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This question already has an answer here:

In a room of 100 leaders, at least 1 leader is honest; and in every pair, at least one leader is dishonest. Find the maximum number of honest leaders, if every leader is either honest or dishonest.

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marked as duplicate by f'', Beastly Gerbil, GentlePurpleRain Aug 16 '16 at 21:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Welcome to Puzzling! Please do not use random tags - make sure the tags you use are applicable to the question. $\endgroup$ – Deusovi Aug 16 '16 at 21:31
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I feel like the question could be a little more clear, but if I'm understanding it right the answer is:

Just that one. If there were more, you would create a possible pair of two leaders such that not every pair contains at least one dishonest leader.

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