Repeating Digits In Different Bases

puzzle

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?

Solution

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

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

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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. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

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