i get that’s the idea behind it, but that is based on the assumption of the cause of silence, which doesn’t leave it as “certainty”, meaning nr1 couldn’t really deduce his own hat, without luck/guess, as his deduction would be based on assumption on a scenario, which isn’t the only potential reason for the silence -depending on parameters
(at least not as i saw it)
what i mean is, nr1 only knows something when nr 3 speaks up “i’m white”, nr 1 then knows he is black,
since in all the other variations, both nr 2+3 can be both black or white at the same time, leaving them silent, but still leaves the option for 1 to be black if they are either both white or nr3black nr2 white, , or nr 2 white, nr3 black, -so he’d need boths uncertainty (in saying “i’m either black or white”) at the same time to know for certain he couldn’t be black, a wisemans person’s silence just serve to reinforce the the uncertainty of the others in that scenario-without guessing/luck
(unless i’m missing a rule or something)