Eighteen

Apr. 13th, 2008 11:19 pm
rbandrews: (Kayla)
[personal profile] rbandrews
The number 1818 is a number, 18, repeated twice.

If you add together the digits, 1+8+1+8, you also get 18.

There is no other number with this property.

Date: 2008-04-14 09:26 pm (UTC)
From: [identity profile] wheeerdball.livejournal.com
The proof for why this is the only answer can easily be re-constructed for alternative basis. The part about how you can only have two digits in the sub-number applies to all basis n > 2. From there, the number is then uniquely determined to be 1 (n-2) 1 (n-2).

If the basis is n = 2, then the proof needs to be modified to state that there can be no more than three digits. But the number 1 0 1 0 still works, and by trial and error it can still be solved to show that there is no other answer.
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