However how do i prove 11 divides all of the possiblities? Prove that $a^a \\ b^b \\ge a^b \\ b^a$, if both $a$ and $b$ are positive. You'll need to complete a few actions and gain 15 reputation points before being able to upvote
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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
