Looking into the literature, I think we need to assume that the array is promised to be a permutation of 1, 2, ..., n, which rules out my example. Then, your condition is indeed equivalent to being far in Hamming distance.

Wait, I guess it depends how you define "10% entries must be moved". Otherwise, you need to distinguish 1, 2, ..., n and 1, 2, 0.9n - 1, n + 1, 0.9n + 1, 0.9n + 2, ..., n, which are the same except two elements. Or I am missing something?

(Well, Claude in my case, but the same idea :))

Without ChatGPT it would have been "slaughter" not "wrestling". ;-)

Yay! I am in the process of waiting for mine. Good luck!!

Do you also remember your exact arrival date? I feel every immigrant does. :D