How much data anonymization is good enough? The problem is harder than you think
Consider this classic puzzle, called The Dot-Town Suicides:
Each resident of Dot-town carries a red or blue dot on his (or her) forehead, but if he ever figures out what color it is he kills himself. Each day the residents gather; one day a stranger comes and tells them something—anything —non-trivial about the number of blue dots. Prove that eventually every resident kills himself.
“Non-trivial” means here that there is some number of blue dots for which the statement would not have been true. Thus we have a frighteningly general version of classical problems involving knowledge about knowledge. (Source)