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Hushai Elite user St. Louis, Missouri, USA 460 Posts 
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In going through my books today I've found two more that give interesting suggestions for using the Nine Principle: "The Complete Idiot's Guide to Magic Tricks," by Tom Ogden, in the chapter he calls "Arithmetricks," and "Magic with Everyday Objects," by George Schindler, in the chapter on mentalism. I'm sure I've run across this fascinating principle in lots more books, too. I've figured that something like that observation by Martin Gardner that Nir mentions must be the case, but I've never been mathematician enough to be sure.
-- Hushai |
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Sid Mayer Special user Santa Fe, NM 656 Posts
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Think of any two digit number.
Subtract from it the sum of its two digits. The result will always be a multiple of nine. And, of course, the digital sum of any multiple of nine is nine. Explanation, if needed, is: Let A equal the first digit and B equal the second digit. Thus, the original two digit number is of the form 10A+B. Subtract the sum of the two digits (A+B) like so: 10A+B-(A+B)=9A. This is arguably the simplest way to force a nine. Sid
All the world's a stage ... and everybody on it is overacting.
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Bill Hallahan Inner circle New Hampshire 3226 Posts
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The two digit case to force a nine is exploited in a number of simple tricks. The technique extends to more than two digits, and it doesn't matter if you combine the digits continuously. If you add the digits of any base 10 number, and subtract the resulting number from the original number, then you will get a multiple of 9! And of course, it's digits will sum down to 9. This is the principle of "casting out nines" that used to be used by accountants to check arithmetic before the advent of computers.
For example, staring with the number 1567, 1567 1 + 5 + 6 + 7 = 19 1567 - 19 = 1548 = 9 * 172 1 + 5 + 4 + 8 = 18 and 1 + 8 = 9 Also, you can repeatedly add the original digits down to fewer digits before subtracting, i.e. 1 + 5 + 6 + 7 = 19 1 + 9 = 10 1 + 0 = 1 1567 - 1 = 1566 = 9 * 174 You still get a multiple of 9, and of course those digits all add repeatedly until just 9 is obtained. There is a lot more that can be written about this relating to sums, products, and quotients, but subtraction is always used in magic to get directly to a given result. Most of the effects that use this "directly" are not strong, since many people realize that if you use a number on itself, then there can be some kind of cancellation leading to a predetermined result, even if they don't understand the relationship. I write "most" because there are some strong applications. A really cool application of this principle is The Flash Mind Reader. (Give this page time to load.) By the way, this extends to other base systems, i.e. in base eight, you would cast out sevens. Of course, in the case of base two, the binary system, where you cast out twos, the result is trivial, and just reduces to parity, i.e. whether the number has an even or odd number of ones in it.
Humans make life so interesting. Do you know that in a universe so full of wonders, they have managed to create boredom. Quite astonishing.
- The character of ‘Death’ in the movie "Hogswatch" |
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Steven Steele Chief of Staff 1868 Posts
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I don't know the principle or the mathematics involved (I would love to know), but I do a trick with two stacks of six cards arranged in a palendromic order to each other. The two piles contain identical cards (for example each pile contains the Ace through 6 of Spades). Cards are dealt one at a time from the top to the bottom and the dealer is randomly told to switch piles as a word is spelled. At the end of the spelling, the top cards are shown to match. They are removed and another word is spelled one letter at a time, following the same procedure.
Anybody know why this works and any history associated with this principle?
Coram Deo
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Hushai Elite user St. Louis, Missouri, USA 460 Posts
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A fun trick that works purely by probability (and thus belongs on this thread, I guess) can be found at http://magic.about.com/library/tricks/bltrick42a.htm
I first encountered this in Garcia & Schindler's "Magic with Cards." I present it as a sleight-of-hand trick I've been working on and haven't quite perfected, because I can get two cards of the same value together, but haven't been able to get them to be the same SUIT yet. I put the deck behind my back for a second and just riffle the cards, pretending to be instantly rearranging them, sight unseen, after the spectator has just shuffled them thoroughly. As I said, it's fun, and must be THE easiest magical effect anyone ever did. -- Hushai |
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dlhoyt Regular user 176 Posts
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Quote:
On 2003-06-17 00:47, Steven Steele wrote: Steven, this principle is explored in Max Maven's recent book, RedivideR (note the palindromic nature of the title). It is also the basis of an effect by Larry Becker -- Will the cards match, which can be found in Stunners, Plus. The Maven book has many effects that exploit the principle. Dale Hoyt |
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Eric Rose Regular user Franklin, IN 160 Posts
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My favorite math principle has to be the devilish little faro shuffle. My favorite faro based trick is Chaos by Pit Hartling. I love pattering about the precision necesary since its fully mathematical (entirely true) while chaotically placing cards and apparently mixing them horribly. Its a rare trick that makes an anti-faro entertaining.
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highmagic Veteran user 399 Posts
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I shall also mention the "Jackpot Coins", a simple mathematical effect illustrated by Gerard Croiset in the 18th century, and recently refurbished by Barrie Richardson in his "Theater of the Mind"
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Brandon Harper Loyal user Austin, Texas 207 Posts
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I have been performing the following trick for quite some time. Many magicians are surprised to learn that this effect was created using a simple mathematical trick.
A deck of cards is shuffled and the spectator is asked to choose four cards, a free choice. You tell them that based on the cards chosen, the deck will reveal personal information about them. You turn the cards over and begin to reveal information about the spectator. Of course, you are completely wrong. You offer to try again, so you add enough cards to each chosen card to equal 10 (e.g. if the card is a six, you add four cards to that pile, if it is a Jack you don't add any). You then "read" these cards as well. Again, WRONG. You offer to try one more time. You add the values of the original four cards together and deal that many cards into a pile as well. You then tell the spectator that the next card is their lucky number. It is turned over and is a seven. You then deal the next seven cards face up and ask if they are relevant to the spectator. After a few seconds, the spectator will realize that the seven cards are their telephone number. |
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Scott Cram Inner circle 2678 Posts
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Quote:
On 2003-06-23 11:21, highmagic wrote: If you like Jackpot Coins, you'll love Stewart James' "Dollars and (Sixth) Sense", written up in Bob Farmer's Flim-Flam column in the February 1995 issue of MAGIC. Here's the effect as written in the column: Quote:
Effect: Several coins and three bills, a one, a five and a ten are tabled. Four spectators, A, B, C and D, are watching. While I can't reveal the method, I can tell you where to find it. The way you reveal the number of coins D is holding is the same as used in "Jackpot Coins" (generically known as "Debit & Credit", BTW). The way you determine who has the 1, 5 and 10 is written up in Martin Gardner's "Encyclopedia of Impromptu Magic" under "Matches: Mathematical Tricks" (look at Item #10). With those two clues, it shouldn't be hard to put the method together. |
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highmagic Veteran user 399 Posts
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Thanks Scott - I'll check Gardner's book for the final part
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Scott Cram Inner circle 2678 Posts
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Here's yet another cool mathemagical principle!
Check out Lewis Jones' "The Pattern Principle" in Steve Beam's "Semi-Automatic Card Tricks, Vol. 3". The principle itself isn't a math principle, however, it would be next to impossible for it to work if the mathematics of it weren't worked out properly. Basically, it minimizes the work required to remember the order of the colors in the deck. One read through the principle, and the included effects, "Red Alert 1, 2, 3 & 4," and I was well, like this: 
There's some great & unexplored potential in the "Pattern Principle". |
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domclarke Regular user Windsor, UK 147 Posts
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"Reversal" in Banachek's Psychological Subtleties.
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landmark Inner circle within a triangle 5194 Posts
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Here's a mentalism effect from Buckley's Gems of Mental Magic that uses a math idea that very few know. The effect, called Devious Digits as described by Buckley:
Here is a miracle in which a number that runs into the quintillions is reached by multiplication of a random selection of numbers. Yet a spectator who calls a friend of the performer by telephone is given this long number accurately while it is being worked out by the assistant in the room. The multiplication involves a 15-digit number times any number from one to thirteen. While the first number is not really random, the second is freely selected. It's a killer! landmark Another favorite old-time gag is the Piano Card Trick from Royal Road. Though simple, it's amazing how many people you can fool with it if you present it as a sleight of hand trick. landmark
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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riberts New user Yorkshire, UK 52 Posts
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Quote:
On 2003-05-13 18:38, Magictrickster wrote: I agree Brian it's a good effect. There's a similar use of this principal used by Roger Curzon (from Sheffield's Magick) in his booklet "Blood on the Tricks". Effect is - a spectator 'shuffles' a packet of 9 differently numbered cards; - 1 or 2 spectators randomly generate a number using a calculator The 9 cards when dealt out form the 9 digit number generated. Not a math effect per se, but very powerful - can be dressed up as either (im)probability of events occurring, the power of the subconscious etc, etc... Cheers |
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Ben Blau Inner circle 1475 Posts
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Lately I've been doing a lot of work with Bob Hummer's "3 object divination" principle. It's very versatile. A good description is in Bill Simon's Mathematical Magic book.
Ben Blau
Ben Blau
http://www.benblaumentalism.com |
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Magicmike1949 Special user 643 Posts
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There's a trick in Scarne on Card tricks, with a name I don't recall, that's very good. The spectator shuffles the deck. Upon getting it back, you ribbon spread it face up and get a quick look at the third card from the bottom as you show that the cards are well mixed. Now write a prediction and keep it face down on the table, which names this card. Have someone reach into deck and pull out any ten cards (except for the bottom 3). Now mix those ten up and have someone pick any 4 of them & turn them face up. Now if you can, for each of those 4 cards transfer enough cards from the top to bottom to make each one equal ten. E.g., if a 3 shows, transfer 7 cards to the bottom, if a 10 or face card shows, don't transfer any. If you can do this without visibly counting so much the better, but sometimes I do it openly. Then look at the 4 cards that were selected from the 10. Add their values. Openly deal that number face up but stop when you get to the number and hold that card face down. Turn over your prediction and show it. Now turn over the card. They will match.
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bobmcmathman New user Arizona 43 Posts
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Does anybody else use Gardner's cube root and fifth root 'calculations'? I find people seem to enjoy these as an amazing demonstration of memory. (I don't present them as lightning calculations, but instead patter about how I have been honing my memory by memorizing tables of roots.) I usually precede this with some actual easy calculations of squares of 2-digit numbers ending in 0 or 5.
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Nir Dahan Inner circle Munich, Germany 1390 Posts
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Cube and fifth root are great demonstrations especially to an audience who is more mathematically oriented.
If you can do other mental calculations using logarithms for instance, it absolutely kills. |
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stick New user 30 Posts
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By far the best trick using mathematics is to be found in the “Royal Road to Card Magic”, page 148 and is called “An Incomprehensible Divination.”
It kills laymen and some magicians. I have used it for years. |
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Posted: Jun 4, 2003 12:53 am 
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