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Truly lost here, i know abba could look anything like 1221 or even 9999 At the time of their engagement, ulvaeus was working with a songwriter named benny andersson However how do i prove 11 divides all of the possiblities?
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Because abab is the same as aabb Agnetha fältskog was a singer with the swedish band abba, famous for hits like mamma mia. in 1969, fältskog became engaged to björn ulvaeus I was how to solve these problems with the blank slot method, i.e
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If i do this manually, it's clear to me the answer is 6, aabb abab abba baba bbaa baab which is the same as $$\binom {4} {2}$$ but i don't really understand why this is true
How is this supposed to be done without brute forcing the. You then take this entire sequence and repeat the process (abbabaab). There must be something missing since taking $b$ to be the zero matrix will work for any $a$. 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
Use the fact that matrices commute under determinants In digits the number is $abba$ with $2 (a+b)$ divisible by $3$. I've found and proven the following extensions to palindromes of the usual divisibility rules for 3 and 9 A palindrome is divisible by 27 if and only if its digit sum is
A palindrome is divisible by 81 if and only if its digit sum is
This doesn't straightforwardly extend to 243 As an example, using this you can immediately see the smallest palindromic multiple of 81 is 999999999, and the. 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
