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The Magic Cafe Forum Index » » Magical equations » » DeBruijn using 52 cards and 6 cards and any stack (0 Likes) Printer Friendly Version

glowball
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It took me about 2.5 hours to create the below 52 bit de Bruijn cycle during Monday night football on Oct 8, 2018 while watching Drew Brees break the all time passing yards (a lot of trial and error and just got lucky with some choices but it works perfectly - did several hours of testing and debugging later):

October 8, 2018 Larry Finley starting from scratch created a 6 bit non-repeating de Bruijn sequence in a 52 bit circular cycle:
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

Spectator cuts the 52 card deck as many times as they want and then from face down deck they deal 6 cards face down in a horizontal row on the table. The magician can identify the sixth card (the cards are not marked nor changed in any way from the manufacturer).

You must use a one-way backed deck.
You can use any stack memorization technique that you have mastered ie: Aronson, Tamariz, simple Bridge order, Ace thru King of each suit etc.
Place your mental stack position card in the appropriate place below.
Example your 22nd card is first, your 44th card is second, your 24th card is third and so on (for position 0 and 53 and greater - the problem 12 cards see the next paragraph, it is easily handled).
22 44 24 48 32 0 +1 +3 +7 +15 +31 +63
62 60 56 +49 +35 6 +13 26 52 40 +17
34 4 +9 +19 38 12 +25 50 +37 +11 +23
46 28 +57 +51 +39 14 +29 +59 54 +45 +27 +55 +47
30 +61 58 +53 +43
The positions that have a plus sign means the card is oriented normally in the deck whereas the non plus sign cards are oriented upside down in the deck (using a one way back design).

Place your memorized stack number card in the matching position above and for the odd ball 12 cards do the following:
Place your position card to the following position:
0=your stack position 2
53=your stack position 33
54=your stack position 41
55=your stack position 5
56=your stack position 16
57=your stack position 10
58=your stack position 8
59=your stack position 18
60=your stack position 20
61=your stack position 21
62=your stack position 42
63=your stack position 36

Aronson Stack cards are in my Yelnif 52 - 6 card sequence deck as follows:
AH 6S 3D QS 10D KC +JS +5C +3H +7D +4D +JD
9H 5S 8C +6D +10C AS +2D QH 9D 3C +3S
JH 2H +8D +7S 10H 5H +7H QC +4S +10S +8S
8H 7C +AC +2C +6H KD +4H +AD 2S +4C +5D +9S +9C
KH +QD 6C +JC +KS
Reminder: the positions that have a plus sign means the card is oriented normally in the deck whereas the non plus sign cards are oriented upside down in the deck (using a one way back design).

Note that 40 of the numbers are within the range 1-52 so we can plug our mem stack cards at those 40 places.
Now the challenge is to mentally associate the 12 invalid values (the 11 greater than 52 and the value 0) with the 12 missing mem stack numbers and plug them in at those places.
Below are some general memory tricks to help associate the problem 12 numbers with the 12 cards:.
0 plus 2=2 (maybe O-2 as in Oxygen)
53 minus 20=33 (just say to self 53 33)
54 switch digits=41 (think "car 54 where are you" police car 2 spades to dig up bodies)
55 minus 50=5 (55 just use one 5)
56 minus 40=16 (56 chevy's attractive to 16 year old boys)
57 minus 47=10 (57 chevy's have 10 inch tail fins)
58 minus 50=8 (58 chevy's have 8 tires (not true) but use for memory method)
59 minus 41=18 (59 chevy's have high hp for 18 yr olds)
60 minus 40=20 (must be 20 years old to drive '60 supersport)
61 minus 40=21 (must be 21 years old to drive '61 supersport)
62 minus 20=42 (the 62 year old has a 42 year old wife)
63 switch digits=36 (63 reverse digits to 36)
Then use the translated number to remember your stack position card.

I use Aronson so instead of doing memory translation twice in my head I use direct memory tricks for the problem 12 cards:
0=King of Clubs at north pole zero degrees
53=Jack of Clubs like 33
54=car 54 police 2 Spades in back of the car to dig up bodies
55=9 Shovels digging up speed limit sign
56=8 Clubs in back seat of a 56 chevy to prevent someone from stealing the car
57=Ace of Clubs pasted on Heinz 57 ketchup bottle and a club symbol plugging top opening
58=6 Clubs (3 or each side) on weird oval tail lights of 58 Chevy
59=Ace of Diamonds (Perry Mason 1959 Hans Breel is an Ace diamond cutter)
60=The 60 Minutes clock face has the 5 of Spades pasted on it
61=I graduated in 61 and the homecoming Queen had Diamonds on her neck
62=My wife graduated in '62 and had 9 suitors of her Heart (not true but mem trick)
63=Jack of Diamonds reverse of 36
glowball
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Just to clarify the construction of the Yelnif 52 de Bruijn deck.
Below:
First column is DeBruijn physical position in Yelnif 52 deck.
Second column is the card to use from the position in your mental stack.
When performing: the DeBruijn 6 card binary value will equal your mental stack number with the exception of 12 values (see asterisks) which you will need to memorize.
1 22
2 44
3 24
4 48
5 32
6 2* (0=2)
7 1
8 3
9 7
10 15
11 31
12 36* (63=36)
13 42* (62=42)
14 20* (60=20)
15 16* (56=16)
16 49
17 35
18 6
19 13
20 26
21 52
22 40
23 17
24 34
25 4
26 9
27 19
28 38
29 12
30 25
31 50
32 37
33 11
34 23
35 46
36 28
37 10* (57=10)
38 51
39 39
40 14
41 29
42 18* (59=18)
43 41* (54=41)
44 45
45 27
46 5* (55=5)
47 47
48 30
49 21* (61=21)
50 8* (58=8)
51 33* (53=33)
52 43

Orient the backs normally in the Yelnif 52 de Bruijn deck in physical positions:
7, 8, 9, 10, 11, 12, 16, 17, 19, 23, 26, 27, 30, 32, 33, 34, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 51, 52
Orient the backs the reverse direction in the de Bruijn 52 deck in physical positions:
1, 2, 3, 4, 5, 6, 13, 14, 15, 18, 20, 21, 22, 24, 25, 28, 29, 31, 35, 36, 40, 43, 48, 50

More about the 12 odd ball values:
Example using the 37th card (physically in the de Bruijn 52 stack example):
37 10* (57=10)
When you are performing you will never see the binary total 10 come up within the six cards but you may see the total of 57 come up which you must translate in your head to your stack position 10 card. Just create a mnemonic story for each of the 12 numbers and its card. Note that these odd ball values are outside the normal range of 1-52 (53 thru 63 and 0) therefore they will not interfere with your normal 1-52 memorizations.

For the computer nerds out there: note that any 52 bit Debruijn non repeating 6 bit cycle will produce some values above 52 because the bit configuration 111 and 1111 (and some others) are legitimately needed in the low order bits to represent numbers 7, 15 etc. but when those bits cycle to the high order positions they become 56, 60 etc. Because of this there will be missing normal totals in the 1-52 range and that is what the 12 odd ball values are in my de Bruijn (calling it Yelnif 52) cycle.
glowball
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Glowball,
This is your alter ego here. Your scheme means the first card of the six dealt could be worth 32, the second 16, and so on. How can I make your scheme work where the first card dealt could be worth 1 point, the second 2 points, the third 4 points, the fourth card 8 points etc and still have the bulk of the values point to my stack card numbers?
glowball
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Easy, just construct your deck differently as shown below:

The below (using low to high 6 bit binary scheme) has the 12 bad numbers (those greater than 52 and 0) replaced with good numbers (ignoring the plus and minus signs this is the completed index to your stack positions):
-26, -13, -6, -3, -1, -2, +32, +48, +16, +20, +42, +9,
-31, -15, -7, +35, +49, -24, +44, -22, -11, -5, +34,
-17, -8, +36, +50, -25, -12, +38, -19, +41, +52, +4,
-29, -14, +39, +51, +10, -28, +46, +5, -27, +45, +37, +18, +21,
-30, +47, -23, +43, +33,
Note that the position numbers with the minus sign are the binary 0 cards whereas the ones with the plus sign are the binary 1 cards. Therefore orient the card backs that have the minus sign in the opposite direction from those with the plus sign.

Place your memorized stack number cards in the physical order shown in the index above thus giving you a 52 card DeDruijn 6 bit "low to high bit" deck.

Reminder that for the odd ball 12 cards when performing: if you get the odd ball value in the left column below then that means the sixth card is your stack value card in the position indicated:
0=your stack position 2
53=your stack position 33
54=your stack position 37---
55=your stack position 5
56=your stack position 16
57=your stack position 10
58=your stack position 4---
59=your stack position 18
60=your stack position 20
61=your stack position 21
62=your stack position 42
63=your stack position 9---

Create your own mnemonics to remember these 12 odd ball values and the cards associated with them.
Low to high binary scheme note: the 3 dashes --- for positions 54, 58 and 63 are just to let you know the only ones of the odd ball 12 that are different from the high to low binary scheme odd ball 12.

Note: because we are using the same 52 bit binary pattern for the low to high binary scheme the card's back positions to orient one direction and those to orient the opposite direction are exactly the same as in the high to low binary scheme (but there are different cards sitting in those positions).

If using Aronson memorized values then below is the DeBruin 52 card sequence to use (using low to high 6 bit scheme):
-QH, -2D, -AS, -5C, -JS, -KC, +10D, +QS, +8C, +5S, +9H, +8D,
-4D, -7D, -3H, +10C, +6D, -3D, +6S, -AH, -10S, -9S, +JH,
-3S, -6C, +JD, +QC, -7H, -5H, +10H, -7S, +2S, +9D, +2H,
-4H, -KD, +6H, +2C, +AC, -7C, +8H, +9S, -5D, +4C, +4S, +AD +QD,
-KH, +9C, -8S, +KS, +JC
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