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Math Help - card 'trick' and group theory

  1. #16
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    A true swindle!

    Try this on one of your "smarter" friends.

    Use the spot-cards from Ace to Six and arrange them on the table like this:

    . . . \begin{array}{cccccc}A\diamondsuit \\ 2\diamondsuit \\ 3\diamondsuit \\ 4\diamondsuit \\ 5\diamondsuit \\ 6\diamondsuit \end{array}<br />
\begin{array}{cccccc}A\clubsuit\\2\clubsuit\\3\clu  bsuit\\4\clubsuit\\5\clubsuit\\6\clubsuit\end{arra  y}<br />
\begin{array}{cccccc}A\heartsuit\\2\heartsuit\\3\h  eartsuit\\4\heartsuit\\5\heartsuit\\6\heartsuit\en  d{array}<br />
\begin{array}{cccccc}A\spadesuit\\2\spadesuit\\3\s  padesuit\\4\spadesuit\\5\spadesuit\\6\spadesuit\en  d{array}

    You and your victim will take turns removing cards and keep a running total.
    The first to reach 31 (without going over) wins the game.

    If you play first, take a 3.
    Whatever he takes, take the "7-complement".
    . . If he takes a 5, take a 2. If he takes an Ace, take a 6.
    The totals (after your turn) will be: 3,\,10,\,17,\,24.
    . . And after his next move, you will reach 31 with your next move.


    If he plays first, try make the total 3 or 10 as soon as possible.
    . . And proceed as described above.


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    So far, this game is not very impressive, is it?

    Here's where the swindle comes in.

    Eventually he will catch on that you always start with a 3
    . . and he may discern the rule of the 7-complement.
    (Better yet, have a "shill" take him aside and explain the winning strategy.)

    Confident that he will win, he may even raise the stakes
    . . (not that I encourage gambling, mind you).

    He begins by taking a 3.
    You take a 3. .He will take a 4. .Total: 10
    You take another 3. .He takes another 4. .Total: 17
    You take a 4. .He takes a 3. .Total: 24
    You take a 4.

    He will reach for a 3 and find to his horror that there are no more 3's!

    He must either go over 31 and lose . . . or go under 31 and allow you to win.

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  2. #17
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    Another long trick

    . . . . . The Twenty-Card Mystery

    I'll give you the preparation first; it requires considerable practice.
    Then you can decide if you want to read any further.


    Memorize these four words: ATLAS, BIBLE, GOOSE, THIGH.

    You must imagine these words written in large letters on the table:
    . . . \begin{array}{cccc}A\;T\;L\;A\;S \\ B\;I\;B\;L\;E \\ G\;O\;O\;S\;E \\ T\;H\;I\;G\;H\end{array}

    Note that each letter appears exactly twice in the arrangement.
    . . There are two A's, two T's, two L's, and so on.

    Now you must practice dealing ten pairs of cards on to this array.

    Deal the first two cards onto the two A's.
    Deal the first card onto the first "A", then locate the second "A" mentally.
    . . (Think of the four words you memorized.)

    Deal the next two cards onto the two T's.
    The first "T" is easy; where is the other "T"?
    . . It's the first letter of THIGH.

    Deal the next two cards onto the two L's . . . and so on.


    At first you will be dealing very slowly; you must stop and think of each letter
    . . and locate the second location of that letter.
    With some practice, you will be dealing faster and smoother.
    The object is to appear to be placing the cards randomly on the table.

    When you are fairly good at dealing the cards as described above,
    . . try some variations.
    Start, for example, with the two G's, then the two L's, etc.

    When I deal the cards into the array, I get "sloppy".
    The cards are not lined up neatly and they're slightly tipped.
    After the dealing, I straighten them slightly, as if it doesn't matter.

    Once you can deal the ten pairs smoothly without obvious pauses,
    . . you are ready to perform a small miracle.

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Presentation

    You can have as many as ten volunteers for this trick.

    Have someone shuffle the deck.
    Take the deck and deal off ten pairs of cards,
    . . tossing them randomly onto the table.

    Have each volunteer choose any pair of cards and remember them.
    Have them place the cards face down on the table.

    Pick up the cards, a pair at a time, in any order, and make a single packet of cards.
    . . (Use both hands and make it look as casual as possible.)

    Now deal the twenty cards face up onto the ATLAS-BIBLE-GOOSE-THIGH array
    . . as smoothly and randomly-appearing as possible.

    As one of the volunteers "Which rows are your cards in?".
    (You might sweep your hand from left to right to indicate the rows.)

    When he tells you the rows, you can immediately tell him his two cards.

    Suppose his says "The first and third rows" (or just points to them).
    Imagine the words for these two rows: ATLAS and GOOSE.
    What lettter appears twice? . . . the "S".
    Point to the cards in the location of the S's.

    Suppose the second volunteer says "Both in the second row."
    The word is BIBLE . . . and there are two B's.
    His cards are at those locations.

    Continue in this manner for each of the volunteers.

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  3. #18
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    Another silly trick

    In the array below,

    [1] Touch any Red card.

    [2] Touch the screen at the nearest BLACK card
    . . .which is to the left or right of your chosen card.

    [3] Touch the screen at the nearest RED card
    . . .which is vertically up or down from the black card.

    [4] Touch the screen at the nearest BLACK card
    . . . which is diagonally adjacent from this card.

    [5] Touch the screen to the nearest RED card
    . . .which is down or to the right of this card.


    . . \begin{array}{ccccccc}\boxed{3\spadesuit}\\ \\ \boxed{9\heartsuit} \\ \\ \boxed{Q\diamondsuit} \\ \\ \boxed{4\heartsuit}\end{array}  \begin{array}{cccc}\boxed{K\diamondsuit} \\  \\ \boxed{J\spadesuit} \\ \\ \boxed{4\clubsuit} \\ \\ \boxed{Q\spadesuit}\end{array} \begin{array}{cccc}\boxed{8\diamondsuit} \\ \\ \boxed{2\clubsuit} \\ \\ \boxed{A\diamondsuit} \\ \\ \boxed{7\clubsuit}\end{array} \begin{array}{cccc}\boxed{3\heartsuit} \\ \\ \boxed{6\spadesuit} \\ \\ \boxed{7\heartsuit} \\ \\ \boxed{2\spadesuit}\end{array}


    Concentrate on your final card.

    Your card is:
    (drag cursor between the asterisks)

    . . * The Ace of Diamonds *

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