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Math Help - Has anyone ever heard of "Magic base Cards"?

  1. #1
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    Has anyone ever heard of "Magic base Cards"?

    How do you make a set of base 3 magic card?
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  2. #2
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    Hello, t-lee!

    How do you make a set of base-3 magic cards?

    Could you describe these "magic cards"?
    What are they supposed to do?

    I know of a base-2 set of cards that enables us to determine a thought-of number.
    Is it anything like that?

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, t-lee!


    Could you describe these "magic cards"?
    What are they supposed to do?

    I know of a base-2 set of cards that enables us to determine a thought-of number.
    Is it anything like that?

    Are those the ones that you add the numbers in the first row and colomn?

    The reason why I am asking is that in your profile it says you do magic, well I also do it on a serious level. Card magic especially (closer related to card cheating but it looks like magic).
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  4. #4
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    Hello, TPHacker!

    Yes, that's exactly the type of "magic cards" I'm familiar with.
    . . (Use to get them in a Cracker Jack box.)

    For those unfamiliar with them, here's the secret.
    The base-2 cards have a simple set-up (if you know Binary).

    Let's say the numbers run from 1 to 31 (2^5-1)
    Write them in binary notation.

    \begin{array}{ccccccc}1 = 00001 & 9 = 01001 & 17 = 10001 & 25 = 11001 \\ 2 = 00010 & 10 = 01010 & 18 = 10010 & 26 = 11010 \\ 3 = 00011 & 11 = 01011 & 19 = 10011 & 27 = 11011 \\ 4 = 00100 & 12 = 01100 & 20 = 10100 & 28 = 11100\end{array}

    \begin{array}{cccc}5 = 00101 & 13 = 01101 & 21 = 10101 & 29 = 11101 \\ 6 = 00110 & 14 - 01110 & 22 = 10110 & 30 = 11110 \\ 7 = 00111 & 15 = 01111 & 23 = 10111 & 31 = 11111<br />
\\ 8 = 01000 & 16 = 10000 & 24 = 11000 & \end{array}


    On the first card, write the numbers with a "1" in the first (rightmost) position.
    On the second card, write the numbers with a "1" in the second position.
    On the third card, write the numbers with a "1" in the third position.
    . . \boxed{\begin{array}{cccc}1 & 3 & 5 & 7 \\ 9 & 11 & 13 & 15 \\ 17 & 19 & 21 & 23 \\ 25 & 27 & 29 & 31\end{array}} . . \boxed{\begin{array}{cccc} 2 & 3 & 6 & 7 \\ 10 & 11 & 14 & 15 \\ 18 & 19 & 22 & 23 \\ 26 & 27 & 30 & 31\end{array}} . . \boxed{\begin{array}{cccc} 4 & 5 & 6 & 7 \\ 12 & 13 & 14 & 15 \\ 20 & 21 & 22 & 23 \\ 28 & 29 & 30 & 31\end{array}}


    On the fourth card, write the numbers with a "1" in the fourth position.
    On the fifth card, write the numbers with a "1" in the fifth (leftmost) position.

    . . . . . . . . . \boxed{\begin{array}{cccc} 8 & 9 & 10 & 11 \\ 12 & 13 & 14 & 15 \\ 24 & 25 & 26 & 27 \\ 28 & 29 & 30 & 31\end{array}} . . \boxed{\begin{array}{cccc} 16 & 17& 18 & 19 \\ 20 & 21 & 22 & 23 \\ 24 & 25 & 26 & 27 \\ 28 & 29 & 30 & 31\end{array}}


    Effect: Have someone think of a number from 1 to 31.
    . . Have him examine the five cards and give you the cards that contain his number.
    . . You miraculously divine his mentally-selected number.

    Secret: Add the upper-left (smallest) numbers of the cards he returns to you.
    . . That is his selected number.


    To make it more mysterious, scramble the numbers on each card.
    Place the smallest number in another location, say, the lower-left.
    And I'm sure no one will suspect any pattern or method.


    Of course, this can be extended to six cards (numbers 1 to 63) or more.

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  5. #5
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    Here's a set of Magic Cards (base 2) you may like to construct.

    There are six number cards.
    The \bullet denotes holes to be cut out at those locations,
    . . large enough to see the numbers through them.

    \begin{bmatrix}\\ &33 & 49 & 27 & 17 & 21 & 55 & 61 & 39 & \\ &  3 & \bullet & 31 & 51 & 63 & 43 & \bullet & 13 \\ & 15 & 7 & 1 & 19 & 15 & 23 & 59 & 41 & \\ & 57 & \bullet & 29 & 9 & \bullet & 35 & \bullet & 51 & \\ & 53 & 5 & 47 & 25 & 45 & 33 & 11 & 37 & \\ \\ \end{bmatrix} . \begin{bmatrix}\\ &11 & 38 & 62 & 51 & 43 & 26 & 55 & 15 & \\ & 10 & \bullet & 63 & 35 & 31 & 19 & \bullet & 46 &\\& 14 & 3 & \bullet & 59 & 27 & 7 & 58 & 18 &\\& 26 & \bullet & 6 & 47 & 2 & 39 & \bullet & 22 &\\ &54 & 23 & 50 & 30 & 35 & 42 & 11 & 34&\\ \\ \end{bmatrix}

    \begin{bmatrix}\\ & 5 & 47 & 28 & 53 & 61 & 13 & 20 & 52 & \\ & 37 & \bullet & 44 & 30 & 46 & 55 & 4 & 7 & \\ & 22 & 63 & \bullet & 12 & 62 & 14 & 60 & 31 & \\ & 23 & \bullet & 29 & 54 & \bullet & 15 & \bullet & 6 & \\& 45 & 36 & 39 & 21 & 47 & 28 & 63 & 38 & \\ \\ \end{bmatrix} . \begin{bmatrix}\\ & 45 & 63 & 27& 10 & 58 & 9 & 61 & 42 & \\ & 29 & 8 & 11 & 57 & 30 & 59 & \bullet & 62 & \\ & 13 & 24 & \bullet & 60 & 40 & 47 & 14 & 56 & \\ & 45 & \bullet & 12 & 44 & \bullet & 25 & \bullet & 27 & \\ & 43 & 15 & 41 & 31 & 26 & 62 & 12 & 28 &\\ \\ \end{bmatrix}

    \begin{bmatrix}\\ & 54 & 23 & 18 & 58 & 63 & 31 & 26 & 51 & \\ & 29 & \bullet & 61 & 50 & 20 & 27 & \bullet & 52 & \\ & 56 & 28 & \bullet & 17 & 59 & 48 & 21 & 60 & \\ & 31 & \bullet & 19 & 55 & \bullet & 30 & 16 & 53 & \\ & 62 & 49 & 24 & 57 & 22 & 52 & 27 & 25 & \\ \\ \end{bmatrix} . \begin{bmatrix}\\ & 39 & 63 & 54 & 38 & 45 & 61 & 49 & 33 & \\ & 53 & \bullet & 57 & 46 & 43 & 41 & \bullet  & 62 & \\ & 34 & 40 & \bullet & 55 & 42 & 51 & 59 & 35 & \\ & 60 & 32 & 44 & 59 & \bullet & 38 & \bullet & 58 & \\ & 36 & 48 & 50 & 56 & 52 & 47 & 42 & 37 & \\ \\ \end{bmatrix}

    There is a cover-card which has holes cut out at the \bullet locations.

    . . . . . . . . \begin{bmatrix}\\ & .. & .. & .. & .. & .. & .. & .. & .. & \\ & .. & \bullet & .. & .. & .. & .. & \bullet & .. & \\ & .. & .. & \bullet & .. & .. & .. & .. & .. & \\ & .. & \bullet & .. & .. & \bullet & .. & \bullet & .. & \\ & .. & .. & .. & .. & .. & .. & .. & .. & \\ \\ \end{bmatrix}


    Have your volunteer select (mentally) a number from 1 to 63.
    Give him the six number-cards.
    Have him give you the cards on which his number appears.

    When he has done so, square up the cards in your hands
    . . and place the cover-card on top.
    Then add the visible numbers.

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  6. #6
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    Yes those are the types of Magic 2 cards that I know. Now what I am wondering is how I come up with making Magic 3 cards? Could anyone explain to me how to do that? Is there a formula?

    thanks
    t-lee
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  7. #7
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    Soroban...

    If you know how to come up with and do the ''Magic 3 Cards" could you explain it like you did the Magic 2 set? That was great how you explained it. I followed it nicely.

    t-lee
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  8. #8
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    Hello, t-lee!

    I have never seen Magic Cards in base-3.
    In fact, I've never even considered it.

    I've been thinking about it since you posted your query,
    . . and I think I've found them.

    Let's use the numbers from 0 to 26.

    Write them in base-3 notation.

    . \begin{array}{ccccccccc}0 = 000\\1=001\\2=002\\3=010\\4=011\\5=012\\6=020\\7=0  21\\8=022\end{array} . \begin{array}{ccccccccc}9=100\\10=101\\11=102\\12=  110\\13=111\\14=112\\15=120\\16=121\\17=200 \end{array} . \begin{array}{ccccccccc}18=200\\19=201\\20=202\\21  =210\\22=211\\23=212\\24=220\\25=221\\26=222\end{a  rray}


    On a card, write the numbers with a first (rightmost) digit of 0:
    . . 0, 3, 6, 9, 12, 15, 18, 21, 24

    On a card, write the numbers with a first digit of 1:
    . . 1, 4, 7, 10, 13, 16, 19, 22, 25

    On a card, write the numbers with a first digit of 2:
    . . 2, 5, 8, 11, 14, 17, 20, 23, 26

    On a card, write the numbers with a middle digit of 0:
    . . 0, 1, 2, 9, 10, 11, 18, 19, 20

    On a card, write the numbers with a middle digit of 1:
    . . 3, 4, 5, 12, 13, 14, 21, 22, 23

    On a card, write the numbers with a middle digit of 2:
    . . 6, 7, 8, 15, 16, 17, 24, 25, 26

    On a card, write the numbers with a left digit of 0:
    . . 0, 1, 2, 3, 4, 5, 6, 7, 8

    On a card, write the numbers with a left digit of 1:
    . . 9, 10, 11, 12, 13, 14, 15, 16, 17

    On a card, write the numbers with a left digit of 2:
    . . 18, 19, 20, 21, 22, 23, 24, 25, 26


    We have nine cards.

    . . \begin{bmatrix} 0&3&6\\9&12&15\\18&21&24\end{bmatrix} . . \begin{bmatrix}1&4&7\\10&13&16\\19&22&25\end{bmatr  ix} . . \begin{bmatrix}2&5& 8\\11&14&17\\20&23&26\end{bmatrix}

    . . \begin{bmatrix}0&1&2\\4&10&11\\18&19&20\end{bmatri  x} . . \begin{bmatrix}3&4&5\\12&13&14\\21&22&23\end{bmatr  ix} . . \begin{bmatrix}6&7&8\\15&16&17\\24&24&25\end{bmatr  ix}

    . . . \begin{bmatrix}0&1&2\\3&4&5\\6&7&8\end{bmatrix} . . . \begin{bmatrix}9&10&11\\12&13&14\\15&16&17\end{bma  trix} . . \begin{bmatrix}18&19&20\\21&22&23\\24&25&26\end{bm  atrix}


    Same routine as before . . .

    Have the volunteer think of a number from 0 to 27,
    . . and give you the cards that contain his number.

    Add the upper-left (smallest) numbers of the cards.


    This can be extended to the numbers from 0 to 80 (3^4 - 1),
    . . requiring twelve cards.

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  9. #9
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    Thank you

    Thank you so much for your help. I hate to bother you, but I have another question. You said to have someone pick a number 0-26 and then they should give you the cards that has their number on it. Once they do this you are to add the upper left numbers together? What does this do?
    Say I pick the number 11 and I gave you the two cards that contained that number...are you saying I would add 2-0? If so, I don't quit understand what that means.

    t-lee
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  10. #10
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    sorry

    Actually I think I found my mistake. There are three cards that contain the number 11. So you would add 0+2+9 and you would get 11. It also shows in the binary numbers too.

    t-lee
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