Very nice exercise! It made me to create a monty hall mini-game.

I suggest to include test with space at the beginning (python version) at least. While in description is said, that string can only start with uppercase ascii, tests proved, that it's necessary to count with case when string starts with space. Still i voted it up. Great test not only for programming abilities.

"You can't convert binary to decimal and vice versa" i assumed that i can't use builtins for it, but can i write my own func? Please make it clear for me. Thanks

I didn't know what barycenter is either. Thank you for this mathematic kata!

You should correct the tested method name(shiftedDiff) to match method name(shifted{underscore}diff) or vice versa. Unless adjusting the test code is part of the exercise. :)