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Thread: Missing digits

  1. #1
    Newbie
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    Jun 2009
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    Missing digits

    Hello everybody,

    i'd appreciate it very much if someone could help me solve this:

    12xy
    11121x1y
    3112111x111y
    ?

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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, alana!

    This is a classic (very old) puzzle . . .


    i'd appreciate it very much if someone could help me solve this:

    . . $\displaystyle \begin{array}{c}12xy \\ 11121x1y \\ 3112111x111y \\ ? \end{array}$

    Each row describes the contents of the row above it.


    The first row is: .$\displaystyle 12xy$

    It contains: .one 1, one 2, one $\displaystyle x$, one $\displaystyle y$.

    The second row is: .$\displaystyle 1\;1,\quad 1\;2,\quad 1\;x,\quad 1\;y \qquad\Rightarrow\qquad 11121x1y$


    The second row contains: .three 1's, one 2, one 1, one $\displaystyle x$, one 1, one $\displaystyle y$.

    The third row is: .$\displaystyle 3\;1,\quad 1\;2,\quad 1\;1,\quad 1\;x,\quad 1\;1,\quad 1\;y \qquad\Rightarrow\qquad 3112111x111y$


    The third row contains: .one 3, two 1's, one 2, three 1's, 1 $\displaystyle x$, three 1's, one $\displaystyle y$.

    The fourth row is: .$\displaystyle 1\;3,\quad2\;1,\quad 1\;2,\quad 3\;1,\quad 1\;x,\quad 3\;1,\quad 1\;y \qquad\Rightarrow\qquad \boxed{132112311x311y}$

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  3. #3
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    Jun 2009
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    :)

    Dear Soroban ,

    thank u sooooo much for the solution and for replying that quickly. It was such a nice explanation. Best wishes and a kiss from Croatia!


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