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Thread: nr 13

  1. #1 nr 13 
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    Hi again!

    This time I wonder if any of you know about a card-trick called "Nr. 13"?

    My teacher showed the class this trick some days ago, and he said it was a complicated mathematical explanation of how the trick actually worked. He said it was to complicated to explain to us. If someone know about the trick and can explain to me how it works, I would be for ever thankful, because I think about it all the time.


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  3. #2  
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    You'll have to give a bit more detail, somebody might recognise it as something else.


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  4. #3  
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    It was about first looking at a card, and then lay all the cards on a table. Then you should first pick out 13 cards and then do a lot of things which I don't exactly remember. It all ended with that the person doing the trick on you could pick out the card you looked at in the beginning.

    I'm not that very good in english, but I hope you understand.
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  5. #4  
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    Many card tricks can indeed be quantified mathematically, however without the exact details of the trick I can't work it out, if anybody else can precisely decribe the trick then I'll have a go.
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  6. #5  
    Forum Professor river_rat's Avatar
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    Most card tricks use mod arithmetic or simple properties of permutation groups to amaze the audience - here is a simple one that uses a "mod 3" permutation of 21 cards to magically read someones mind.

    Start with 21 normal playing cards and slowly deal them face up into three piles, getting your volunteer to choose any card at random but to keep it secret. The only information they are to give you is to point out the pile their card lies in after you have finished dealing the cards. You then collect the piles and place the pile shown in between the other two piles and repeat the process twice, each time getting the volunteer to point out the pile in which their chosen card fell. You then turn the pack over, say the magic words and count of the first 10 cards and flip the next card - which just happens to be the card they picked

    I wont give the game away yet - try work out how this silly trick works on your own (as a hint consider the fixed points of this sequence of permutations of 21 elements)
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  7. #6  
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    Off the top of my head, three piles of 7 cards - I sense a solution here - I reckon it will depend upon the order of piles in which the card is shown, say three piles a,b,c ie six solutions [abc.acb,bca,bac,cab,cba]the '7th' is lost as the cards are moved down a pile. I don't have set of sodding cards though....
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  8. #7  
    Forum Professor river_rat's Avatar
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    You dont need the cards - just a pen, pencil and the patience to write down 21 numbers twice
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  9. #8  
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    Actually, this card trick reminds me of that one I tried to figure out.. I'll ask my teacher if he can show me the trick again...
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  10. #9  
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    OK, I've got the point.

    When you lay the pile with the card between the two other piles, then you know that the card is number 8, 9, 10, 11, 12, 13 or 14 in the row.

    Next time you make three piles and put the one with the card between the other piles, then you know that the card must be number 10, 11 or 12.

    The last time you make three piles, then you put one card in each pile three times before you come to card number 10, 11 and 12, and now you know that the card will be in the middle of one of the piles. It will be card number 4 in that pile. When you then lay this pile between the two other ones, you know that it will be card number 11, because 7 + 4 = 11.
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  11. #10  
    Forum Freshman Faldo_Elrith's Avatar
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    The 13-card trick is really dumb! The procedure is like this: Start with a pack of cards neatly arranged in order. Have different people cut the deck randomly 12 times. Then you make the last 13th cut after secreting thumbing through the deck to locate a king (any king).

    The dumb thing about this is that there's nothing special about the number 13! You can cut the deck any number of times you like (even 2 will do). Explanation? Well, it's because you're only cutting the deck, not shuffling the pack. If you still don't get it, just do the trick yourself with the cards face up. You'll be able to see why. Proof by hands-on practice is worth a thousand proof by mathematical symbols.

    River Rat's 21-card trick is better. Here's a video:

    http://www.expertvillage.com/video/1...-one-trick.htm

    The explanation is this. When your audience has selected a card and you deal the cards in 3 piles of 7 again, his cards will be any of the following cards 1-7:



    After they point out the pile and you put that pile between the other two, their chosen card will be the 10th, 11th or 12th card from the top. (If they chose 1 or 2, it's the 10th card from the top; if they chose 3, 4 or 5, it's 1th from the top; if 6 or 7, it's 12th from the top.) In whatsoever case, the chosen card will be in position A, B or C in the final deal:



    Hence the chosen card will always be the 11th card from the top once the piles are put back the final time.
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