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}

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 learnfunfacts.com. You can find me on Twitter @EdmarkMLaw and Facebook. My email is learnfunfacts@gmail.com
This entry was posted in Mathematics, Puzzles and tagged , , , . Bookmark the permalink.

One Response to Repeating Digits In Different Bases

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

    Liked by 2 people

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s