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Math Help - [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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    Hello, DINO!

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

    \begin{array}{ccccc} & & G & \Theta \\<br />
S & L & \Theta & W \\ \hline<br />
S & T & \Theta & P  \end{array}

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

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


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

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

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

    . . \begin{array}{ccccc} ^1 & ^2 & ^3 & ^4 \\<br />
 & & {\bf{\color{blue}9}} & \Theta \\<br />
S & {\bf{\color{blue}1}} & \Theta & {\color{blue}8} \\ \hline<br />
S & {\color{blue}2} & \Theta & P  \end{array}


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

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

    . . \begin{array}{ccccc} ^1 & ^2 & ^3 & ^4 \\<br />
 & & {\color{blue}9} & {\bf{\color{blue}5}} \\<br />
S & {\color{blue}1} & {\bf{\color{blue}5}} & {\color{blue}8} \\ \hline<br />
S & {\color{blue}2} & {\bf{\color{blue}5}} & {\bf{\color{blue}3}}  \end{array}


    Available digits: . \{0,6\}

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

    . . \begin{array}{ccccc} & & {\color{blue}9} & {\color{blue}5} \\<br />
{\bf{\color{blue}6}} & {\color{blue}1} & {\color{blue}5} & {\color{blue}8} \\ \hline<br />
{\bf{\color{blue}6}} & {\color{blue}2} & {\color{blue}5} & {\color{blue}3}  \end{array}


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

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