Repeating Digits In Different Bases


931 (in base 10) is an interesting number since in two other bases, it’s a repeating 3-digit number, namely, in base 11 and base 30.

931=777_{11} and 931=111_{30}

Can you find the other three-digit numbers with this property?


273=333_{9}; 273=111_{16}

546=666_{9}; 546=222_{16}


About Edmark M. Law

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. I blog at You can find me on Twitter @EdmarkLaw and Facebook. My email is
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One Response to Repeating Digits In Different Bases

  1. Hmmm….still can’t figure it out. (“⌒∇⌒”)

    Liked by 2 people

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