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Topic: 5 card magic trick (Read 1315 times) |
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elway
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5 card magic trick
« on: Nov 28th, 2004, 2:18pm » |
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this is a magic trick performed by two magicians, A and B, with one regular, shuffled deck of 52 cards. A asks a member of the audience to randomly select 5 cards out of a deck. the audience member -- who we will refer to as C from here on -- then hands the 5 cards back to magician A. after looking at the 5 cards, A picks one of the 5 cards and gives it back to C. A then arranges the other four cards in some way, and gives those 4 cards face down, in a neat pile, to B. B looks at these 4 cards and then determines what card is in C's hand (the missing 5th card). how is this trick done?
can someone tell me what it is.
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BNC
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Re: 5 card magic trick
« Reply #1 on: Nov 28th, 2004, 3:13pm » |
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How about this:
In a pack of 5 cards, there must be at least two cards of the same suit. A picks one card of these, and hands it to C, not before remembering it.
Now, he arranges the 4 cards such that the topmost card is of the same suit as the card in C's hands. The orientation of these 4 cards (e.g., horizontalyy / vertically) may convey a number 0-15, so it can easily determine the card number -- and that's without B even having to look at the 4 cards.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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hhhh
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wait, so he puts the card with the same suit on the top, so B knows the suit, but can u explain how he gets the number a little better
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elway
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Re: 5 card magic trick
« Reply #3 on: Nov 28th, 2004, 4:04pm » |
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ok, but do u know how to arrange them?
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BNC
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Re: 5 card magic trick
« Reply #4 on: Nov 28th, 2004, 9:34pm » |
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Any kind of binary representation (i.e., only two options) would work here. I suggested before using the spatial orientation -- that is, placing the cards either "sideways" (longer side facing the magician) or "regularly" (shorter side facing the magician). Another option is placing the cards either facing up or down.
In either case, B gets 4 binary bit values, and converts them to a decimal number. Let's say, for example, that the cards are arranges either facing up (U) or down (D), and the order from top to bottom is UDDD. B will translate this position to the binary represntation 1000. He will then convert that to decimal (if you don't know how, in this example it would be 10002 = 1*23 + 0*22 + 0*21 + 0*20 = 1*8 + 0*4 + 0*2 + 0*1 = 8). So, it would the 8-card with the suit of the topmost card.
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OK?
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| « Last Edit: Nov 28th, 2004, 10:24pm by BNC » |
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Obob
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Re: 5 card magic trick
« Reply #5 on: Nov 28th, 2004, 11:09pm » |
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I believe that the conditions of the question stipulate that the orientation of all the cards must be the same, and that they must all be face down. You have to find a way to do something similar using only the values of the cards.
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| « Last Edit: Nov 28th, 2004, 11:41pm by Obob » |
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Barukh
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Re: 5 card magic trick
« Reply #6 on: Nov 28th, 2004, 11:29pm » |
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There is a thorough discussion of this problem here.
Also: Obob, welcome to the club! 
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ThudnBlunder
wu::riddles Moderator
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There was also an article in Mathematical Intelligencer.
See attached PDF.
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| « Last Edit: Nov 29th, 2004, 4:44am by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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fatball
Senior Riddler
Can anyone help me think outside the box please?
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Re: 5 card magic trick
« Reply #8 on: Nov 30th, 2004, 7:08am » |
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I haven't gone through the thorough discussion yet, but I am thinking if all cards are passed to B face down, how can A convey the message about the suit of the card to B?
BTW, why didn't anybody welcome me yet 
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Barukh
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Re: 5 card magic trick
« Reply #9 on: Nov 30th, 2004, 7:51am » |
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on Nov 30th, 2004, 7:08am, fatball wrote:| IBTW, why didn't anybody welcome me yet |
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Welcome, fatball!
Basically, I do not welcome any new member (maybe, others do?). The reason I welcomed Obob was that we had some interesting discussions with him/her as a guest.
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rmsgrey
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Re: 5 card magic trick
« Reply #10 on: Nov 30th, 2004, 9:31am » |
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The point of passing them to B face-down is to stop people from using binary code by having some cards face-up, and others face-down. Similarly, having them in a neat pile is intended to prevent subtle disarray of the cards from conveying information...
A restatement of the puzzle would be:
A is given a list of 5 different integers between 1 and 52 inclusive. He then picks 4 of them and lists them in some order for C, who then texts B with the 4 numbers in that order. B texts back the 5th number.
Any intended solution for the original version will still work for this one.
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