Little explorations with HP calculators (no Prime)

[3298]

(12-29-2018 12:10 AM)Albert Chan Wrote:  Sorry I do not follow the logic ... (balls cannot be "rearranged", see post #331)

I described how to generate the "special arrangement" mentioned in the challenge. If you call that "rearranging", or "generating a pattern to look for in order to spot the good arrangements", I don't care. It's the same thing.
In case you are referring to

(12-28-2018 11:21 PM)3298 Wrote:  The n-th ball [...] is put back into the line, and the (n+70)-th ball is removed from it.

then I'll point out that this alludes to how Anna is allowed to move balls (by taking them home and leaving the rest for Berta). For this sentence, it's best to imagine that Anna rescinds her decision to pick the range starting at the n-th ball, and picks the range starting at the (n+1)-th one instead. Putting one ball back exactly where it was taken from and grabbing another is what she needs to do to enact this change of mind.