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Quoc Tran Anh Le Coordinator

14/09/2018 at 07:07
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A 3-digit number in base 7 is also a 3-digit number when written in base 6, but each digit has increased by 1. What is the largest value which this number can have when written in base 10?


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    Mr. Bee moderators 24/09/2018 at 03:01

    When written in base 7, the number is a.72 + b.7 + c

    When written in base 6, the number is (a+1).62 + (b+1).6 + c +1

    We get: a.72 + b.7 + c = (a+1).62 + (b+1).6 + c +1, it implies 13a + b = 43.

    This yields a = 3, b = 4.

    When written in base 10, the largest number possible: 3.72 + 4.7 + 9 = 184

    Quoc Tran Anh Le selected this answer.

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