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The Magic Cafe Forum Index » » Magical equations » » De Bruijn 52 Yelnif pure Aronson (or Tamariz etc) great! physical sequence (9 Likes) Printer Friendly Version

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Profile of glowball
In my prior posts I (glowball yelnif) have used a physical DeBruijn sequence of 52 cards but this was awkward. The new approach below is far superior. Instead I now use the physical stack such as Aronson and simply orient the cards in the Aronson deck using a one way back deck (or red back cards for binary "0" and blue back cards for binary "1").

Effect: the magician gives a deck of cards to a spectator to cut as many times as they wish and then deal six cards in a horizontal row. The magician then looks into his "magic prediction" book and tells the spectator what all six cards are.

How its done (note: this is far easier than some of my other DeBruijn 52 posts):
Let's assume that you are using a one way back deck and the normal orientation is binary 1 and the reverse orientation of a card is binary 0 and this deck is never changed, it is permanent in the orientations that you will set now. Therefore your stack should have the first six cards in reverse orientation then the next six cards normal orientation then the next three cards reverse and so on.

Below is complete list of your whole deck orientation starting with the first cards of your stack:
6 reversed
6 normal
3 reversed
2 normal
1 reversed
1 normal
3 reversed
1 normal
2 reversed
2 normal
2 reversed
1 normal
1 reversed
3 normal
2 reversed
3 normal
1 reversed
2 normal
1 reversed
4 normal
1 reversed
1 normal
1 reversed
2 normal
The above numbers add up to 52 and correspond to the yelnif 52 bits.
Note if you are using a mixture of red backed and blue backed cards instead of one way back cards then use red-backed cards where you see the word "reversed" and blue backed cards where you see the word "normal".

Mneumonic story to help you initially set up your deck permanently:
Walking on route 66 then Jim Brown (32) and his 11 year old son are hitchhiking and are teletransported to route 31 where they find a 22 rifle that has 2 barrels the 11 year old son picks it up and shoots 3 targets they then see a 23 year old woman with her 12 yr old daughter and 14 yr old son on an 11 boy football team who had a dozen eggs (12).

Now print the below list (cheat sheet) to lookup yelnif to Aronson first card of six cards and put inside your "Magic Prediction" book (or on the back of a crystal ball etc):

When performing look at the six cards binary pattern and mentally translate that pattern to a two digit normal number and look it up on the cheat sheet in your "Magic Prediction" book. Example: blue, blue, red, blue, red, blue is 110101 which mentally is 110 + 101 which is 48 + 5 equals 53 thus looking at the "cheat sheet" for "53" the first card of the six cards is the Nine of Clubs (Aronson) and you know the following 5 cards because you have the stack memorized (or you could include them on your cheat sheet too).

Below is my glowball yelnif 52 DeBruijn cycle (you don't need to know it. I am just including it as a valuable reference):

0 0 0 0 0 0 1 1 1 1 1 1
0 0 0 1 1 0 1 0 0 0 1
0 0 1 1 0 0 1 0 1 1 1
0 0 1 1 1 0 1 1 0 1 1 1 1
0 1 0 1 1

If you are using some other stack such as Tamariz etc then use the below to assign your cards and then sort the below list by first column numeric order so you can print off your "cheat sheet".
00=first card of your stack
32=second card of your stack
48=third card of your stack
56=fouth card of your stack
60=fifth card of your stack
62=sixth card of your stack
63=7th card of your stack
31=8th card of your stack
15=9th card of your stack
07=10th card of your stack
35=11th card of your stack
49=12th card of your stack
24=13th card of your stack
44=14th card of your stack
22=15th card of your stack
11=16th card of your stack
05=17th card of your stack
34=18th card of your stack
17=19th card of your stack
08=20th card of your stack
36=21st card of your stack
50=22nd card of your stack
25=23rd card of your stack
12=24th card of your stack
38=25th card of your stack
19=26th card of your stack
41=27th card of your stack
52=28th card of your stack
58=29th card of your stack
29=30th card of your stack
14=31st card of your stack
39=32nd card of your stack
51=33rd card of your stack
57=34thcard of your stack
28=35th card of your stack
46=36th card of your stack
55=37th card of your stack
27=38th card of your stack
45=39th card of your stack
54=40th card of your stack
59=41st card of your stack
61=42nd card of your stack
30=43rd card of your stack
47=44th card of your stack
23=45th card of your stack
43=46th card of your stack
53=47th card of your stack
26=48th card of your stack
13=49th card of your stack
06=50th card of your stack
03=51st card of your stack
01=52nd card of your stack

Please give this a try and let me know how well it works.
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Note: my yelnif 52 bit DeBruijn cycle is very valuable and hard (if not impossible) to find a true 52 DeBruijn that wraps and has no duplicates and no missing occurrences. The only other place I found such a cycle was in Leo Boudreau's book Spirited Pasteboards which I just now purchased online download from for $29 just to compare it to mine. Leo's 52 bit cycle is under the effect "Heady Stuff". Leo has an excellent 52 bit cycle which is a little better than mine because his has only 8 odd ball numbers (outside 1-52) whereas mine has 12 odd ball number values however in the effect that I'm describing here there is no difference in efficiency, either 52 bit DeBruijn cycle will work however what I described in the above post the values only work with my yelnif 52 bit cycle. I wish that our "1"s and "0"s were split 26-26 but we both have our's split 28-24 which is not a problem for most effects, but there could be a trick where assignments are made for all the red cards to be binary "1" (or binary "0") which could be a problem for our 52 bit DeBruijn's. However this trick is fine with the 28-24 split.
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Instead of a physical cheat sheet you can use your cell phone as a cheat sheet by making 52 phony names on your phone's contact list and then using your phone's search feature to type in the two digit DeBruijn number and your phone will then show the six cards that are in play.

Below is an example of 1 bogus phone number entry in your contacts list:
26 QS 6D QC 2C 9D JS (that is in the first name field of one contact entry and be sure to put in a fictitious phone number such as 800-555-0026 to make your cell phone software happy). Then make 51 additional entries using the same concept. Now you are set forever.

This is in essence a quick lookup cheat sheet. This will allow you to go to your phone contact search and just type in the number 26 and it will instantly bring up the bogus contact name showing the Queen of Spades as the first card of the six. This way you do not have to memorize the DeBruijn binary number and it's related card of your stack (the first card of the six cards dealt). Actually you don't even have to memorize the stack itself since your phone number name will show all six cards.

Your patter could be something like this "cell phones have magical powers and mine can tell me exactly what your six cards are".
In your cell phone contacts search window type in the two digit yelnif DeBruijn number and then you can see and verbally name the six cards. The bad thing about this way is that the spectators may perceive the phone as the magician and not you? But still impressive.
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Pattern option:
Another way to do the search without having to calculate the binary number (26 in our example) in your head would be to just type in the ones and zeros at the first part of the first name in your phone number contacts in other words for 26 you would type in the pattern you see on the six cards ie: 010110 (low bits first) or 011010 (if doing high bits first).

Note you could use the number 9 instead of 1 in your phone number scheme simply to make your search entries faster and easier to type in because the 9 and the 0 are right next to each other on Android phones (I don't know about Apple phones).

Example: if the six cards that are dealt are (low bits first) first to last: red, blue, red, blue, blue, red (blue backed for binary 1 and red backed for binary 0) then type in 090990 (binary representation of decimal 26).

This assumes they dealt the first card to your right and the 6th card to your left) and your phone number list would have first name of 099090 QS ...). I'm going to try this but I'll put a dash in the middle of the nines and zeros for easier readability.

In other words in our example I would set my phone contact name for 26 as "099-090 QS 6D QC 2C 9D JS" then at performance time I would look at the 6 card pattern and duplicate that pattern by simply typing in 099-090 and wah wah the contact name shows on my cell phone (showing the six card's abbreviated names without any memorized numbers of any kind!).

Try to get them to deal the six cards from your right to your left otherwise you will have to do mental gymnastics to flip the pattern in your mind to enter the pattern into your cell phone contact's search window.

This is somewhat confusing to try to explain but actually easy to do when performing. The reason for the confusion in this post about cell phone contact name searches using binary bits instead of actual numbers is that binary numbers are normally specified from right to left but when using search engines the entries go left to right.

And to make matters even worse when documenting the entries in this post if I say "000999'" then ask yourself which entries were done first, were the zeros entered before the nines or were the nines entered first? not so clear is it.

Therefore in our situation even though our deck is set up for binary low-to-high we must make the cell phone search entries high to low. Either way just be consistent in the way you set up the values in your contacts list and the way you make your search entries at performance time and you'll be fine.
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OK, after studying the situation a little more: if you want to use the pattern technique with your cell phone here is the simple solution: Since the deck pattern that I've specified creates a low bit to high bit binary number with the six cards that are dealt face down then the cell phone entries must also be low bit to high bit sequence.

Don't worry about having the spectator deal the cards left to right or having them deal the cards right to left instead focus your attention on which card is dealt first and which card is dealt second and so on and make your entries into the search window in that same sequence.

In our example of red blue red blue blue red the magician enters 0 then 9 then 0 then a dash then 9 then 9 then 0 so it looks like this on the screen: 090-990 then the cell phone software brings up the entire entry of: "090-990 QS 6D QC 2C 9D JS"
Of course the Queen of Spades is the first card that the spectator dealt, the six of diamonds the second card dealt and so on.

In summary: for the cell phone Yelnif 52 pattern technique using red and blue backed cards: use the number 0 for red cards and number 9 for blue cards. If using a one way back then use the number 0 for reversed oriented cards and number 9 for normal oriented cards.

The pros and the cons of four methods to obtain the "cheat sheet" info during performance:

Cell phone Two digit pros:
You only tap two digits (vs seven taps for the pattern method).
Cell phone Two digit cons:
You mentally have to convert the binary value to the two digit decimal (which is not that hard once you get used to it).
There is a bit of time to initially prepare this info into your cell phone.

Cell phone Pattern method pros:
Simple, no math at performance time.
Cell phone Pattern method cons:
You are tapping your cell phone seven times which may look more suspicious than the two digit method.
There is a bit of time to initially prepare this info into your cell phone.

Hard copy Cheat sheet method pros:
Don't need a cell phone.
Hard copy Cheat sheet method cons:
You mentally have to convert the binary value to the two digit decimal (which is not that hard once you get used to it).
You need a plausible reason to look at something that secretly has the cheat sheet (this can be acceptable).

Brute memory method pros:
Don't need to enter a bunch of stuff on your cell phone nor peek at a cheat sheet.
Brute memory method cons:
You mentally have to convert the binary value to the two digit decimal (which is not that hard once you get used to it).
You must memorize an extra two digit number for every card in your memorized stack (example: the Queen of Spades in Aronson is 48 but you also would need to know that 26 is the Queen of Spades for this effect). I don't need another number to clutter my brain with therefore I will use one of the other three methods.
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Best cell phone lookup on Android phone (may be fine for other phones):
I did a lot of experimenting and here is what worked best (red back cards are binary 0 blue back cards are binary 1 or in the case of one way backs the reversed cards are binary 0 and the normal cards are binary 1). The example below is for cards back color dealt: red, blue, blue, blue, red, red (or one way cards of reversed, normal, normal, normal, reversed, reversed):

Prepare your phone ahead of time with 52 cheat sheet entries (Yelnif - Aronson), this particular pattern should have the entry: *14-099900 4d Td Jc Jh Tc Jd
Notice that I have combined the two digit method and the pattern method together on one entry that way I can use either method. Also the astrisk at the beginning of the entry is important so that your number will show up at the first of a list that may accidentally have legitimate contacts in the list. This way you will always see your entry as the very first row if there are multiples.

Also notice that a ten card is expressed as a capital letter "T" and that the suits are expressed in lower case. This is to save space on the line when viewing so that the last part of the entry does not get chopped off from your view at performance time.

Also notice that I have abandoned the idea of putting a dash in the middle of the pattern of zeros and nines because it just slows the entry process down.

At performance time after The Spectator deals the six cards face down in a row then you the magician open up your cell phone contacts search feature and merely type in the two digit number in the search window as represented by the six cards (do not type in the asterick at performance time because it will slow you down and the software ignores it for searching purposes).

In our example if you have mentally translated the 6 cards to a two digit number then just type in that 2 digit number (in our example type in 14) and then your phone will show you the six cards. Or you can type in the pattern (in this example 099900) and your phone will show you the six cards.
Your phone will show you:
*14-099900 4d Td Jc Jh Tc Jd
Therefore you know the first card dealt down was the four of diamonds and the second card was the ten of diamonds etc.
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Profile of Claudio
Great effort on the DeBruijn sequence, glowball. Though I do not have much to say on the DeBrujn aspect per se, I might be able to contribute a bit on the trick side.

When performing look at the six cards binary pattern and mentally translate that pattern to a two digit normal number and look it up on the cheat sheet in your "Magic Prediction" book. Example: blue, blue, red, blue, red, blue is 110101 which mentally is 110 + 101 which is 48 + 5 equals 53 thus looking at the "cheat sheet" for "53" the first card of the six cards is the Nine of Clubs (Aronson) and you know the following 5 cards because you have the stack memorized (or you could include them on your cheat sheet too).

I think using octals as a short cut here would be safer and quicker than adding numbers to get a decimal value.

Instead of adding the two triplets, juxtapose the two digits (one per triplet) to form a unique octal number. For example, in the case above, read the binary number 110101 as two triplets (110-101) of 6 and 5 to create 65. Basically you use the octal value as a key without the additional steps of converting to decimal and adding the values to obtain a decimal number (53). The advantage is that’s relatively painless to visually learn and convert the 8 different binary patterns to their octal equivalent so that no mental effort is required:


You can then set up a crib sheet using the octal values (though they read like decimals). Here’s below a table that reproduces the first list you gave in your original post. I’ve left the decimal values for reference, but they should be omitted in the final crib sheet as they are useless.

(Decimal) Octal Card Name
(00) 00=JS
(01) 01=9D
(03) 03=2C
(05) 05=3S
(06) 06=QC
(07) 07=AC
(08) 10=5S
(11) 13=8C
(12) 14=3D
(13) 15=6D
(14) 16=4D
(15) 17=8D
(17) 21=7S
(19) 23=QH
(22) 26=7D
(23) 27=4C
(24) 30=2D
(25) 31=8S
(26) 32=QS
(27) 33=10H
(28) 34=10C
(29) 35=KH
(30) 36=KS
(31) 37=6C
(32) 40=KC
(34) 42=AD
(35) 43=10S
(36) 44=QD
(38) 46=7H
(39) 47=10D
(41) 51=5D
(43) 53=8H
(44) 54=KD
(45) 55=6H
(46) 56=JD
(47) 57=6S
(48) 60=5C
(49) 61=5H
(50) 62=AH
(51) 63=JC
(52) 64=7C
(53) 65=9C
(54) 66=3C
(55) 67=4S
(56) 70=2H
(57) 71=JH
(58) 72=4H
(59) 73=2S
(60) 74=9S
(61) 75=9H
(62) 76=AS
(63) 77=3H

As you mentioned the following numbers are missing:

(Decimal) Octal
(02) 02
(04) 04
(09) 11
(10) 12
(16) 18
(18) 22
(20) 24
(21) 25
(33) 41
(37) 45
(40) 50
(42) 52

If you were to use a crib sheet, you could possibly turn your back to the audience and consult it while calling the sequence.

A second aspect which could be simplified if you don’t know a memdeck, is to use a Sequential stack, such as Si Stebbins, so that once you know the start of the sequence you can determine the remaining.

Here’s an excellent free online resource to get more ideas:

Finally, though I like the smartphone idea, I find the whole set-up a bit convoluted and I believe that it would be more impressive if the performer did not consult the address book himself. How?

I have thought-up of a few handlings and I’ll develop below one which has the merit of requiring little memory work. In a nutshell, once the 6 cards have been dealt face down on the table, you bring you smartphone out, launch the contact application and hand it over to the spectator. You tell the spectator the name of a person to call. That person is your medium friend. The helper reads out the phone number (for instance) and you know the card sequence.


Key in the first and last names and phone numbers that give you the info required by creating a contact list using the Mnemonic Major System ( In a nutshell you create a list of 8 first names starting with a specific letter which code the digits 0 to 7 and another list for the last names. You now combine them all (actually only 52 and not 64 (8 x8) are required so leave the extra ones out) so that whatever octal number you obtain, you know which name to call.

So for example, here’s a list of first names that I might use as they are among the first ones to come to my mind:
6->ch-> Cheryll

And here’s a list of last names I might use:

6->ch-> Churchill

You then create as many combinations as necessary, i.e. 52. Actually, you do not have to key in an entry for 00 as it actually the 1st card of your stack and therefore easy to remember.

Remember that these octal numbers are not necessary: 2, 4, 11, 12, 18, 22, 24, 25, 41, 45, 50, 52. Therefore there’s no need to enter a contact for them.

I would enter the names in FirstName LastName format so that the search facility shows different last names associated with the same first name. Keying the last name first would display up to 8 entries with the same last name and this would be weird.

Sarah Smith
Sarah Trump
Sarah Martin

Tim Smith
Tim Trump

Kevin Kane

Once you’ve entered all the names, you have to decide how to code the first card of the sequence. You could code it in the last two digits of the phone number, or in the address field or using many other possibilities. But I’ll describe here my preferred way which might be funny and eerie to a lay audience.

When you create your contact list, add a Notes field to each contact. In this field type something like ‘Sorry, I’m out of reach right now but I’ll still try to help you. The 5th card from top of deck is XX1 and the bottom card is XX2.’

Instead of XX1 you key in the card which is 11 cards further down from the 1st card of the 6 card sequence, and for XX2 the card which precedes the 1st card of the 6 card sequence.

In performance you would ask your helper to read aloud the Notes field, using some motivation. You or your helper would count to the 5th card from the top of the deck and show that the “medium” was right and then show the bottom card to show he/she was right again. Of course this bottom card will tell you that the 1st card of the tabled sequence is the next one in your stack (memdeck or Si Stebbins).

You can now reveal the 6 tabled cards.
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Thanks for your creative ideas I especially like the octal suggestion (that simplifies the mental effort to come up with a two digit identifier) and I have converted all my cheat sheet and phone entries to octal with one minor modification: I flipped the two octal digits so that instead of 14 use 41 etc. because for my setup the cards are coming off the deck low order bits first. I will need to break old habbit of mentally converting entire 6 binary bits. I wrote my first computer program in 1967 when I was 24 years old so have been dealing with binary for many years! But your octal method is so much easier!

As to your thoughts on pretending you have an assistant to call on the cell phone: I tried it and had problems with this on my Android phone: to get to the comments area you have to go into edit mode and do a bit of drilling down just to get to the comments and a spectator would have to do the same thing at performance time and of course you never make the phone call, awkward on Android.

Your concept would be ideal for someone to write an app (that can run in airplane mode) to simulate calling the "medium" and as you suggested a programmed response that lets the magician know the first Aronson (or Tamariz etc) card number of the six cards "I'll be gone for 1 hour" (Jack of Spades), "I'll be gone for 2 hours" (King of Clubs), "I'm not home we are celebrating our 23rd anniversary" (8 of Spades).

For now I will use a cheat sheet of some kind. Am thinking about using a large sharpie pen and cut a slot in a portion and then have a tube with all the crib sheet info on 8 rows that can be twisted and brought up in the slot to show perhaps 7 answers on one row.

Or maybe a clipboard with sheets of paper to "write their thoughts on" and a little flip down card at the top with the cheat sheet info or something like that. Or as a last resort I may do a brute force memorization (yuck) of the DeBruijn first card octal number tied to the Aronson card (but at least it will be a one way memorization ie: number to card but no need to remember card to number).

Thanks again for your thoughts they are much appreciated!
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Profile of Claudio
Thanks glowball. I have enjoyed working on this, so thanks to you for starting this thread.

Yes, I think the octal bit of business is easy to grasp and apply, even for non-math people, as all that is required is associating a pattern with a digit. By the way, I worked for 30 years in IT (as a developer), less than you, but still quite a bit. I started with ‘C’ and not Assembly Language as you probably did.

I don’t have the problem you mentioned about the querying of the contact list. I suppose the difference of behaviour is maybe due to different versions of the Android OS, and almost certainly to the pre-installed contact apps on our phones.

In any case, I wanted to use a different phone contact list app for this effect that would only contain the phony contacts. I actually imported all contacts (as I had already keyed in the phony ones) in the new app and only kept the ones necessary for the trick.

I have installed True Contacts. It’s nice as it allows you to search for the contact and tap it to display it (in read only mode) with the extra field Notes visible without having to scroll down.

You might want to give it a try. Furthermore, I have a permission management app on my phone which is rooted, but there are apps that’ll work on non-rooted devices for OS 6.0+, and have denied the ‘Make Calls’ privilege from True Contacts, so even a wrong manipulation from the spectator wouldn’t have unattended consequences.

Obviously, if one were to market this effect, the route you suggested (i.e. developing a fake contacts app) would be the best solution. But, in all honesty, the whole thing is more an exercise to fool savvy magicians/mentalists than the public at large as it would be equivalent to using a sledge-hammer to crack a nut, IMHO.

The fact is that if you use a memdeck (or why not marked cards?), there’s really no need for any of this (the De Bruijn sequence etc.). It’s only necessary to peek the bottom (or top) card to know the sequence. There are very subtle ways to do just that. I use one method that relies on a rigged card case that’ll fool even very observant people.

But, as I have been so far down the road with this, and have had lots of fun, I’m going to test it on regular audiences and on magi and report back Smile
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