a “mental giant,” a mathematical genius? There’s that desire to entertain, to elicit all that admiration, to be the center of attention.

And hey, I admit it, I’m still that way.

But, I don’t do a lightning-calculation act anymore. I do still demonstrate some of the stuff for social and business friends. I’m proud of the number tricks I’ve researched, discovered, devised and invented through the years.

I’ve demonstrated some of my own ideas for “true” (real) mathematicians and I’m pleased to say that they didn’t know/understand how I was accomplishing what I was accomplishing. I confused them!

I’m giving away some of that good stuff in this book. Now, I could have made the book many times its present size. But I believe that it’s my selectivity,

Foreword

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the selectivity I’ve developed over half a century, that’s much to your benefit.

I’ve omitted so much of the number manipulations that I had to wade through and then realize that they had no entertainment value. Most were boring and cumbersome, not really designed to maintain interest, to hold on to that attention. I’m not belittling them; that was not their purpose, not their intention.

Anyway, I’m saving you all that time and effort—I’ve done it for you!

I’m including those number stunts that I know are interest holders, attention grabbers—entertaining. And that will make you appear to be a mathematical genius. Really! That’s the point!

I’ve also included some “lovely” conversation pieces or conversation openers—“ice breakers.” Some have stood me in good stead for decades. Also some head-to-head games that you’ll always win! And—a bit of serendipity: In order to teach some of the lightning-calculation stunts I also had to teach some shortcut methods of adding, subtracting, multiplying, etc. You can use those handy shortcuts in “real life.”

I’ve done something else that, to my knowledge, no one has done before— I’ve included presentation. It’s not usually enough to just do a mathematical (or magic) feat, you need to present it entertainingly and in a way that makes sense. You need to know how to build a stunt, how to move toward that strong ending, how to make it memorable. I’ll teach you how.

Understand that I’ve included a few similar-to-each-other stunts and ideas; slightly different perhaps, different methods, different presentations—purposely. (In some instances you can predict a mathematical outcome, or do some “mindreading” rather than do “quick” mental arithmetic, or even show that you have a fantastic memory!) I do not intend for you to use them all. That would be boring, repetitious. What I intend is for you to read and learn them and then decide (perhaps after trying them a few times) which is better for you.

Please be aware that I’ve taken some “writer’s license.” I’ve quite often used digits (“3, 4, 5”) instead of written numbers (“three, four, five”) out of and within quotes. I’ve done that to save space but mainly, and certainly more importantly, to make it easier for you to follow. Where I felt that writing out numbers was cumbersome, or possibly confusing for you, I simply didn’t write them out. I believe you’ll agree with my choices.

Obviously I can’t please “all the people all the time.” I’ll teach some mathematical feats that you won’t be interested in, won’t fit your personality or “style.” That’s to be expected. It certainly is not my intention for you to use

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all the items in this book. It is my intention to give you plenty of items from which to select.

But let me caution you to go through all the items. Within my write-up of something you may originally feel is not to your liking you may find a hidden gem that you’ll love and use! One example that jumps to mind is my discourse on squaring numbers. I’m well aware that some will love the entire thing and that some won’t. But, there are a few, again, hidden gems lurking there that are instantaneously learned, and that can make you appear to be the mathematical genius you want others to think you are! The point is—read it all, dammit, or those “gems” may remain hidden from you forever.

And, some of the really juicy items, which are usually much easier to learn and to do, are found as you go deeper and deeper into the book.

I stopped doing the lightning-calculation act as I approached my near-tolate teens; I started to be paid to do card magic. Then, another childhood interest started to “emerge.” I started to entertain (key word) by demonstrating my (in the words of my first publisher) “phenomenal memory.” Demonstrating it, writing it, (14 books, a television course), teaching it (all over the world), infomercializing it on TV, motivational speaking it, conducting seminars, etc.

Now, that’s another long, long, story . . .

HARRY LORAYNE