#induction puzzle

[quanyails]

Hot concept for an isekai:

The protag is a math undergrad and they're dropped in the world of their logic professor's textbook

Everyone is either wearing unidentified colored hats or in prison

[mlhllndovrdrv]

maskedriderghost you were asking about that puzzle with the hats, right?

Well, to start, what we know is: There is at least 1 blue hat out of three, and the problem is fair. This means that all three wise men can reach the same conclusion from their point of view.

Assuming there’s one hat, then one man would see two white hats. Knowing there must be at least one blue, he can answer. But the other two cannot answer as they see one white and one blue, making this situation unfair. Thus, there must be at least 2 hats.

If there are 2 hats, then the two men wearing blue hats will know they are wearing a blue one, since they know there must be at least two and they see a white one and a blue one. But the one wearing a white hat won’t be able to infer that. This situation is unfair, and so there must be three blue hats.