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Truly lost here, i know abba could look anything like 1221 or even 9999 To gain full voting privileges, However how do i prove 11 divides all of the possiblities?

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You'll need to complete a few actions and gain 15 reputation points before being able to upvote Prove that $a^a \\ b^b \\ge a^b \\ b^a$, if both $a$ and $b$ are positive. Upvoting indicates when questions and answers are useful

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Instead, you can save this post to reference later. For example a palindrome of length $4$ is always divisible by $11$ because palindromes of length $4$ are in the form of $$\\overline{abba}$$ so it is equal to $$1001a+110b$$ and $1001$ and $110$ are You then take this entire sequence and repeat the process (abbabaab).

Although both belong to a much broad combination of n=2 and n=4 (aaaa, abba, bbbb.), where order matters and repetition is allowed, both can be rearranged in different ways