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### Mathematical Card Trick Source

Posted: **July 23rd, 2015, 12:58 pm**

by **Magic Tony**

I learned the following mathematical card trick about 20 years ago. Unfortunately, I don't remember from whom I learned it, and I have had no luck tracking down the source of the effect. Thus, I'm turning to you! Here's the trick:

- Cards of a single suit are arranged from A-K (face to back)

- Spectator thinks of and spells the value of any card in the group by taking cards from the face of the pack and placing them at the back for every letter in the word (e.g., Q-U-E-E-N, etc.).

- Then, they spell the name of the card that is on the face of the pack after the first round of spelling.

- Finally, they spell the name of the card that is on the face of the pack after the second round of spelling.

- After the third round of spelling, the outcome always converges upon the same solution, bringing everyone to the king regardless of their starting point.

Does anyone have a source for this effect?

Thanks in advance,

Tony Barnhart

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 1:17 pm**

by **Bill Mullins**

See "The Kruskal Principle" by Martin Gardner in *Pallbearer's Review* Jun 1975 p 967. As written up there, it uses a whole deck instead of a single suit, and uses numerical values instead of spelling to advance through the cards, but it is the same effect otherwise.

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 1:24 pm**

by **Magic Tony**

Hi Bill,

Thanks for your response. (I think we may have met at the Gathering 4 Gardner a few years back.) I think it's unlikely to operate on the Kruskal principle, which is probabilistic and can let you down. My understanding is that the Kruskal principle depends upon a large N...That is, given enough items it will likely converge upon one solution eventually. This effect works with 100% accuracy (assuming the participant knows how to spell.)

Best,

Tony

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 1:49 pm**

by **Bill Mullins**

This is the Kruskal principle, it's just that the packet is set up so the convergence always happens.

Consider: by picking a card at random and spelling, you enter the stack at only one of three cards (4,5 or 6) since all card values can be spelled with either 3, 4 or 5 letters.

The four spells to eight, but five and six both spell to nine (since six has one less letter than five). So three chains have collapsed to two. Now, since nine has one less letter than eight, they both will spell to the king, and you've collapsed to one chain.

Most tricks using the Kruskal principle will _probably_ converge, as you say. But this one does always work, so it is a little more special than the average trick that uses the Kruskal principle as a method, and as such I'd revise my post to say that the Pallbearer's trick is at best a parent of it. I don't know the credit for your trick and would be interested in finding it as well. (Perhaps one of Jim Steinmeyer's Impuzzibilities booklets?)

And I'm sorry to say I don't recall meeting you specifically at the G4G (did you introduce yourself as "Magic Tony"?), but I've been to a number of them and have met lots of really great folks there. If you go again, look me up and remind me of this exchange.

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 1:59 pm**

by **Magic Tony**

Thanks, Bill. My interest in finding a source for this effect was reinvigorated after a chat with Colm Mulcahy at The Amazing Meeting, last week. He's been emailing his friends to find a source and has also come up short, so far.

I doubt I introduced myself as Magic Tony. However, I did perform under that name in the close-up show. (I think you may have been the "host" at one of the tables.) I was really there to speak on a panel about the psychology & neuroscience of magic with Dan Simons, Steve Macknik, and Susana Martinez-Conde. It was a fun (and expensive!) event.

Tony

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 2:02 pm**

by **Bill Mullins**

Was Dan the guy who distributed the champagne cork holders for an optical illlusion? I've gotten so much mileage out of that. A great impromptu trick.

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 2:14 pm**

by **Magic Tony**

No...I believe those came from Steve & Susana. Dan had mini versions of the Jastrow Illusion.

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 2:23 pm**

by **Max Maven**

A few days ago, Colm e-mailed me this same question. This is what I wrote in reply:

*Hi, Colm.*

While I have not seen this precise trick, the method is not new.

One might define it as a Restricted Kruskal Principle.

One of the earliest related items in print is an effect by Karl Fulves entitled (if memory serves) "Logic Dice" in an issue of Pallbearers Review, circa 1970. Others have explored the idea, myself included. The closest antecedent would be a trick by Jim Steinmeyer that involved counting around a clock face.

For the record, Colm did not agree with the connection to Kruskal -- so Bill, I'm happy to see that you independently *do* agree.

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 2:26 pm**

by **Bill Mullins**

Anytime I find myself on the other side of a mathematics question from Colm, I have to reconsider . . .

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 2:34 pm**

by **Magic Tony**

Hi Max,

Thanks for entering the fray. Indeed, Colm forwarded your assessment my way. While I do see the similarities, I'm still hung up on the probabilistic nature of the Kruskal principle. It feels fundamentally different from the unusual and surprising mathematical regularity of this standard arrangement of playing cards. I fully admit that I'm no "mathemagician," and that I'm rather uneducated within this specific domain. That's why I turned to Colm with my question! I've been using this demonstration in my Psychology of Magic classes for years without being able to provide an adequate citation.

I hope you're well. I was hoping we'd cross paths at TAM!

Best,

Tony

### Re: Mathematical Card Trick Source

Posted: **July 23rd, 2015, 4:32 pm**

by **Bill Mullins**

Part of the problem of saying whether an effect takes advantage of Kruskal's Principle is that there is no obvious statement of what that principle is. The

*Pallbearer's* trick doesn't define or state it; you just have to recognize what is going on from the description. To me, the key is that chains that start from various beginning points collapse and converge to a smaller number of ending points (ideally a single ending point for magic tricks).

Max Maven wrote:One of the earliest related items in print is an effect by Karl Fulves entitled (if memory serves) "Logic Dice" in an issue of Pallbearers Review, circa 1970.

Possibly an even earlier related item:

In

*Ibidem* #11 is a trick called "Sum Total" (p. 232 in the K&G reprint volume). In

*Ibidem* #12 p. 258, Tom Ransom modifies the trick with a small stack at the end that forces you to land on the face card of a deck. The "magic" element of the trick is that even though you start with a random card on top (a block has been pulled from the center and placed on top) the sum of the values of all the cards that were stepping-stones to the last one add to 52("Kraus's Principle"). But the gist is the same -- a card near the start is the 1st element of a chain, and by having that card be randomly selected you start with any number of possible chains, but progressing through the links of the chains they converge to the last 13 cards, all of which converge to a final chain which ends on the face card. Kruskal's principle in disguise.

Charles Hudson, in The Linking Ring Dec 1977 p 82, says "Mr. Ransom did not, of course, invent this setup; and he was not the first to apply it to the progressive countdown." So there may be other earlier tricks that do the same thing.

### Re: Mathematical Card Trick Source

Posted: **July 24th, 2015, 1:15 am**

by **Max Maven**

I would frame it this way: A "Restricted Kruskal" is to the Kruskal Principle as a Perfect Faro is to a Riffle Shuffle.

### Re: Mathematical Card Trick Source

Posted: **August 13th, 2015, 7:55 pm**

by **Bill Mullins**

Colm Mulcahy

points out that "Kruskal Count" anagrams to "Outranks Luck".

### Re: Mathematical Card Trick Source

Posted: **November 28th, 2016, 7:29 pm**

by **lybrary**

Michel Cayrol and Jean-Marie Beckers just released a new very interesting Kruskal-type method which is 'shuffle hard'. In other words, the spectator can shuffle the deck before the counting procedure, yet the landing card is unchanged and known in advance. In that way this new method shares a characteristic of Gilbreath's principle. They have released it in an ebook called "A Bumblebee's Flight'. More details here

http://www.lybrary.com/a-bumblebees-fli ... 91875.html

### Re: Mathematical Card Trick Source

Posted: **April 29th, 2017, 3:34 pm**

by **Bill Mullins**

There is a

Wikipedia game that sure seems related to the Kruskal principle.

### Re: Mathematical Card Trick Source

Posted: **April 29th, 2017, 4:58 pm**

by **John Bowden**

Was there also a system whereby any page is chosen in a book (near the beginning) and the letters of the first word is counted and added to the page number to give you a new page and then the first word on that page is counted and the number added to the page and so on until you run out of pages and that brings you to the same page number each time.

I seem to recall this as a party stunt back in the seventies rather than a magic trick.

### Re: Mathematical Card Trick Source

Posted: **April 29th, 2017, 8:09 pm**

by **Steve Bryant**

Martin Garner posted a letter per word count version, using the first three verses of Genesis, here:

https://blogs.scientificamerican.com/ob ... 010-05-26/It's pure Kruskal.