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


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

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


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:


Perform the procedure described above to the concatenated number:


1 4 5


Do it once again:


1 2 3


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.


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 @EdmarkLaw and Facebook. My email is edmarklaw@learnfunfacts.com
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24 Responses to .As Easy As 1-2-3: A Little Numerical Curiosity

  1. 3C Style says:

    So cool! One more reason to love math.

    Liked by 1 person

  2. paolsoren says:

    I do wish I’d known you back when I taught mathematics to Middle school recalcitrants. Back then the only fun fact was talking about Fibonacci numbers.

    Liked by 1 person

  3. Edmark, you are toying with our minds. Never the less, I like it and say 1, 2,3, time to go.

    Liked by 1 person

  4. Vayuputrii says:

    Superb serendipity 🙂

    Liked by 1 person

  5. David says:

    Similar to what I’ve said before this is a curiosity but so is the who and why of its discovery.

    Liked by 1 person

    • 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

  6. Jeff Rab says:

    Scratching my head….will have to play with this to see it for myself…because in the words of a child I heard recently…”How do it know?”

    Liked by 1 person

  7. Peter Klopp says:

    Amazing number curiosity! I would love to see an explanation. Happy new year!

    Liked by 1 person

    • 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

  8. Thank you for the follow Edmark. I look forward to reading more of your blog through this connection. 🙂

    Liked by 1 person

  9. Viola Bleu says:

    May I just getch my dictionary first … (love a new word; concatenate) !!
    Now I shalt do the number thing – I always loved number games!!

    Liked by 1 person

  10. Indira says:

    Season’s Greetings! ❄️🌲

    Liked by 1 person

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