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Thread: addition

  1. #1
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    addition

    NR
    + RN
    _______
    ABC


    The addition problem above is correct. If N, R, A, B, and C are different digits, what is the greatest possible value of B+C?
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Judi
    NR
    + RN
    _______
    ABC


    The addition problem above is correct. If N, R, A, B, and C are different digits, what is the greatest possible value of B+C?
    A is clearly 1
    N+R is a two digit number.
    B=C+1
    We have to find max. value of C
    since N and R are different
    N=9, R=8
    C=7,B=8,A=1
    Answer is 15

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  3. #3
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    Sorry, Malay . . .

    Hello, Judi!

    Code:
      1 2 3
    
        N R
      + R N
      -----
      A B C
    The addition problem above is correct.
    If N, R, A, B, and C are different digits,
    what is the greatest possible value of $\displaystyle B+C$?

    In column-1, we see that $\displaystyle A = 1.$
    Code:
      1 2 3
    
        N R
      + R N
      -----
      1 B C

    In column-3, we see that $\displaystyle R + N$ ends in $\displaystyle C.$
    In column-2, we see that $\displaystyle N + R$ ends in $\displaystyle B.$

    Then $\displaystyle R + N \geq 10$ and there is a "carry" to column-2
    . . where we have: $\displaystyle N + R + 1 \:=\:10 + B$


    For maximum $\displaystyle B + C$, let $\displaystyle \{R,N\} = \{8,9\}$
    . . But we find that this results in duplicated digits.

    For $\displaystyle R = 9$ we have:
    Code:
        N 9
      + 9 N
      -----
      A B C

    But we get: $\displaystyle B = N.$
    . . (If $\displaystyle N = 9$, then $\displaystyle B = R.$)

    Hence, neither $\displaystyle R$ nor $\displaystyle N$ can be $\displaystyle 9.$


    The next largest sum occurs for: $\displaystyle \{R,N\} = \{7,8\}$ and we have:
    Code:
        8 7
      + 7 8
      -----
      1 6 5
    Therefore: $\displaystyle B + C \,= \,11$

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  4. #4
    Super Member malaygoel's Avatar
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    I made a mistake: Duplicate Values....Sorry

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  5. #5
    Junior Member
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    thanks...
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