In the "hold a competition" case of leader selection we need a special kind of puzzle that has a few important properties:
Difficult to solve, but easy to verify. A human-type puzzle that fits this description would be a jigsaw puzzle: it takes a long time to figure out where all the pieces go, but once complete anyone can check whether it is correctly solved by merely glancing at it.
Given a set of equally powerful contenders, the outcome should be random.
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