The 2014 ACM North Central Region programming contest contained a problem about a group of v bandits who want to use multiple locks to seal their treasure and distribute keys in such a way that no group of less than m bandits can open all the locks. The problem asks for an algorithm that will determine the number of locks needed for any set of parameters (v, m). I will present an analytic solution that produces a minimum number of locks, a recurrence relation solution, and a constructive algorithm that can print out a table showing the locks and which subset of bandits hold keys for each lock. Each table forms a balanced incomplete block design (BIBD). The parameters of the BIBD can be uniquely determined from v and m.
Gossett, Eric, "Designing for Mistrust" (2015). ACMS Conference Proceedings 2015. 7.
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