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Andy Moss Special user 713 Posts |
Does anyone know of any ideas as to how to present a mental effect utilising this mathematical idea? Since I have posed the challenge I should I guess offer to you my own idea first.
I am thinking that one might be able to use children's digit figures and have a spectator choose any five of them whilst the magician's back is turned. They would then rearrange the digits to make up any "random" number with these five digits and write it down on a slip of paper before handing the same digits figures to a second spectator to do the same.That second made up "random" number is then written down on a separate slip of paper. Finally the five digits are returned back to the bag and the two slips of paper are handed to a third spectator who subtracts one of the numbers away from the other using a calculator (it does not matter which) to create a third number. This third spectator then takes out these new digits corresponding to this new number from the bag. One might proceed to have this third spectator physically push the five digits forward into the centre of the table and to mix them up keeping any one digit for themselves to be hidden in their hand. Since you don't want the spectator to choose a 0 an idea might be to steer them towards "any digit between and including one and nine".Whilst all this has been going on the magician's back from start to finish has been turned. Only at this point in the proceedings does the magician turn around and -without bringing any undue attention to them- sweeps the disregarded digits together into the bag secretly adding them up as he does so.Thus the magician gets rid of the only evidence.No back tracking is now possible on the part of the audience. Then the 'casting off the nines's' approach can be used to ascertain the digit hidden in the third spectator's hand. Everything can be examined.The figure digits and the bag. Andy. |
TomasB Inner circle Sweden 1144 Posts |
That's my favourite way of forcing a number to be a multiple of nine.
I think it's convenient to simply do it for a single person. Have her write down any number, at least five digits and at most what the calculator can take or what she'd feel comfortable with if there is no calculator. "Now form a number you didn't even know you were going to write down, by rearranging the digits." After the subtraction, say "Circle one of the digits, but not a Zero since it's already a circle." Have her call out the other digits in any order, crossing each digit out as she goes along so she doesn't make any mistakes. The reason for rearranging the digits is a bit hard to justify even though I try in the above presentation, so maybe we can get rid of that. Gilbreath comes to mind: Have a number deck shuffled and the top five cards removed by a spectator. Another spectator removes the next five cards. Gilbreath makes sure that the two sets are identical. They form a number each and the difference is recorded. Gilbreath is of course overkill for this since you know exactly which digits the first spectator gets and can force that number to have digital root 0, or simply memorize its digits, so you don't even need a second spectator or any calculations. Maybe some other principle can force the two sets to be identical, but more random and not as powerful as Gilbreath? /Tomas |
Scott Cram Inner circle 2678 Posts |
Casting out the nines, also known as determining the digital root, is a great mathematical principle.
One great use for it, without ever involving a multiple of 9 itself (unless one happens to be chosen), is demonstrated here by Frank Wang (scroll down and click on "The Death-Defying Feat"). |
TomasB Inner circle Sweden 1144 Posts |
Great, Scott! Thanks for that one.
/Tomas |
Andy Moss Special user 713 Posts |
Thank you both for your input. I have now had the chance to experiment with the Gilbreath idea. As you say with the Gilbreath approach both sets of number cards will be identical and of course do not need to be in order for the casting out of the nines.
I was reminded of one of Leo Broudeau's generous offerings called "Zener Card Stack Divination" (as located via a link on Scott's wonderful website).The simple formula's relating to a Zener card stack (X+1 and 6-X) could be so easily adapted for number 1 to 9 digit cards (ie X=1 and 10-X).If the number cards were marked on the back then we could work out all the cards in all the piles from the top cards of each dealt out pile. In this later approach both created numbers would appear to be more random with some digits potentially appearing more than once in the same created number.This idea might have some potential for a strong presentation.I wonder if there is such a thing as a 'marked number deck' on sale somewhere? Andy. |
WilburrUK Veteran user 389 Posts |
Ok, I think I've had a brainwave !!! I'm not sure if this is well known..
if you have all 10 digits 0123456789 and one person chooses 5 and arranges them in any order (Forming number A) and the 2nd person arranges the remainder in any order (forming number B). Then A+B is divisible by 9. Proof: to make B into a number that has the same digits as A we use C=999999-B then A-C is divisible by 9, so: A-(999999-B) is divisible by 9 A+B-999999 is divisible by 9 and since 99999 itself is obviously divisible by 9 so is A+B. Only 10 cards needed. No Gilbreath, and no subtraction. |
TomasB Inner circle Sweden 1144 Posts |
That's what the digial root is mostly used for; to check the digital root before and after a calculation which shows you if you made any errors. So it's obvious that the digital root of any sum of any numbers formed by using those digits once is zero, since 0123456789 has the digital root zero. For example 120 + 43 + 56 + 978 has the digital root zero.
I quite like the idea of them getting 10 cards which has a known digital root, since you know that any sum formed by any numbers made up by all those cards will have the same digital root. Maybe make them get the set of cards via Gilbreath? /Tomas |
WilburrUK Veteran user 389 Posts |
Yeh that kind of dawned on me on the drive home from work. I guess I was looking at it from a different direction before.
Oh well. |
lboudreau Loyal user Alexandria, Virginia 288 Posts |
Quote:
On 2009-09-17 06:13, Andy Moss wrote: Andy, You will find a recent discussion of the principle here. http://www.maa.org/columns/colm/cardcolm200908.html Colm Mulcahy chose to call it the Bligreath Principle to distinguish it from Gilbreath.
LEO
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Andy Moss Special user 713 Posts |
Thanks for the link Leo.The explanation is interesting.Your principle would I feel give rise to a very effective means of divining numbers.The formula (First stage) X+1 and (second stage) 10-X as I say could work well with digit cards one to nine.
After the spectator has choosen their pile by pointing to it I would simply note the identity of the top card of their respective pile before I ask the specttaor to take their cards and to mix them in their hand. Thus any possibly perceived cyclical pattern is broken. The cards will seem random. I can now work with this remembered digit and with the top card digit of the preceeding pile. The following thoughts come to mind with respect to the use of the Blibreath approach:- 1)You might choose to go along the line of presenting the divination of a missing digit as with the standard 'casting out of the nines' presentation.Only in this case the casting calculation is not at all necessary. 2)There is the potential for a strong 'card calling effect' where you are able to visualise every card in the choosen hand of cards. 3)Card Shark (Christian Schenk) sells gorgeous looking blank faced heirloom cards marked on the back from which one might easily create a set of marked digit cards. 4)Any pile of digit cards might be compared with the digit cards that are in another pile. All the piles would contain different combinations of numbers (unlike with the Gilbreath approach)This opens up the potential to repeat the effect without suspicion with another pile. I do realise that the topic has steered a little away from the original 'Casting out of the nines' principle but hope that the above idea gives food for thought. The effect 'Zener card stack divination' can also be located on this very site via a Café search. Thanks Leo for the inspiration. Andy. |
Andy Moss Special user 713 Posts |
Oh and the use of the Rosetta shuffle would work so well with respect to giving the impression that the digit cards have been thoroughly mixed/messed up on the table!
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TomasB Inner circle Sweden 1144 Posts |
Quote:
On 2009-09-17 19:00, lboudreau wrote: Karl Fulves has a thorough book on this in "Riffle Shuffle Set-Ups" where he writes: "A riffle shuffle set-up is one which produces controlled results even though the spectator gives the deck an honest riffle shuffle." In "Principles of Riffle Shuffle Set-Ups" he mathematically shows position control when the groups in the two shuffled packets are general. They do not have to be in the same order or reverse order, but those cases are of course included. You guys would absolutely love reading it. It contains so many groundbreaking ideas. /Tomas |
GALIER New user Spain 37 Posts |
Hi guys,
in fact, the so-called Bligreath principle can also be interpreted as a consequence of the properties of the riffle-shuffle. In the twenties, Charles Jordan studied several applications of this shuffle. Maybe is it a hybrid between the Gilbreath and riffle-shuffle properties? |
GALIER New user Spain 37 Posts |
Good idea!
The digital root of the product equals to the product of the digital roots of the factors. Quote:
On 2009-08-22 14:17, Scott Cram wrote: |
The Magic Cafe Forum Index » » Magical equations » » Casting out the nines. (0 Likes) |
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