This was a fun problem, but I think lookup table solutions are possible given the way the way the test suite is configured. Maybe you could add a string parser to see if the test suite correct solutions are included in the answer code?
Television Screen Dimensions
Given a matrix, swap the 2nd & 3rd columns
Is it an Armstrong number?
05 - Vector Equations 2
5th Time's a Charm
Number construction III
Return the sequence element III
Mean number of letters per word (Hard)
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