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2. Non-Local Strings For this question, a block is a sequence of 20 characters, where each...

2. Non-Local Strings

For this question, a block is a sequence of 20 characters, where each character is one of the 26 lowercase letters a-z. For example, these are blocks:

iwpiybhunrplsovrowyt
rpulxfsqrixjhrtjmcrr
fxfpwdhwgxtdaqtmxmlf
  1. How many different blocks are there?
  2. A block is squarefree if no character appears two times consecutively. The first and third example above are squarefree, but the second example is not because of the two consecutive occurrences of r. How many squarefree blocks are there?
  3. A block is non-local if the number of characters between any two occurrences of the same character is at least 2. The first example above is non-local. The second example is not, because there are two occurrences of r with no characters between them. The third example is not because there are two occurrences of m with only one character between them. How many non-local blocks are there?
  4. A block is k-non-local if the number of characters between any two occurrences of the same character is at least k. Write a formula for the number of k-non-local blocks that is valid for any k∈{0,…,20}.

Sanity check: The formula you get for 2.4 gives the answer to 2.2 when k=1 and gives the answer to 2.3 when k=2.

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milcah answered 1 year ago
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