

glowball Special user Nashville TN 662 Posts 
Need ternary 4 bit deBruijn
I need a ternary 4 bit unique for 52 bits that cycles back to the first bit. I plan to use three bicycle deck types (rider, maiden, mandolin) to do "eyes closed if red" type deBruijn trick without the equivocate "closing their eyes" and not based on red cards therefore instead of two bits have 3 bit types (not just 0 and 1 instead have 0, 1, 2) and 4 occurrences in the string which would yield 3x3x3x3 = 81 which is more than enough to cover 52 cards. Next is to develop this specialized ternary (not binary) debruin string ie 11110000222200110220102.... etc. The reason for this special deBruijn is I want to cut the number of selected consecutive cards down from six to four. This way I will have just four people on stage instead of six. Also I could easily do the trick close up with just two people that each have two cards (one in each hand). I also want to use a full 52 card deck (no repeating cards). I plan to use this in conjunction with a mem deck (four cards taken in sequence) and have a crib card to reference for the different 4bit patterns, and once I determine the first of the four cards based on that pattern I will know the other 3 cards because I have the whole deck memorized. Just think of this 52 tri bit 4 bit pattern as overlaying the mem deck cards so that each card has a unique 4bit pattern. Let's say rider back = 0, maiden back = 1, mandolin back = 2. You get the idea. It's kind of like having marked cards without having any marks and the magician can read the pattern from a great distance. I could use one way backs but there is always the danger that a spectator may rotate their card 180 degrees. I've seen examples on the internet of the sixbit version done with two different color cards (red and blue) but that is obvious to spectators in the know. By using three very similar backed cards the spectators should not know and they can look at their individual card and find no secret markings. I think there are some of you out there that have software that could give me the appropriate ternary deBruijn sequence. tomasB, jmbulg, claudio, others, your help is much appreciated! Thanks. Larfin glowball 
glowball Special user Nashville TN 662 Posts 
I played around with some hodgepodge numbers (did manually, no computer) and had to do some tweaking and finally came up with the following sequence:
111100002222 000111222120 102201221011 021020112002 0012 Above is broken down into the below 52 patterns and I moved it to a spreadsheet and sorted them as text so it was easy to spot any duplicates and I double checked twice and there are no duplicates! Therefore it is a good trenary 4 bit 52 deBruijn wrapping sequence to overlay on a mem stack and then use rider backs in the zeros positions, maiden backs in the ones positions, and mandolin backs in the twos positions. Next I'll make a cheat sheet for my Aronson stack and post it below. I'll make one up for the Tamariz stack and post it also. 1111 1110 1100 1000 0000 0002 0022 0222 2222 2220 2200 2000 0001 0011 0111 1112 1122 1222 2221 2212 2120 1201 2010 0102 1022 0220 2201 2012 0122 1221 2210 2101 1011 0110 1102 1021 0210 2102 1020 0201 2011 0112 1120 1200 2002 0020 0200 2001 0012 0121 1211 2111 
glowball Special user Nashville TN 662 Posts 
In case I don't get around to posting the Tamariz and Aronson cheat sheets (I'll be 79 next month) Below are instructions on how to do it for any memorized stack:
The way you make a cheat sheet is first list 4 bit patterns from my prior post into column A of a spreadsheet program such as Google sheets or Excel. example: 1111 Will be in cell A1 1110 Will be in cell A2 1100 will be in cell A3 and so on until you have 52 cells filled in. Next in the B column of the same spreadsheet you type in each card of your mem stack. example for Tamariz: 4C will be in cell B1 2H will be in cell B2 7D will be in cell B3 and so on until you have 52 entries in the B column. next copy the A column to the C column then copy the B column to the D column. Make sure all 4 of these columns are defined as text before you do any of this. Next use column C as your sort column (ascending) but specify that column C and D Will move together. If you are not familiar with spreadsheet commands just ask someone who is familiar, this is very easy to do. After sorting columns C and D highlight the 52 cells in column C and D and then print them off. This is your cheat/crib sheet. The sorting allows you to quickly find the pattern you see on the four cards otherwise you might have to visually scan nearly all 52 rows to find your pattern. Tamariz example if I see the pattern Maiden, Maiden, Rider, Rider I mentally translate that to 1100 and look down on my cheat sheet and see just to the right of 1100 is 7D therefore I know all four cards the spectators are holding. For an Aronson cheat sheet that same pattern would mean 1100 is 5C etc. For Tamariz if you see the pattern: mandolin, mandolin, rider, maiden that translates to 2201 which on the Tamariz cheat sheet would show 2201 is 2C (the 27th card in the stack). 
Claudio Inner circle Europe 1757 Posts 
Hi Larfin,
I haven't had time yet to digest what you posted but it looks promising. Meanwhile, here's a link about the DeBruijn Card trick from Grey Matters which has a few interesting links as well on a 4bit method. I suggest you read the Grey Matters article before watching the video which has an error. PS: Congrats on soon reaching 79!! 
glowball Special user Nashville TN 662 Posts 
Claudio, thanks, I've had my two shots and my booster and I just got over a mild case of covid. For last 3 years I have eaten strictly plantbased and whole foods and my health numbers have become excellent so hopefully I'll be around a while to do some more postings.
Yes several years ago I had seen James Grime (YouTube name: singingbanana) video using four bit based binary deBruijn and 16 cards but I had not read that particular gray matters article that you referenced and it's pretty cool the way they used mnemonics to remember the binary patterns, so thanks again. Before I started this thread I had planned to use James' deBruijn wrapping pattern 1111000010011010 to make up a deck of 8 riders and 8 maidens (the maidens would be in the ones position because they have a little more vertical narrow white area and look somewhat like the number one). Then of course I will duplicate those 16 cards two more times giving 48 cards. Everything has pros and cons and my thoughts about James' 4 bit 16 times 3 binary deck versus my ternary 4 bit 52 deBruijn deck are as follows: James 4 bit 16 times 3 binary deck: pros: only 16 patterns so you can use mnemonics much easier to remember the patterns, also with only 16 cards then it's also easier to memorize the cards and have a simple scheme and not need a cheat sheet cons: when showing the deck face up it must be very brief, also at the end of the trick the deck cannot be examined, you must phish to get the pattern ("who has red cards") Larfin glowball 4 bit ternary 52 deck using rider, maiden, mandolin cards: pros: whole deck can be spread face up and looked at by the spectators, can use with an existing mem deck (Aronson, Tamariz etc), no phishing is done, the pattern can be read from a considerable distance, easy to set up since the magician has the 52 cards memorized cons: requires the use of a cheat sheet to tie the 52 patterns to each card (cheat sheet could be printed on the ad cards), the backs of the cards cannot be scrutinized together however an individual card held by a spectator can be scrutinized. I plan on making up both decks but for James deck I plan on using riders and maidens and thus don't have to phish for red cards and I plan to use the first 16 cards from a mem (in my case Aronson) deck (times 3) and use a simple 16 row cheat sheet on the back of an ad card. I've got a couple of magic club meetings coming up so I'll try both decks and see how it goes over. Later I may simply try to memorize each of the 52 patterns onto my Aronson cards and thus eliminate the need for a cheat sheet when using my ternary deck. 
glowball Special user Nashville TN 662 Posts 
Ternary 4 Bit (4 card) Sorted Aronson Cheat Sheet
0000  9S 0001  2D 0002  AS 0011  KD 0012  6D 0020  8H 0022  3H 0102  3D 0110  JH 0111  7D 0112  9H 0121  QC 0122  4H 0200  9C 0201  3C 0210  4S 0220  QH 0222  6C 1000  2H 1011  JC 1020  6H 1021  JD 1022  7H 1100  5C 1102  TC 1110  KC 1111  JS 1112  8C 1120  KS 1122  3S 1200  6S 1201  AH 1211  2C 1221  KH 1222  AD 2000  5H 2001  QS 2002  4C 2010  8S 2011  2S 2012  7C 2101  TD 2102  TH 2111  9D 2120  QD 2200  TS 2201  5D 2210  4D 2212  5S 2220  AC 2221  7S 2222  8D Note that the 4 card pattern reveals the first card of the four. Note that this whole ternary based magic trick is useless without a cheat sheet. 
glowball Special user Nashville TN 662 Posts 
Tamariz cheat sheet.
Ternary 4 bit (4 card) 52 sorted Tamariz cheat sheet: Tam 0000  4H Tam 0001  QC Tam 0002  6D Tam 0011  8H Tam 0012  TD Tam 0020  QD Tam 0022  AS Tam 0102  TC Tam 0110  TS Tam 0111  6S Tam 0112  4D Tam 0121  6C Tam 0122  8D Tam 0200  7C Tam 0201  4S Tam 0210  7S Tam 0220  KD Tam 0222  5H Tam 1000  3C Tam 1011  8C Tam 1020  AD Tam 1021  JC Tam 1022  5D Tam 1100  7D Tam 1102  KH Tam 1110  2H Tam 1111  4C Tam 1112  5S Tam 1120  AC Tam 1122  9H Tam 1200  9C Tam 1201  8S Tam 1211  AH Tam 1221  5C Tam 1222  KC Tam 2000  3D Tam 2001  QS Tam 2002  JS Tam 2010  6H Tam 2011  7H Tam 2012  3H Tam 2101  JD Tam 2102  TH Tam 2111  9D Tam 2120  3S Tam 2200  QH Tam 2201  2C Tam 2210  KS Tam 2212  JH Tam 2220  2S Tam 2221  2D Tam 2222  9S Note that the four card pattern reveals the first card of the four. Note that the first digit designates the type of back design for the card. Example "0122  8D" the first digit in this case "0" means the 8 of diamonds must be a RIDER backed card (for a Tamariz deck). Note in the above example spectator one is holding a rider back, spectator two is holding a maiden back, spectator three is holding a mandolin back, spectator four is holding a mandolin back. This signals that spectator one is holding the eight of diamonds. Example "1021 JC" the first digit in this case "1" means the Jack of clubs must be a MAIDEN backed card (for a Tamariz deck). Example "2120  3S" the first digit in this case "2" means the three of spades must be a MANDOLIN backed card (for a Tamariz deck). 
glowball Special user Nashville TN 662 Posts 
I'm making a very slight change to my ternary sequence. Position 36 changed from a "1" to a "2". Normally you cannot change a deBruin sequence number willynilly because you will create duplicate patterns (a duplicate pattern is a bad thing, means that it's not a true deBruijn). I lucked out because it is still a true "no duplicate" four bit sequence. The reason for this change is that the old sequence had a total of 18 zeros, 17 ones, 17 twos but I want a breakdown of 18 zeros, 16 ones, 18 twos because of future possibilities that I won't get into here.
This is the new better ternary wrapping deBruijn with the 36th bit changed to a 2: 111100002222 000111222120 102201221012 021020112002 0012 Because of this small change I will replace the maiden back Jack of diamonds (in Aronson deck position 36) with a mandolin back Jack of diamonds and create a better sorted Aronson cheat sheet (see below): Better Aronson Sorted Ternary Cheat Sheet: Aron 0000  9S Aron 0001  2D Aron 0002  AS Aron 0011  KD Aron 0012  6D Aron 0020  8H Aron 0022  3H Aron 0102  3D Aron 0111  7D Aron 0112  9H Aron 0120  JH Aron 0121  QC Aron 0122  4H Aron 0200  9C Aron 0201  3C Aron 0210  4S Aron 0220  QH Aron 0222  6C Aron 1000  2H Aron 1012  JC Aron 1020  6H Aron 1022  7H Aron 1100  5C Aron 1110  KC Aron 1111  JS Aron 1112  8C Aron 1120  KS Aron 1122  3S Aron 1200  6S Aron 1201  AH Aron 1202  TC Aron 1211  2C Aron 1221  KH Aron 1222  AD Aron 2000  5H Aron 2001  QS Aron 2002  4C Aron 2010  8S Aron 2011  2S Aron 2012  7C Aron 2021  JD Aron 2101  TD Aron 2102  TH Aron 2111  9D Aron 2120  QD Aron 2200  TS Aron 2201  5D Aron 2210  4D Aron 2212  5S Aron 2220  AC Aron 2221  7S Aron 2222  8D Reminder that the above cheat sheet uses a mandolin jack of diamonds. 
glowball Special user Nashville TN 662 Posts 
Better sorted Tamariz ternary 4 bit 52 wrapping deBruijn:
Tamar 0000  4H Tamar 0001  QC Tamar 0002  6D Tamar 0011  8H Tamar 0012  TD Tamar 0020  QD Tamar 0022  AS Tamar 0102  TC Tamar 0111  6S Tamar 0112  4D Tamar 0120  TS Tamar 0121  6C Tamar 0122  8D Tamar 0200  7C Tamar 0201  4S Tamar 0210  7S Tamar 0220  KD Tamar 0222  5H Tamar 1000  3C Tamar 1012  8C Tamar 1020  AD Tamar 1022  5D Tamar 1100  7D Tamar 1110  2H Tamar 1111  4C Tamar 1112  5S Tamar 1120  AC Tamar 1122  9H Tamar 1200  9C Tamar 1201  8S Tamar 1202  KH Tamar 1211  AH Tamar 1221  5C Tamar 1222  KC Tamar 2000  3D Tamar 2001  QS Tamar 2002  JS Tamar 2010  6H Tamar 2011  7H Tamar 2012  3H Tamar 2021  JC Tamar 2101  JD Tamar 2102  TH Tamar 2111  9D Tamar 2120  3S Tamar 2200  QH Tamar 2201  2C Tamar 2210  KS Tamar 2212  JH Tamar 2220  2S Tamar 2221  2D Tamar 2222  9S Reminder that the above Tamariz cheat sheet uses a mandolin Jack of Clubs (36th position). 
glowball Special user Nashville TN 662 Posts 
After trying this card trick on some friends I have another change to make. I want to make the mandolin cards represent "0" Instead of "2" because I have come up with a scheme that uses the bright white cherubs in the upper corners to represent the numbers "0", "1", "2".
When standing at a distance and looking at the backs of the 4 selected cards there are no bright objects in the upper left and upper right corners of each mandolin card. The mandolin card design has a small butterfly and a large feather in those areas but they are NOT a bright white therefore it appears as nothing thus it means "0". The maiden backed cards will still represent the number "1". The rider back cards will now represent the number "2". Of course I have to physically get the appropriate cards in my deck (get rid of the current mandolin backed and rider back cards and replace them with the correct back design cards in the right places. To further enhance the magician's visual perception I have used a waterbased paint pen to dull the brightness of the cherub (or is it a mermaid) in the upper right corner (and of course the lower left corner) of the maiden backed cards. So now there is only one bright object in the upper portion of the maidenbacked cards. The audience doesn't notice this minor difference. So now it is much easier to see the ternary pattern from a distance by noticing how many bright objects there are in the upper left and upper right corner of each card. If I see zero bright objects this means "0". If I see one bright object this means "1". If I see two bright objects this means "2". Not only does this method make it easier to see it also makes the mental translation from image to number much easier. More about the dulling of the cherub/mermaid: for a blue back card use a black (not blue) waterbased (nonpermanent) paint pen. For a red back card use a red waterbased (nonpermanent) paint pen. After applying a very small amount of paint to the appropriate white areas I used a moistened finger to smear/blot that area. Try not to get any paint on the tiny face of the cherub/mermaid because that looks a little weird but not a big deal if you do. There should not be any paint lines or large amount of paint making the paint itself noticeable. Done correctly the cherub/mermaid will just be dull. First try this on a few old junk cards. The problem with permanent sharpie pens is they are harder to blot and they make unwanted permanent noticeable lines and dark unnatural blobs. I have experimented and been a little bit successful with the permanent pens that have a sharp point and by making tiny little dots and quickly smearing them but the nontoxic waterbased pens from Dollar Tree have worked much better for me. This new method (number of bright cherubs/mermaids) of determining 0, 1, 2 does not change the cheat sheet. I made a red backed Aronson deck and a blue back Aaronson deck using this technique (replacing the appropriate cards with mandolin and maiden cards and dulling the maiden cards as explained above) and in both cases my almost 79yearold eyes wearing prescription glasses could consistently read the four card pattern from 25 ft distance. Then glanced at my cheat sheet numbers (glued onto advertisement cards) openly casually held in my hand and correctly identified the first card of the four cards (then of course I knew the other three cards from the Aronson stack). 
glowball Special user Nashville TN 662 Posts 
Hmmm, why use mandolin or maiden back cards at all because the dulling technique could be applied using all Rider back cards! Thus saving the expense of special decks. Another benefit is the back designs are all the same IE Rider backed.
This could be done using any mem stack. 1111000022220 0011122212010 2201221012021 0201120020012 Using the above 52 bit ternary pattern as a guide dull the cherubs has follows: The cards that are in the one's position have their upper right and lower left cherubs dulled. The cards in the zeros position will have all four cherubs dulled. Nothing done to the cards that are in the twos position. There are a few pros and cons mostly pros for using all Rider backs: Pros: cheaper (saves about $15 to $20 that mandolin plus maiden would cost), easier to obtain the Rider cards Walmart etc, deck of Rider cards are all the same back design. Cons: time consuming to dull up the entire deck (on average it takes me right at about 1 hour to create one of these all Rider back decks). Note that using mandolins and maidens that will also take some time, about 20 minutes to initially assemble that type of deck. For the all Rider back deck you cannot truthfully say "these cards are not marked" but when are magicians known for being truthful. lol I know we are just actors saying the lines of a fictitious magician, but it does bother me to lie to my audience, well, just a little bit "these cards are shuffled" yeah, right (sarcasm). I know, I know don't run if you're not being chased but in this case you are being chased because how else standing 25 ft away the whole time could the magician know what the four cards are. I am thinking about dispelling that thought by saying something like "I am standing so far away because people in the past have falsely accused me of using marked cards so I do not want to be close when the deck is cut three times nor when the 4 cards are dealt on the table nor when you hold the four cards to your forehead to transmit your thoughts". Creation process: 1. Buy/obtain Bicycle Rider back deck. 2. Put the cards in your memorized stack order 3. Using the above 52 bit ternary pattern dull the appropriate cherubs per instructions above. 4. create a cheat sheet for your memorized stack then sort it and print it off (If you are using Tamariz or Aronson then you're in luck because those sorted cheat sheets are in this thread further above see Tamar list and Aron list). 
glowball Special user Nashville TN 662 Posts 
I thought of another small negative about the dull technique on all Rider back cards:
if a spectator notices something strange about the cards the magician does not have the same verbal "out" as when using mandolins and maidens. Example when using mandolins, maidens, and riders together in one deck and a spectator notices any difference the magician can just quietly mumble "oh they must have gotten mixed in accidentally but not a problem I can fix that easily when I get home". It's easy to see how the cards could have accidentally gotten mixed in and people understand that. With a dulled up all rider back deck that excuse statement does not make good sense. I guess the magician could say "yeah these cards are getting old I need to get a new deck" and just proceed like nothing has been noticed. I have done this trick about three times and no one has noticed any strange looking cards when I used all rider back dulled cards nor when I used the mandolin and maiden back cards. I'll do this trick a bunch more times with the all rider back cards and I suspect no one is going to notice so this may be a moot issue about what to do if someone does notice strange cards. 
glowball Special user Nashville TN 662 Posts 
Based on the below definition from Wikipedia the term trinary is synonymous with ternary. Also instead of calling the 52 digits "bits" I should have called them "trits"!
Wikipedia: "A ternary /ˈtɜːrnəri/ numeral system (also called base 3 or trinary) has three as its base. Analogous to a bit, a ternary digit is a trit (trinary digit). One trit is equivalent to log2 3 (about 1.58496) bits of information." 
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