Tritium stack challenge

I would like some of the computer/software experts out there to come up with a deck/stack that can do a three card "Suitability" trick and do a six card "eyes closed if red suit" trick, both tricks using the same deck.

I would like this stack to be expressed in this thread with the digits one through four
(1 = spades, 2= hearts, 3= clubs, 4 = diamonds) thusly:
As an example:
My Hamilton stack "eyes closed if red suit" de Bruijn is based on the following deBruijn from jmbulg:

0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1,
0, 1, 0,1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1,
0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0,
1, 1, 1, 1, 1, 0

But I moved the first 13 bits (cards) to the bottom thus making what was the 14th bit the first bit of the 52 bits and I flipped all the bits (the ones became zero, and the zeros became one). This means the black suit cards are the "1"s and the red suit cards are the "0"s. Don't ask me why because I have forgotten, but there was a reason and that's the way it is. So here is the "eyes closed if red suit" deBruijn that I am currently using:

1010110011
1110001011
1010010100
0110000011
1001001101
10

Let's just refer to the above as the "Red Suit Base deBruijn".

Below is my Hamilton stack expressed in terms of suits (note that it is consistent with the Red Suit Base deBruijn). Note that the red suits are binary zero in the above deBruijn.

3434112213
1114223213
1434214322
4334424433
1421423121
32

But this suit arrangement will not do a three card "suitability" nor will it do a four card "suitability".

If we can rearrange the suit order (but keep the red suits in the same positions and the black suits in the same positions) and achieve a three card suitability pattern then this would be one powerful mem deck!

This would then be called the "Tritium Stack".

I would suggest starting with the above deBruijn pattern of ones and zeros because it has a very nice mixture, but it is okay to come up with a completely different deBruijn sequence of ones and zeros (as long as it works for the eyes closed if red suit trick) in order to make the "suitability" pattern viable.

Some of you may have software that can go through thousands of combinations of deBruijns versus "Suitability" patterns to see if you can find a 3 card "Suitability" pattern that also satisfies a six card deBrujin pattern.

The winner (first to post the solution) gets bragging rights as the co-creator of the Tritium Stack.

If there are multiple solutions submitted then maybe we could call them Tritium-A, Tritium - B, Tritium-C, and so on.
---------

Why the word "Tritium"? The word Tritium has the "Tri" in the first part of the word and the "Suitability" feature uses three ("tri") cards dealt. Also Tritium is a unique powerful radioactive isotope of hydrogen. So we have a unique powerful stack magicians can do something with that no other stack can do.

Also it is convenient to have a simple unique name "Tritium" so that future readers of this thread will know exactly what stack we are talking about.

Reminder that the solution needs to be posted in the following type of format:

3434112213
1114223213
1434214322
4334424433
1421423121
32

But of course it will be an entirely different sequence. There must be thirteen "1"s, thirteen "2"s, thirteen "3"s, thirteen "4"s.

If you are so inclined, please help create this stack.

Thanks much.
Larfin glowball.

Once we have a proper solution expressed by the numbers 1 through 4 then we have a lot of freedom as to which particular cards go into these positions as long as they are of the correct suit.

This means we can easily have a 10 card Jonah sequence built in when we come to assigning the specific cards to the specific positions.

4122233441
3231143142
4433322123
2414442243
2112141133
13


Goody: With the same stack, you can also play a game with FOUR participants and a question on whether their cards could be part of a royal flush (A,K,Q,J,10) or are very low values (2,3,4,5) or medium cards (6,7,8,9). Just put the values of these three groups (0 for the high values 1 and 2 for medium/low or low/medium) with the following pattern (respecting the suit pattern of the Tritium stack, so the first cards should be a royal-flush card of suit 4). Knowing four consecutive group identities allows to know where you are in the stack.

0201101012
0010020002
1210112120
2211120102
0210000122
22

A version with less repeated suits and colors:

2434121241
4431221313
3242441343
3422331421
4114321132
32

and another goody: with four participants and three groups ("picture cards? 0) and for the remaining non picture cards: even or odd 1/2 or 2/1)

2220202121
2011110210
1012110112
1002212211
1202222102
01

To jmbulg:
This is great! Thank you, thank you, thank you!
Winner winner chicken dinner!

Your sequence of suit numbers is very valuable:
4122233441
3231143142
4433322123
2414442243
2112141133
13

The above representations of the suits (note that odd numbers are black suits and even numbers are red suits or could be vice versa) will allow the creation of a gazillion different stacks that will be able to do a six cards dealt "eyes closed if red suit" DeBruijn and can also do a 3 card dealt "suitability" trick!

To my knowledge this is the first such pattern.

To all reading this thread please print off the above 52 digits and save it somewhere in case we ever lose the Magic Cafe.

Here is my first application:

Since this is a wrapping sequence you can cut the deck/sequence anywhere so I elected to move the card at position 52 (which is a club) up to become the first card just so I could have the Four of Clubs as the first card because my wife and I have used the 4C as the mentalism force card so I want to have it handy. I know I could have treated the "4"s and the "2"s as clubs and spades and the "1"s and "3"s as diamonds and hearts and thus have the Four of Clubs as the first card that way, but it was easier to keep the jmbulg solution and just move one position.

My first application Tritium-JmLf1:
4C, 6D, 8S, 9H, QH, 7H, 5C, AC, 4D, 2D, 10S, 3C, 5H, 6C, JS, 5S, KD, JC, 6S, JD, 6H, 5D, 3D, 8C, QC, 10C, 4H, 8H, 3S, JH, 7C, AH, 8D, KS, 7D, 10D, 9D, KH, 3H, AD, 9C, 2H, QS, 2S, 10H, 4S, QD, 9S, AS, 2C, KC, 7S

I have a 10 card (2 handed, five cards each) Jonah routine built in using the five of hearts through the five of diamonds.

Translating jmbulg suits into deBruijn bits of ones and zeros (red suits are one, black suits are zero):

10111 0011001 0001 00 1111 000 11 010110
111111 0100 101 000000

And I moved bit 52 around to become bit number one:

010111 0011001 0001 00 1111 000 11 010110
111111 0100 101 00000

I haven't had a chance to fully test everything but will do. Note that jmbulg has been very good at everything he's submitted so I'm assuming this all works.

Happy as a lark thanks to jmbulg!
glowball.

PS: I just saw jmbulg 2nd post and may work with it.

----------------------

Even more balanced looking version:

1314344112
4433234122
4142121413
2213343123
1342324243
21

with no sequence of three cards of the same suits, no sequence of 6 or 5 cards of the same color.

Goody version with three groups (pictures, even numbers, odd numbers) with only one sequence of four cards of the same group (numbers)

2012021120
0121221112
1102002210
2101222022
2120111101
12

Note: Tritium-Jm1Lf1 stack:
I did NOT accommodate the phishing feature of: Royal flush/low cards/medium cards, but did accommodate the six card red suit DeBruijn feature and did accommodate the three card suitability feature.

I also created two sorted cheat sheets (one for the "six cards dealt eyes closed" if red suit, and another cheat sheet for the three cards dealt suitability trick) and everything worked perfectly.

However jmbulg's newer Tritium-Jm2 suit pattern looks even better, and I especially like the odd number cards versus even number cards phish capability better than the low cards versus medium cards phish.

It's amazing how much he's got packed into the Tritium-Jm2 suit sequence pattern:
1. Suitability with three cards dealt.
2. Eyes closed if red suit six cards dealt.
3. Phish court cards, odd, even (four cards dealt).
We can probably finesse a 10 card Jonah sequence into it.

Another nice thing about his Jm2 version is that when doing the "eyes closed if red suit" trick you will never have all six people with their eyes closed nor all six people with their eyes open which would look bad (you will have at least one person that is different, and most of the time a good mixture).

I definitely plan to create a stack based on his Jm2 pattern and plan to create two sorted cheat sheets for it.

If all goes well, I plan to memorize the whole stack (sequence and card positions). I will call the stack Tritium-Jm2Lf2. Will probably also memorize the cheat sheet for the six cards dealt "eyes closed if red suit" trick.

Will probably stick with a cheat sheet for the three card suitability trick because I've got a unique cheat sheet method (completely different from Larsen and Wright's) that will make it super fast at performance time.
----------------------

Final (?) version, now also the goody version well balanced (no situation with four cards of the same group)


2113213322
1242323131
4144243241
2344134312
1434114223
34

2201202212
0110021222
1110112121
0122100121
1021122021
02

Tritium-Jm3 from jmbulg. Great again!

To all:
The above "goody" pattern: the "0"s are the face cards. The "1"s are the odd numbered cards, the "2"s are the even number cards (or you could use vice versa).

Here is the Tritium-Jm3 notation combined with the "goody" feature.

Note that I have used the following two character notation convention:
First character will be one of three characters:
F or O or E (Face card, Odd number, Even number).
Second character will be the suit: S, H, C, D (Spades, Hearts, Clubs, Diamonds).

Tritium-Jm3 card pattern:

EH, ES, FS, OC, EH, FS, EC, EC, OH, EH,
FS, OH, OD, FH, FC, EH, OC, ES, EC, ES,
OD, OS, OD, FD, OH, OD, EC, OH, ED, OS,
FH, OC, ED, ED, OS, FC, FD, OC, ES, OH,
OS, FD, EC, OD, OS, ES, ED, FH, EH, OC,
FC, ED

Print/save the above pattern because it is very valuable! Remember all the things that a stack based 100% on this incredible pattern can do!

Of course you could flip-flop the red suits for the black suits and you could also flip-flop the even numbers for the odd numbers, but keep it simple and just use the above pattern.

There are a gazillion stacks that will fit the above pattern. None currently exist (unless someone has created one in the last few days). I will create one shortly.

----------------------

Here is the red suits versus the black suits deBruijn to be used with the six cards dealt trick:

0111011100
1000101111
0100001001
0100110110
1010110001
10

The above deBruijn is just for reference so I can see any clumping of suit colors and all in all it's about as disperse as you can get.

----------------------

Here is my Jm3Lf2 stack (has a 10 card Jonah sequence after the 7S ie: 4S thru JS):

6H, 6S, JS, 7C, 2H, KS, 8C, 2C, AH, 10H, QS, 7H, 9D, KH, QC, 8H, AC, 8S, 10C, 2S, AD, 9S, 5D, KD, 3H, 7D, 4C, 5H, 2D, AS, QH, 5C, 8D, 10D, 3S, KC, JD, 3C, 10S, 9H, 5S, QD, 6C, 3D, 7S, 4S, 6D, JH, 4H, 9C, JC, 4D

The stack I want to memorize will be the above sequence but the top card will be the 4C (just cut the above deck so the 7D is on the bottom and keep the deck that way when doing memdeck positional tricks).

Tritium-Jm3Lf3 stack (notice that the stack above I'm calling it Lf2 whereas the below Stack I'm calling Lf3):

4C, 5H, 2D, AS, QH, 5C, 8D, 10D, 3S, KC, JD, 3C, 10S, 9H, 5S, QD, 6C, 3D, 7S, 4S, 6D, JH, 4H, 9C, JC, 4D, 6H, 6S, JS, 7C, 2H, KS, 8C, 2C, AH, 10H, QS, 7H, 9D, KH, QC, 8H, AC, 8S, 10C, 2S, AD, 9S, 5D, KD, 3H, 7D

Of course the deck can be cut anywhere when doing the six card "eyes closed if red suit" trick or doing the three card "Suitability" trick, or doing the four card "goody" trick. Of course if doing the 10 card Jonah trick then cut the deck so the 7S is the bottom card of the deck (note that the 9C is the Jonah card).

Before I memorize Tritium-Jm3Lf3 above, I plan to develop cheat sheets for all its features and test everything out. Once tested/proven then I plan to memorize the thing and make it my main performance deck.

Octal Crib sheet for Tritium-Jm3Lf3 to know identity of first card of six cards dealt (of course you must have the whole stack memorized in order to know the other five cards):

Each octal digit is 4+2+1 (if red suit):
02=AC..20=QC..30=JC..45=JD..61=4D
04=6S..21=7C..31=5C..46=4H..62=8D
05=8S..22=KC..32=4C..47=3D..63=JH
06=KS..23=6C..33=2C..50=KH..64=9D
10=JS..24=5S..34=4S..51=QD..65=5H
11=3S..25=TS..35=QS..52=9H..66=3H
12=3C..26=AS..36=9S..53=2D..67=AH
13=TC..27=2S..41=8H..54=QH..71=6D
14=9C--------------42=6H..55=7D..72=7H
15=8C--------------43=2H..56=TH..73=KD
16=7S--------------44=TD..57=AD..75=5D

Reminder about the six cards dealt that the first three cards if a red suit add up to make the first octal digit and the second three cards if a red suit add up to make the second octal digit. Of the three cards: The first one dealt is worth 4 points (If it is a red suit), the second card dealt is worth two points (If it is a red suit), the third card dealt is worth one point (If it is a red suit). Add the three values to know the first octal digit.

You do the same thing for the second three cards to know the second octal digit.

This becomes very easy and you will recognize the three card pattern that make the octal value of 0 thru 7, but of course you have to ask the 6 spectators to indicate that they have a red suit by holding up their hand, or standing up, or stepping forward, or closing their eyes or something. You mentally segregate the six spectators into two groups of three in order to mentally form the two octal digits.

For those who may want to use the stack but do not want to memorize the stack, I plan to post the same crib sheet as above but with all six cards for each octal code. Because there will be six two character card names after each equal sign, this means the crib sheet will be much bigger and also harder to perform because you will have to glance at it multiple times (few magicians can remember all six cards with one glance at the crib sheet).

Memorizing the stack and using the smaller crib sheet above is the better way.

Even better still is to memorize the stack and memorize the small crib sheet, which I plan to do.

Also I am working on a crib sheet for the three cards dealt suitability trick and another crib sheet for the goody trick and plan to post them here.
---------

Tritium-Jm3Lf3 crib for 6 cards dealt Octal red suit trick (all six cards shown):
02=AC,8S,TC,2S,AD,9S 22=KC,JD,3C,TS,9H,5S
04=6S,JS,7C,2H,KS,8C 23=6C,3D,7S,4S,6D,JH
05=8S,TC,2S,AD,9S,5D 24=5S,QD,6C,3D,7S,4S
06=KS,8C,2C,AH,TH,QS 25=TS,9H,5S,QD,6C,3D
10=JS,7C,2H,KS,8C,2C 26=AS,QH,5C,8D,TD,3S
11=3S,KC,JD,3C,TS,9H 27=2S,AD,9S,5D,KD,3H
12=3C,TS,9H,5S,QD,6C 30=JC,4D,6H,6S,JS,7C
13=TC,2S,AD,9S,5D,KD 31=5C,8D,TD,3S,KC,JD
14=9C,JC,4D,6H,6S,JS 32=4C,5H,2D,AS,QH,5C
15=8C,2C,AH,TH,QS,7H 33=2C,AH,TH,QS,7h,9d
16=7S,4S,6D,JH,4H,9C 34=4S,6D,JH,4H,9C,JC
20=QC,8H,AC,8S,TC,2S 35=QS,7H,9D,Kh,QC,8h
21=7C,2H,KS,8C,2C,AH 36=9S,5D,KD,3H,7D,4C
----------------------
41=8H,AC,8S,TC,2S,AD 56=TH,QS,7H,9d,Kh,QC
42=6H,6S,JS,7C,2H,KS 57=AD,9S,5D,KD,3H,7D
43=2H,KS,8C,2C,AH,TH 61=4D,6H,6S,JS,7C,2H
44=TD,3S,KC,JD,3C,TS 62=8D,TD,3S,KC,JD,3C
45=JD,3C,TS,9H,5S,QD 63=JH,4H,9C,JC,4D,6H
46=4H,9C,JC,4D,6H,6S 64=9D,KH,QC,8H,AC,8S
47=3D,7S,4S,6D,JH,4H 65=5H,2D,AS,QH,5C,8D
50=KH,QC,8H,AC,8S,TC 66=3H,7D,4C,5H,2D,AS
51=QD,6C,3D,7S,4S,6D 67=AH,TH,QS,7H,9D,KH
52=9H,5S,QD,6C,3D,7S 71=6D,JH,4H,9C,JC,4D
53=2D,AS,QH,5C,8D,TD 72=7H,9D,Kh,QC,8h,AC
54=QH,5C,8D,TD,3S,KC 73=KD,3H,7D,4C,5H,2D
55=7D,4C,5H,2D,AS,QH 75=5D,KD,3H,7D,4C,5H

Note that the cafe editing software and my Google docs and Google keep software don't line up too well but the information is accurate. I had every other line in bold notation and better spacing but the cafe software stripped it.

Tritium-Jm3Lf3 Suitability 3 cards dealt Sorted Crib Sheet:
The 3 spectators tell the magician the suit of their card.

The magician secretly peeks at the
Below crib sheet and names the 3 cards.

The letter is the first card suit.
The second and 3rd card use SHoCkeD
to form the 2 digits in front of the equal sign.

SHoCkeD: Spades=1, Hearts=2, Clubs=3, Diamonds=4.
Note that SHoCkeD is easy because of lobes/points.

C12=3T9
C13=A8T
C14=T2A
C21=72K
C22=2AT
C23=Q8A
C24=452
C32=82A
C34=9J4
C41=637
C42=J46
C43=KJ3
C44=58T
D11=374
D12=2AQ
D13=T3K
D14=A95
D21=466
D22=6J4
D23=9KQ
D24=K37
D31=J3T
D32=745
D34=Q63
D41=8T3
D42=5K3
H11=66J
H12=TQ7
H13=2K8
H14=95Q
H21=ATQ
H23=J49
H31=8A8
H32=KQ8
H33=49J
H34=Q58
H41=52A
H42=79K
H43=374
S13=6J7
S14=746
S21=T95
S23=AQ5
S24=Q79
S31=8T2
S32=J72
S33=K82
S34=3KJ
S41=2A9
S42=46J
S43=5Q6
S44=95K

Print off the above crib list and then cut the list into the 4 suit groups of 13 and glue somewhere (front of the tuck case, or back of ad card, or on a clip board etc. where you can secretly glance at it after they name their suits.

Note that after you look down to the proper row there are only 3 characters after the equal sign which makes it very easy to silently repeat to yourself those 3 characters (those are the 3 cards, you are no longer concerned about the suit because they have told you the suit). You use the 3 suits to find the proper row, but once found you concentrate on the 3 characters after the equal sign.

Example:
The deck was cut several times (by a neutral person) and then 3 cards dealt face down to 3 spectators who each look at their card.
The magician asks for the suit name from each spectator.
Spectator 1 says "Clubs".
Spectator 2 says "Clubs".
Spectator 3 says "Diamonds".
Based on those 3 suits he magician thinks "C34" then secretly looks down the crib sheet to see the C34 row and then sees "9J4" and mentally keeps repeating "9J4" over and over.


The magician can reveal the 3 cards in any order. I like to start with the 2nd person. In this example:
"Sir, I see a high card, it is the Jack, what was your suit? Clubs, oh yes the Jack of Clubs".
Then the third person "the Four of Diamonds".
Then the first person "You are thinking of a Nine, what was your suit? Oh yes the Nine of Clubs".

In my book, Mathematical Stacks, the Suit Bracelet Stack in chapter four, supports both three suits identifying a card as in Larsen and Wright's trick named Suitabiliy, and also supports a six-card red-black binary bracelet code.

The Two Suits Suitability Stack in chapter six, supports three suits identifying a card, and also any two suits chosen also form a six-card binary bracelet code.

Wow! Didn't know that! Well, one thing that Tritium has that may be different (not sure) from Bill Hallahan's stacks is that the Tritium stack also has a 10 card Jonah routine built-in.

If I had known about Bill's stacks I probably would not have pursued Tritium and just used one of his stacks as my main mem deck supplanting Aronson.

Recently Bill sent me a copy of his stuff and I only had time to read one part which was how to present a three card suitability. This alone is worth the price of his book. So I highly recommend anybody who's doing the suitability trick with three cards (or other deBruijn type stacks) to get Bill's book. I think you can get it on lybrary.com.

If you are doing the suitability trick for a lay audience imo they will not have a clue because there is no hint of a pattern with the presentation that Bill outlines.

Bill, if you are out there could you verify where to buy Mathematical Stacks and post it here?

Thanks.

"Mathematical Stacks" by Bill Hallahan https://www.lybrary.com/mathematical-stacks-p-926418.html
A very interesting ebook, if I may say so myself.

Thanks Chris.

Glowball, these are the descriptions of those stacks in the book.

In Chapter Four:


and in Chapter Six:


Features of other stacks in the book are listed at Mathematical Stacks.

The book has the most comprehensive explanation of card-to-position and position-to-card for a Si Stebbins Stack in any source that I'm aware of.

The book is at the link that Chris provided, i.e. https://www.lybrary.com/mathematical-stacks-p-926418.html.

Check out the link below on how to do the "Suitability" trick using the Tritium-Jm3Lf3 stack without a cheat sheet:

https://themagiccafe.com/forums/viewtopi......orum=205

The same principle can be applied to Bill Hallahan's Suitability type stacks but of course a whole different set of mnemonics would need to be developed.