math riddle: King and His Prisoners (no content, long)

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If the king knows who the counter is then would't he be the first one invited into the center room and then left forever in his cell?

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No. The "rules" stipulate that each of the prisoners must be called out at least x times for all x. So the counter must be called as many times as he wants.

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that's not how I read it.

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The king will call the prisoners in any order he pleases, and he can call and recall each prisoner as many times as he wants, as many times in a row as he wants. The only rule the king has to obey is that eventually he has to call every prisoner any arbitrary number of times. So maybe he will call the first prisoner in a million times before ever calling in the second prisoner twice, we just don't know. But eventually we may be certain that each prisoner will be called in ten times, or twenty times, or any number you choose.

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Lets say John is the counter. King calls john on day 1 ( and each consecutive day until our arbitrary number has been met). John then stays in his cell until he his dead never having counted at all. Game over.

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If the king knows who the counter is then would't he be the first one invited into the center room and then left forever in his cell?

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No. The "rules" stipulate that each of the prisoners must be called out at least x times for all x. So the counter must be called as many times as he wants.

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that's not how I read it.

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The king will call the prisoners in any order he pleases, and he can call and recall each prisoner as many times as he wants, as many times in a row as he wants. The only rule the king has to obey is that eventually he has to call every prisoner any arbitrary number of times. So maybe he will call the first prisoner in a million times before ever calling in the second prisoner twice, we just don't know. But eventually we may be certain that each prisoner will be called in ten times, or twenty times, or any number you choose.

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Lets say John is the counter. King calls john on day 1 ( and each consecutive day until our arbitrary number has been met). John then stays in his cell until he his dead never having counted at all. Game over.

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You're missing the point. The arbitrary number can never be met. It isn't set in advance. We're saying that each prisoner will be called out an infinite number of times.