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?

Solution

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.

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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

14 thoughts on “Curious Number Substrings

  1. Pingback: Nichole Smith
    1. This is just a wild stab in the dark (happy to be proven wrong) but I don’t think such a number is possible: the sum of the substrings will always be less than the original number.

      Like

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