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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It turns out 941 also has this property, as I explain here: https://nicholesuomi.wordpress.com/2018/07/24/960/

Cool fun fact!

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

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This is too complex for my simple brain.

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

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This is so interesting to share with my son 🙂

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

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

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wow. That’s interesting!

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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…

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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.

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At least for three digits I have a proof that you’re right 🙂 (Second section)

https://nicholesuomi.wordpress.com/2018/07/24/960/

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Reblogged this on Let’s Math.

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