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Math Help - Simple Math problem

  1. #1
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    Simple Math problem

    There are two number a and b. both are four digit numbers . a is reverse of b and a is four time of b.
    a = reverse(b)
    AND
    a = 4*b
    how to find a and b? with explaination
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  2. #2
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    Re: Simple Math problem

    Write the digits of a as "pqrs". The a= 1000p+ 100q+ 10r+ s and b= 1000s+ 100r+ 10q+ p. a= 4b becomes 1000p+ 100q+ 10r+ s= 4(1000s+ 100r+ 10q+ s).

    If p, q, r, and s could be any real numbers there would be an infinite number of solutions. But here we know that p, q, r, and s must be integers from 0 to 9 (and, presumably, neither p nor s are 0).
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  3. #3
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    Re: Simple Math problem

    Hello, ashoksingh!

    \text{There are two four-digit numbers, }a\text{ and }b.
    . . a\text{ is the reverse of }b.
    . . a\text{ is four times }b.

    \text{Find }a\text{ and }b.

    \text{Let }\,\begin{Bmatrix}a &=& DCBA \\ b &=& ABCD \end{Bmatrix}


    \text{We have an "alphametic":}

    . . \begin{array}{cccc}_1&_2&_3&_4 \\ A&B&C&D \\ \times &&& 4 \\ \hline D&C&B&A \end{array}


    \text{In column-1 }(c_1)\text{, we see that }4A \,=\,D.
    \text{Since }D\text{ is a digit, }A\text{ must be }1\text{ or }2.

    \text{In }c_4\text{, we see that }D\times 4\text{ ends in }A.
    . . \text{Hence, }A\text{ must be even: }\:A = 2.


    \text{We have:}

    . . \begin{array}{cccc}_1&_2&_3&_4 \\ 2&B&C&D \\ \times &&& 4 \\ \hline D&C&B&2 \end{array}


    \text{In }c_1\text{, we see that }D = 8\text{ or }9.
    \text{In }c_4\text{, we see that }D\times 4\text{ ends in }2.
    . . \text{Hence: }\,D \,=\,8


    \text{We have:}

    . . \begin{array}{cccc}_1&_2&_3&_4 \\ 2&B&C&8 \\ \times &&& 4 \\ \hline 8&C&B&2 \end{array}


    \text{In }c_2,\,4B+ \text{(carry)}\,=\,C.
    . . \text{Hence, }B\text{ must be }0\text{ or }1.

    \text{If }B = 0\text{, then }c_3\text{ says: }\,4C + 3\text{ ends in }0.
    . . \text{This is impossible, so }\,B = 1.


    Finally, we have:

    . . \begin{array}{cccc} 2&1&7&8 \\ \times &&& 4 \\ \hline 8&7&1&2 \end{array}
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  4. #4
    Senior Member sakonpure6's Avatar
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    Re: Simple Math problem

    I can do a C++ program for you to solve the problem if you want?!
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  5. #5
    Forum Admin topsquark's Avatar
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    Re: Simple Math problem

    Quote Originally Posted by sakonpure6 View Post
    I can do a C++ program for you to solve the problem if you want?!
    It's a nice gesture, but I wouldn't think that a program would help the OP learn the method all that well...

    -Dan
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