No, we can't.
This function calls itself recursively with a smaller array as an argument each time.
We start with all the balls (the whole array) and call it the second time with a smaller array (up to 3 balls).

This function is pure : it doesn't modify any of its arguments.

[0,1,2,3,4,5,6,7] are all the 8 balls.
At each step we use dichotomy to only keep one third of these balls.
The w function process one step of the algorithm and calls itself recursively.

One s is missing at Sibling__s__.

No, it isn't. If so, you can declare your parameter final.

I just didn't want to add a new String() to make a copy. I wanted it to stay as clear as possible.

Don't seem to work at all.

The description is quite vague. Sould a simple "return" of the pattern work ?

What loops would you expect in the solutions ?

A day is not around 90,000 ms but 86,400,000.
Your input seems to be in s and not ms.

You're missing simple cases for empty string or list containing only one element.

Missing many test methods.
Wrong name for takeWhile.
This method isn't tested.

Way better.

There is an undefined r in your base test cases.

Thanks for your feedback, I updated the description.