Although this is a perfect refactor of the code, I don't see it as being the best practice for this excersise, since the job was explicitly to debug the existing code (for practicing loops) and not entirely refactor it to something else.

yes starting value of range() is 0 so defining it as 0 makes no difference.

Could be improved by caching the previous result and just multiplying it by 2 instead of calculating the whole 2^n.

this one is should be the top solution

this is probably the fastest solution, possibly because it does not use the ** (square) operator. I compared these top two solutions using timeit

used timeit to compare the performance of your solution with the top two above, and it outperformed them

have heard coders criticize the general use of generic for loops, but timeit has convinced me that my solution is performant—after comparing it with three other solutions.

how does this work?

have you used timeit to compare the performance of your Counter() solution with this one? I personally believe that your solution could be 10X slower.

[[]] <-- nothingburger

thanks for bringing this up. actually a 0 dimensional matrix because it fails to contain any values. it is an empty shell; a random tests byproduct for frustration purposes. would help to see this specific empty matrix in standard tests.