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# shuffling algorithm for letters in a word

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If there is a word , then will swapping 2 adjacent letters at the beginning of string will give me a new word (not necessarily a meaningful word) and then swapping the next 2 letters will give me a new word. After switching the last 2 letters , we go back to the beginning of the word and continue.
example: If the word is ABCCD , it becomes BACCD , then BCACD , BCCAD, BCCDA, then CBCDA and so on ..

Ignoring the swapping of the same two letters (like BCCDA) , will this algorithm give me all the words of all permutations ? I Tried for few number of letters and it works , but I want to know how to prove for any no. of letters. I have no idea how to prove it , it seems to work . By the way ,it is not a puzzle .

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It looks like you're taking the first letter and essentially rotating it through the different positions while the other letters remain in the same order. I noticed that all the possible permutations begin with two letters that were next to each other in the original sequence (or in the first and last spot). For example, I don't think you can get a sequence starting with AC. So this does not seem to hold up.

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Yes , I see that some of the permutations do not show up. Thanks!

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• 11 months later...

there is a way however to permute through all possibilities by swapping two letters.

ABC -> ACB -> BCA -> BAC -> CAB -> CBA

ABCD -> ABDC -> ACDB -.> ACBD -> ADBC -> ADCB ->

BDCA -> BDAC -> BADC -> BACD -> BCAD -> BCDA ->

DCBA -> DCAB -> DBAC -> DBCA -> DACB -> DABC

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