Hi everyone,
I'm doing research at a University in the United States regarding the intersection of mathematics and card magic, and working to come up with some new math that will help motivate selfworking card tricks.
Something we're working on right now is, generally, the following:
Have a pack of cards where the sum of any 2 adjacent cards is unique, and all possible sums are achieved. Example: (9 cards)
[A, A, 2, 2, 3, 4, 4, 5, 5] If you sum any two adjacent cards you get these sums [2,3,4,5,7,8,9,10,6]. Note that the six comes from adding 5 and 1, as the sequence is cyclical, (which means this pack could be cut n times and still preserve its properties). We also achieve all sums inclusive between the absolute minimum possible sum (A+A) = 2 and maximum (5+5) = 10 given the cards.
The problem I'm facing is working this nicely into a worthwhile trick, and I was wondering if anyone could help me or know someone's past work that could. The most obvious use for this property is simple for identifying two cards; if you know their sum, you can know what two cards were picked, as that sum is completely unique to the set of cards. However, I'm hoping to come up with something even more interesting, which is why I am asking for your help.
Does anyone have any interesting ideas for integrating this into some kind of effect that is more than just identification if two cards? I appreciate any ideas or references, as I think this is problem could be solved by an informed brainstorming session.
Some final things that I think may be helpful in thinking about this:
1. The number of different values of cards can be changed. IE in the example I did A5, but you could use up to AK (1  13).
2. Instead of adding adjacent cards for their sums like I showed in my example, we can also make sequences where you add 3 or 4 consecutive cards to achieve unique sums.
Feel free to ask any questions about anything I didn't explain sufficiently, and thank you in advance for your time and thoughts!
Ben
University Research on SelfWorking Card Magic
 Marco Pusterla
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Re: University Research on SelfWorking Card Magic
The concept of "bracelets" has been explored in magic for more than a quarter of a century, with notable simplifications on practical terms concentrating on properties of the cards other than values (like color, suits, parity, etc). I would suggest you check the works of Leo Boudreau from the late 1980s (particularly "Spirited Pasteboards") or some of Phil Goldstein's works (I'm thinking of "Thequal"). Charles Jordan also explored this venue, as did T. A. Waters (I have a vague recollection he did...). I did explore the principle with ESP cards, which being a set of 5 values, proved to be exceedingly practical for performance, but did not publish anything. The identification of two cards is just a starting point for this principle, but most of the published effects deal with the identification of a few cards or the location whence one (or more) hidden selection comes from.

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Re: University Research on SelfWorking Card Magic
For a revolutionary use of math for magic, see:
https://www.lybrary.com/thebammotarod ... 23866.html
https://www.lybrary.com/thebammotarod ... 23866.html