de Bruijn Card Trick


Hello, everyone! Before Christmas, I showed you some sequences of numbers. They were called de Bruijn sequences. And they’re designed to contain every combination of some numbers without repeating any combinations. For example, this sequence [1111 2222 1221 1212] contains every combination of 1 and 2 of length four. So 1111 is in there. 2212 is in there. And even something like 1211 is in there, but it wraps around–it goes back to the start. So, the inventor of these sequences, Nicolaas de Bruijn, he died in February, I’m afraid. But don’t feel too bad for him– he was 93. But in honor of Nicolaas de Bruijn, I’m going to show you a card trick that uses this sequence. So this is the idea: you get a pack of cards, and these can be cut, as many times as you want, and you can give them to your volunteers, and they can cut them. And then you get four volunteers and they each take a card off the top of the pack. So Volunteer 1, Volunteer 2, Volunteer 3, and Volunteer number 4. So they each pick a card, And you say, “Oh, right. I’m going to read your mind. Ah, but with four of you, it’s a bit difficult. The transmission is not getting through. To clear up the transmission, which ones of you have a red card?” And, hopefully, your volunteers with a red card will give you a little wave. And you’ll go, “Oh, right, that helps. Thank you. I can now name your cards.” And you’ll be able to name each volunteer’s card, and get it right. Now, how does this work? Let’s take a look. We’re going to use this sequence that we saw before, but instead of ones and twos, I’m now going to change this into blacks and reds. So the sequence now looks like this. [BBBB RRRR BRRB BRBR] To make this card trick work, we’re going to have to memorize 16 cards in this order. Now, you’re free to pick your own sequence of 16 cards, but here’s one that I’ve made up. Now, my idea here was to split it into four blocks of 4, to begin each block with ace, two, three and four, and the cards in each block increase by four. So I’ve got ace, five, nine, and king. Then I have two, six, ten and ace. And so on. The suits I’ve tried to keep in CHSD [‘chased’] order. That’s C-H-S-D. Clubs, hearts, spades and diamonds. So the first block of four was clubs-spades-clubs-spades. The last block of four is actually in CHSD order. The third block of four is a bit of a cheat. I’ve started off in CHSD order– clubs and hearts– then I’ve had to do a little switch there so it’s diamonds and spades. Now, if you can memorize this sequence, you can do this trick. I made this sequence four times over, [edit: I meant 3 times over] using four decks of cards, put them together, and you’ll make 4 times 16 lots of cards, [3×16=48] which is 48 cards. So you’ve got a deck of 48 cards. When you cut the pack, that doesn’t affect the sequence at all. And if your volunteers give you a wave, to show you which ones are red, you can use that to identify where in the sequence you are, and you can name their cards. So, for example, you’ve got your four volunteers, and maybe the first, second and fourth volunteer have a red card. Then you’re looking for the sequence RRBR. And if you can use that memorized sequence of 16, you know that they have picked the 10 of Hearts, the Ace of Diamonds, the 3 of Clubs, and the 7 of Hearts. Now, you do have to memorize this sequence. So it’ll take some practice. Or maybe you can use a cheat sheet hidden somewhere. But it can be done, and that’s a challenge to the magicians out there. So over to you! And if you have been, thanks for watching.




Comments
  1. you are a genius, just like me, but im smarterer than you 😎 (only joking im not really smarter, not even close!) 🙂

  2. Since the example there showed 16 cards, when you start the next block in the sequence ( 5th Block) do u start BBBB again?

  3. I think he would mean that you would wrap around and return to the first block. Not too sure myself however, but that seems to be the only thing running through my head.

  4. Have you played real poker against real people who are actually good? They are experts in reading people, and giving them free information = you lose.

  5. Oh come on people. He put a caption in on screen correcting himself, when he said 4×16 = 48.
    It was obviously a mistake – how many of you need to be smart-asses about it?

  6. how does it work when the deck is scrambled then the cards are not at the place of the memorized sequins so how can it work then????

  7. The deck isn't shuffled – it is only cut a few times. This doesn't affect the trick, as he explained how the sequence wraps around the end to go back to the start.

  8. Dr Jim besides being extremely intelligent and influential, I have to admit … you're quite aesthetically pleasing.

  9. He's a mathematician. As far as I know, those are very bad at mental calculations (being a physicist myself, I'd say those are not much better at it). It doesn't mean you don't know, it just means you spent your time understanding numbers in stead of memorising them.

  10. It wasn't really meant as an opposing point. I just wanted to add some extra argumentation 🙂

  11. i saw a similar trick in a library that book shows how this trick can be done with a full deck of playing cards with even 5 spectators. i'll post my performance i did back then as a vid response 😀

  12. Was this on Penn and Teller's Fool Us? Half of it sounds familiar, but the other half didn't. Maybe it was just similar to this!

  13. Did you got this from Magical Mathematics? It's a great book explaining mathematical card tricks and the math behind it.

  14. Perhaps make two sets?= 32 cards.
    AC,5S,9C,KS,2H,6D,10H,AD,3C,7H,JD,2S,4C,8H,QS,3D
    AS,5C,9S,KC,2D,6H,10D,AH,3S,7D,JH,2C,4S,8D,QC,3H.
    Add any five cards to the top and then to the bottom of the deck.(Does anyone ever cut that shallow or deep?) Total of cards in stack=42 all different.No duplicates.Magician false shuffles deck.Spectator cuts deck.Cards distributed/remembered/buried/deck shuffled by spectator.Any overlap of the two sets can be discerned in pattern.Deck is left examinable.

  15. I've actually done this, however just with one deck! And I must say it's pretty cool, although the deck only has 48 cards in it…

  16. They way I do the trick, is I have each subsequence have a length of six (opposed to four) so the de Bruijn sequence is 64 digits long. To get this down to 52, the number of cards in a deck, I removed the first and last six digits, which were both six consecutive digits of the same type (all one, zeroes, blacks, reds or whatever you are using). While this sequence does not contain all the combinations, there are no repeats, meaning you avoid the awkward 1/16 scenario that nobody has a red card.

  17. So I decided to learn your method of arranging the cards.. then I just examined it in the video by pausing the video at 4:14. And in about five to ten minutes I memorized the pattern and could perform the trick afterwards! 😀

  18. an easy beginner method would be:
    -have the deck in si stebbins order (google that,its just an cyclical order,that allows you to tell what the next/previous card/cards are by looking at one)
    -let them cut the deck as often as they want
    -let them pick a card from the top
    -under the action of removing the deck from the table,or something like that : peek at the bottom card
    -> you now know the identity of the picked cards

  19. It seems the hardest part of this trick would be to get the audience to accept just cutting the deck instead of properly shuffling it!

  20. they use many decks in poker :/ there was a documentary on a guy with an astounding memory. he went to play blackjack and tried to count cards, but gave up and just went on luck (and his mathematical mind doing percentages) and won… in poker if you're playing against others then it is more than just counting cards and doing percentages. there are variables that could throw him off such as bluffing. he might have advantage of being a P.hd in maths but it might do him little in the big league

  21. But then you still have to memorize the sequence, and it involves cheating (peek at the bottom card), what if they spot you doing that?

  22. did you even read what I wrote? and do you understand what Logic means? Logic is essentially common sense in a cause and effect terms of way. i.e.: Decision making. Poker is a maths game that is based purely off of how well you can bluff, and how good you are on basing whether or not you should draw or play. Do you play poker? legit? with real people? or even watch pros play games? Poker is an extremely tough mind game with alot of calculations and guesstimating on what your opponents have

  23. you cheat, so to speak, you don't use a regular 52 card deck, you just use the same sequence of 16 cards tripled for a 16×3 = 48 card deck. thus it doesn't matter at all where the cards are cut or re-cut, the sequence will always be the same.

  24. I am not saying what you said at all =.= and you want to play that silly little name calling game? grow up

  25. what do you mean by "cheating"? this is a card trick, "cheating" is the whole point of it 😉

    you don't have to memorize anything,just how the cycle works,which is dead easy.
    yes you have to peek,be casual,noone is gonna notice

  26. I can't do this trick! I have followed exactly, but it doesn't work. Do you have to use 3 decks? Because I use just one to try, and doesn't work. When u give the cards, they might be in sequence or not! Can anybody help?

  27. Because the sequence wraps around. So taking the top few cards and putting them at the bottom will still continue the sequence. The only thing that changed is at which card the sequence starts/ends.

  28. It should still work even with only a single de Bruijn sequence, did you accidentally allow them shuffles or moves other than cuts? (take arbitrary amount of cards from top and place them at the bottom)

  29. I laughed when he said the cards can be cooked as many times as you want and you can give them to volunteers to cook as well.

  30. it would be fantastic to cut it a couple times in front of them, even shuffle it while keeping your eye on a n area of the cards that do not move, then letting them shuffle, with 4+ cards cupped in your hand.

  31. There is a card setup called the Cy Stebbins that stacks the entire deck: 10 K 3 6 9 Q 2 5 8 J A 4 7 the suits alternate CHSD. So, for example, the first few cards would be:
    10c Kh 3s 6d Qc 2h 5s …..

    The entire deck can be cut repeatedly. As long as you can use a shiner (reflective surface) or a sneaky peek to look at the BOTTOM card, you can rattle off the cards of the ENTIRE DECK in order.

    Plus 3, next suit.
    Plus 3, next suit.

  32. Hey, bist du das Mädchen aus der Ringbahn, dass mich angesprochen hat? Ja das hier ist das richtige Video. Brown / Brujin kann man schon mal verwechseln
    https://www.youtube.com/watch?v=kQZmZRE0cQY&app=desktop

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