Vestigium: trivial O(n*n) solution scanning rows and columns for duplicates.
Nesting Depth: linear solution comparing the current depth with the next digit.
Parenting Partnering Returns: O(n log n) solution performing a linear scan on sorted activities.
ESAb ATAd: very fun interactive problem, solved by querying two specular bits every 10 queries to detect the kind of "quantum fluctuation".