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John

11/03/2017 at 07:30
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The digits of the three-digit integers a, b, and c are the nine nonzero digits 1, 2, 3, ..., 9, each of them appearing exactly once. Given that the ratio a:b:c is 1:3:5, determine a, b, and c. 


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    American moderators 12/03/2017 at 09:08

    a: b: c =1: 3: 5

    a, b, c have 9 nonzero digits with each of them appearing exactly once. The smallest possible number: 123 The last digit of c should be a multiple of 5 ending in 5, so the first digit of a should end in an odd digit (3, 7, or 9). The first digit of a should be 1 because if it were larger, then c would be four digits. Process of trial and error:

    a: b: c =1: 3: 5 = 123: 369 : 615 3 and 6 repeated

    a: b : c = 127: 381: 635 1 and 3 repeated

    a: b: c = 129: 387 645 This works!  

    So: a=129, b = 387, c = 645. 

  • ...
    In the name of love 12/03/2017 at 14:41

    a, b, c have 9 nonzero digits with each of them appearing exactly once. The smallest possible number: 123 The last digit of c should be a multiple of 5 ending in 5, so the first digit of a should end in an odd digit (3, 7, or 9). The first digit of a should be 1 because if it were larger, then c would be four digits. Process of trial and error:

    a: b: c =1: 3: 5 = 123: 369 : 615 3 and 6 repeated

    a: b : c = 127: 381: 635 1 and 3 repeated

    a: b: c = 129: 387: 645 This works!  

    Answer : a=129, b = 387, c = 645. 


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