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Thread: [SOLVED] Letter and number substitution problem

  1. #1
    DINO
    Guest

    [SOLVED] Letter and number substitution problem

    Need help I am a parent of a Yr 8 student and she has asked me to help her with Maths problem. I cant do it!


    Problem

    Each letter stands for a different digit. If WAIT = 8472,what does STOP represent.

    Given that

    GO
    +SLOW
    ---------
    STOP


    Any help would be appreciated.
    Thanks
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, DINO!

    Each letter stands for a different digit.
    If $\displaystyle WAIT = 8472$, what does $\displaystyle STOP$ represent?

    $\displaystyle \begin{array}{ccccc} & & G & \Theta \\
    S & L & \Theta & W \\ \hline
    S & T & \Theta & P \end{array}$

    We given: .$\displaystyle W=8,\;A=4,\;I=7,\;T=2$
    . . Available digits: .$\displaystyle \{0,1,3,5,6,9\}$

    . . $\displaystyle \begin{array}{ccccc} ^1 & ^2 & ^3 & ^4 \\
    & & G & \Theta \\
    S & L & \Theta & {\bf{\color{blue}8}} \\ \hline
    S & {\bf{\color{blue}2}} & \Theta & P \end{array}$


    In column-3: $\displaystyle G + \Theta$ ends in $\displaystyle \Theta$

    $\displaystyle G$ could be $\displaystyle 0$ (zero).
    Then there would be no "carry" to column-2 and $\displaystyle L = 2.$
    Since $\displaystyle T = 2$, this is not possible.

    Hence, $\displaystyle G = 9$ and $\displaystyle L = 1.$
    . . And there is a "carry" from column-4.

    . . $\displaystyle \begin{array}{ccccc} ^1 & ^2 & ^3 & ^4 \\
    & & {\bf{\color{blue}9}} & \Theta \\
    S & {\bf{\color{blue}1}} & \Theta & {\color{blue}8} \\ \hline
    S & {\color{blue}2} & \Theta & P \end{array}$


    Available digits: .$\displaystyle \{0,3,5,6\}$

    In column-4: $\displaystyle \Theta + 8$ ends in $\displaystyle P.$
    The only combination is: .$\displaystyle \Theta = 5,\,P=3$

    . . $\displaystyle \begin{array}{ccccc} ^1 & ^2 & ^3 & ^4 \\
    & & {\color{blue}9} & {\bf{\color{blue}5}} \\
    S & {\color{blue}1} & {\bf{\color{blue}5}} & {\color{blue}8} \\ \hline
    S & {\color{blue}2} & {\bf{\color{blue}5}} & {\bf{\color{blue}3}} \end{array}$


    Available digits: .$\displaystyle \{0,6\}$

    It assumed that a number will not begin with zero.
    . . Hence: .$\displaystyle S = 6$

    . . $\displaystyle \begin{array}{ccccc} & & {\color{blue}9} & {\color{blue}5} \\
    {\bf{\color{blue}6}} & {\color{blue}1} & {\color{blue}5} & {\color{blue}8} \\ \hline
    {\bf{\color{blue}6}} & {\color{blue}2} & {\color{blue}5} & {\color{blue}3} \end{array}$


    Therefore: . $\displaystyle S\,T\,O\,P = 6\,2\,5\,3$

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