Curious Number Substrings

old metal numbers

If you add all the substrings of 891, the sum is 198, which is the reverse of 891:

891 → 8 + 9 + 1 + 89 + 91 = 198

This is the only 3-digit number that has this property.

There is also one 4-digit number with the same property. Can you find this number?


As I said above, there is only a single solution. The answer is 2931:

2931 → 2 + 9 + 3 + 1 + 29 + 93 + 31 + 293 + 931 = 1392

To solve this kind of problem, you may resort to trial and error but it could get cumbersome. A simple Python or C++ code can do the trick for this.

Now, you may try to figure out if there is a 5-digit number solution.


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 You can find me on Twitter @EdmarkLaw and Facebook. My email is
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14 Responses to Curious Number Substrings

  1. Pingback: Curious Number Substrings - breaking news, vital journalism, quizzes, videos, celeb news, Tasty food videos, recipes, DIY hacks, and all the trending buzz you’ll want to share with your friends. Copyright eComSub, Inc. All rights reserved.

  2. nicholesuomi says:

    It turns out 941 also has this property, as I explain here:
    Cool fun fact!

    Liked by 1 person

  3. Pingback: Nichole Smith

  4. azephyrrose says:

    I love this post! My brain does things like this naturally, but I never knew there was a name for it. Thanks!

    Liked by 1 person

  5. This is too complex for my simple brain.

    Liked by 1 person

  6. Interesting to know. The 5 number is too much for me. Love the Blog.

    Liked by 1 person

  7. This is so interesting to share with my son 🙂

    Liked by 1 person

  8. As a total ignoramus when it comes to math, I can only say WOW!

    Liked by 1 person

  9. John says:

    Amazing!😊 I like this, you have made some post about this before and it’s awesome!😊

    Liked by 1 person

  10. Amartya says:

    wow. That’s interesting!

    Liked by 1 person

  11. Jack Shalom says:

    I guess the obvious question is: is there a 3 or 4-digit number whose substrings sum to the original number itself? Unless you’ve already done a post on that…

    Liked by 1 person

  12. Reblogged this on Let’s Math.

    Liked by 1 person

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