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Math Help - addition

  1. #1
    Junior Member
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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 B+C?

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

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

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


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

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

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

    Hence, neither R nor N can be 9.


    The next largest sum occurs for: \{R,N\} = \{7,8\} and we have:
    Code:
        8 7
      + 7 8
      -----
      1 6 5
    Therefore: 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
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    thanks...
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