wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> hard >> 5 card magic trick
        
(Message started by: elway on Nov 28^th, 2004, 2:18pm)

Title: 5 card magic trick
Post by elway on Nov 28^th, 2004, 2:18pm

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.

Title: Re: 5 card magic trick
Post by BNC on Nov 28^th, 2004, 3:13pm

How about this:
[hide]
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.
[/hide]::

Title: Re: 5 card magic trick
Post by hhhh on Nov 28^th, 2004, 3:44pm

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

Title: Re: 5 card magic trick
Post by elway on Nov 28^th, 2004, 4:04pm

ok, but do u know how to arrange them?

Title: Re: 5 card magic trick
Post by BNC on Nov 28^th, 2004, 9:34pm

::[hide]
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.
[/hide]::

OK?

Title: Re: 5 card magic trick
Post by Obob on Nov 28^th, 2004, 11:09pm

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.

Title: Re: 5 card magic trick
Post by Barukh on Nov 28^th, 2004, 11:29pm

There is a thorough discussion of this problem here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1028012962;start=).

Also: Obob, welcome to the club! :D

Title: Re: 5 card magic trick
Post by THUDandBLUNDER on Nov 29^th, 2004, 3:34am

There was also an article in Mathematical Intelligencer.
See attached PDF.

Title: Re: 5 card magic trick
Post by fatball on Nov 30^th, 2004, 7:08am

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??? :-/

Title: Re: 5 card magic trick
Post by Barukh on Nov 30^th, 2004, 7:51am

on 11/30/04 at 07:08:43, fatball wrote:

IBTW, why didn't anybody welcome me yet??? :-/

Welcome, fatball! :D

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.

Title: Re: 5 card magic trick
Post by rmsgrey on Nov 30^th, 2004, 9:31am

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.