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Freedonia has fifty senators. Each senator is either honest or corrupt. Suppose you know that at least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt. Based on these facts, can you determine how many Freedonian senators are honest and how many are corrupt? If so, what is the answer?

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Suppose we assume that within those 50 person, A and B are honest and rest 48 are corrupt. Now in the question it is mentioned that whenever we take 2 person at least one of them is corrupted. Like it maybe possible that both are corrupted but there is no chance that both person are honest. So, when we will choose A and B it is not possible that both are honest because it is contradicting the question statement. It’s also mentioned that at least one person is honest.

So, it is clear that only 1 person is honest and rest 49 are corrupt.
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Based on the given information, we can determine that at least one senator is honest, but we cannot determine the exact number of honest and corrupt senators.

We know that at least one senator is honest, but we do not know how many honest senators there are. It could be that only one senator is honest, or it could be that multiple senators are honest.

We also know that given any two Freedonian senators, at least one is corrupt. This means that if we choose any two senators, we know that at least one of them is corrupt. However, we cannot determine the number of corrupt senators based on this information alone. It could be that all but one senator is corrupt or that a majority or minority of the senators are corrupt.

Therefore, while we know that there is at least one honest senator and that given any two senators, at least one is corrupt, we cannot determine the exact number of honest and corrupt senators.

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