An unintuitive logic puzzle okay so if that's not valid, then when you start out unsure if you're on an island with m blue eyed people or m-1 blue eyed people, you can't rely on it being true that "if there were m-1 blue eyed people, they would have left in m-1 days - therefore there are more than m-1 people with blue eyes, therefore I can leave on night m"
Because that's what this is about at root. There are only 2 possibilities from the perspective of a blue eyed person: either there are m-1 blue eyed people, or m. He's trying to deduce which world has in.
If he's waiting to see if m-1 people maybe don't leave in m-1 days, but it turns out to be FALSE that m-1 people would leave in m-1 days, then waiting for that doesn't tell him what world he's in. He could be in a world where m-1 people have blue eyes, or m people have blue eyes.
These guys don't want to get tortured for eternity. They can't rely on iffy reasoning. They have to be SURE. No guessing allowed. Only deductions.
So if it's at all possible that m-1 people WOULDN'T leave in m-1 days, then we absolutely cannot then say, "oh well I didn't see m-1 people leave in m-1 days, so therefore there must be m blue eyed little"
So if m is 100, each blue eyed person sees 99 blue eyed people and they, as perfect logicians (not perfect planners, not perfect committers to rules), have to ask themselves, can I really be sure 99 people would leave in 99 days? If they're anything less than deductively sure, they can't leave in 100 days.