# .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,

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.

### Posted by 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. 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 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.

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1. And it works well in Art, Science, Maths and Magic.

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

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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 :D

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3. 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?”

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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.

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

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1. Glad you liked it :)

Concatenate is a common word in number theory so I forgot that it’s not commonly used :D The word is quite handy though :).

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1. I love that you used it.
Your extra knowledge is shared and ours to accept and bank. If I may …. (oh, sorry, I already have!) :))

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