If my over-use of str2num has in any way caused offense, I hereby beg leave to apologize.
My hat's off to you for such a solution. I'm baffled as to how to decode it (pun intended). I know that there has been a lot of furor over the use of regexp and other string-based functions, conversions, etc. to lower solution sizes for problems in general, but this problem is string-based, so I see no problem in solving it via arcane string methods.
DNA N-Gram Distribution
First non-zero element in each column
Construct an index vector from two input vectors in vectorized fashion
Getting the indices from a matrix
Combined Ages 1 - Symmetric, n = 3
Divisible by 4
Self-similarity 2 - Every third term
Lights Out 1 - 5x5, 3 moves
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