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For the first num and the last num in the array, do they have the same "chance" to be switched?
@MindGeek I'm not super sure that I understand your question. However, if you can convince yourself that the brute force analysis is correct, it might help to think about how Fisher-Yates is actually almost identical to it. Essentially, after the ith iteration of the swapping loop,
array[:i] (inclusive) is the result (so far) of the algorithm, while
array[i+1:] is the "hat", or
aux from the brute force solution.