QUESTION
This is an assignment that had confused me for a long time. So I think you guys who study computational biology might be interested. The original question is:
Find the two most similar DNA sequences of length 20 that Blast using a word length of 5 will fail to align.
ANSWER
BLAST works by finding a perfect match between sequences of a length equal to this "word length" and then enlarging it in a standard way -- yet there will be no alignment without this perfectly matched word.
So in your case, you must look for two 20bp sequences with no common 5bp sub-sequence; for instance:
AAAAAAAAAAAAAAAAAAAA
and
AAAACAAAACAAAACAAAAC
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