There are eight of them here, eight in the other region. Each gym leader specializes in a certain type of Pokemon; that can be used to a challenger's advantage by bringing a team strong against that particular type. They give a cash prize in exchange for a defeat, and also award trophies in the form of "badges", which apparently allow for certain benefits to be utilized. They also get more difficult to defeat the farther into the nation a trainer goes, suggesting a sort of gatekeeping mechanism not inconsistent with the notion of "gameplay".
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