.As Easy As 1-2-3: A Little Numerical Curiosity

numbers

Here’s a neat number curiosity that you may find interesting.

Choose any number (preferably, a larger one). For example,

5470315986321981423

Write down the number of even digits, odd digits and the number of digits of the number you selected respectively:

8 11 19

Concatenate the three numbers:

81119

Perform the procedure described above to the concatenated number:

81119

1 4 5

145

Do it once again:

145

1 2 3

123

Now, if you do it again, it’ll loop back to 123. Hence, you will end up getting 123 regardless of which number you start with.

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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

24 thoughts on “.As Easy As 1-2-3: A Little Numerical Curiosity

    1. I found this one by accident while tinkering with another number trick (of which I read from one of Martin Gardner’s books). This one is so trivial so I suppose that somebody had already discovered it before I did. I am now very careful at claiming a discovery after I foolishly thought that I “discovered” the Kaprekar’s constant when I was a teen. The disappointment was real when I learned that it was already discovered half a century ago 😀

      Liked by 1 person

    1. Here’s an easy explanation:

      “Write down the number of even digits, odd digits and the number of digits of the number you selected respectively.”

      The explanation lies here.

      123 has one even digit, 2 odd digts and 3 digits in that order. This is the only number that meets the criteria. So, it doesn’t matter which number you choose, it will eventually reach 123 as there’s only one solution (123).

      Once you reached 123, it’ll just loop back to 123 if you do the process again.

      Liked by 4 people

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