But the summed probability of the “not too far away results” is much higher, i.e. P([93, 107]\{100}) > P([100]).
So if you only shoot 100/100 with your coin, that's definitely weird.
That's true of every result. If you're using this to conclude you have a weird coin then every coin is weird.
Tellingly, Reagan’s America is where I really notice cultural growth dying out and trust vanishing.
The liar doesn't necessarily "have" any hats. Again, the assumption that the liar has hats is incorrect because it's relying on an conversational implication, rather than a specific assertion.
The liar could be lying because they have no hats. They could be lying because they have a non-green hat. We cannot conclude E because it's possible that E is not correct.
It does not. All my unicorns fly. There is no assumption that I have a unicorn. There is an assumption, based on the claim but it is not a fact.
The puzzle also assumes that "my" implies there is some ownership (we'll take for granted "my" means "has" for simplicity), which is another quibble that unravels the whole thing.
E is correct. I don't see how A comes to be the accepted answer.
"All my hats are green" is still false even when I own a red hat and a green hat.
Likewise, when you hear a word for the first time suddenly you hear it five times in a row. Or if you see somebody once you suddenly start running into them all over the place.
It's because it's cheaper to repeat past realities than to create new ones.