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Looking for a way to calculate the number of combinations of letters in the alphabet with the following restrictions:

  1. any number of letters in a combination
  2. no repeat letters (as in a single entry can contain one A, but not two As)
  3. If a set of letters contains letters that are not adjacent, it must also contain all letters between those letters.

It's that third rule that I don't have a clue how to get around.

JonMc
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  • Well, numbering the letters from least to greatest (so $A=a_1$ and $Z=a_{26}$ if you are using the standard English alphabet), we see that your string must be a permutation of ${a_n,a_{n+1},\cdots,a_{n+k}}$ for some $n,k$ so... – lulu Jul 30 '20 at 14:16
  • Note: if by "combination" you mean that the order is not relevant, then the problem is much, much simpler since you aren't concerned about the permutations of the set I mentioned. – lulu Jul 30 '20 at 14:22

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