Hi Guys,
I've been playing with Multiplicative Modulo Groups lately, but I haven't seen any mention of their use in any magic literature. I'm wondering if you guys know of any other work done with them in the magic field.

Some examples where I've used them

1. Trick where the spec riffle shuffles a deck of playing cards and then goes through and stops on the first numeric heart. You tell them what it is. They go on to the next heart and you tell them what it is etc. In this scenario you need to have memorized an order of the numbers 1-10, now this isn't particularly hard to do, but is a simple example of how I'm using the MMG.

In this scenario my order is [7, 5, 2, 3, 10, 4, 6, 9, 8, 1]. to get from any number to the next you multiply by 7 and then repeatedly subtract 11 until you have a number between 1 and 10.

So 7*7=49 , 49 - 4*11 = 5

2. Ordering the trumps of the tarot (using 22 for the fool). I use [7, 3, 21, 9, 17, 4, 5, 12, 15, 13, 22, 16, 20, 2, 14, 6, 19, 18, 11, 8, 10, 1]. This time you still multiply by 7, but you have to subtract multiples of 23.

I've even got some work on this for a full playing card stack and a full tarot deck stack. I'm sure that most would find the math parts a bit too complicated, but with a little practice I find it quite easy.

I've done quite a bit of work on this especially with playing cards, which includes tricks to make the math way simpler and faster for certain sequences.

Anyway, I'm looking for a couple of things, first to know if anyone else has done any work on this, and second to know if the work that I have done would be valuable to the magic community and if so how I should go about getting it out there.

thanks

It would be helpful if you could do a detailed write-up or demo of an effect or two so that you might be able to get some feedback as to its value. You don't need to include method if you don't care to.

Hi nlokers,

I also think it would be helpful if you could describe the effects a bit more in details.

From what I understand of your post, you use the fact that, since n = 11,23,53.. are primes, the multiplicative group (Z/nZ)* is cyclic. Thus 7 (in fact any element of the multiplicative group) is a generator hence induces by iteration a permutation of the element of the group.

So this gives a method to create a seemingly random order of the set {1,...,n-1} by multiplying and taking the modulo n residue. This general idea has been used many time before in magic. For example, similar methods are used to create algorithmic "memorized" decks.

But maybe I did not understand you post... Are you using maths at some other point of your routines or is it only used to set up a particular ordering ?

Thanks for the info

I have just been using it to create the orderings. I know that the mod 13 thing has been used repeatedly, but I don't know of any scenario where these groups have been used, could you point me to any particulars?

Here is a more detailed version of the first effect.

Ask the spectator to name a suit. They name hearts. You give the pack a couple of shuffles and then hand it to them to give it a shuffle or two. You turn your back and have them deal through the cards one at a time, whenever they come upon a heart card that is a number card they stop and focus on it and you tell them what it is.

The other mention of the tarot stack is the same trick except for you give the spec the deck and have them riffle shuffle, then have them go through one at a time and stop on the trump cards.

Clever, Thank you for sharing the idea.

I published a modulo based system for stacked deck or for sorting playing cards in German in Magie, Nr.1,2014, pp.32-35; Hans-Christian Solka "Im Schattenreich der Spielkarten"
(In the playing cards' empire of shadows - the invisible label)

In a nutshell: Every plaing card is defined by value, color and suit. Every playing card have also "shadows" like shadow suit and shadow value. Visible only for those who knows. One can use this features to define groups of playing cards or stacks.