Yeah, I was thinking about if the stranger said something like, “not all the dots are blue.” This is non-trivial by the definition given, and no one would have to kill themselves at all.
In a one red dot town, you could say “there is at least one blue dot”
So let's say there are two people with red dots, let's name them Ruth and Rudy. Ruth now knows that "not all dots are blue" (which is equivalent to "there is at least one red dot"). She sees Rudy with the red dot: Fine, here's the person with the red dot.
But wait a minute, why is Rudy not killing himself? If Rudy is the only person with a red dot, he should have seen only blue dots... however he knows there has to be at least one red dot, so if he only saw blue dots, the red dot must have been him, so he would have killed himself.
But he didn't, so that means he has seen at least one red dot, which isn't him, and isn't anybody else Ruth has seen because she only saw blue dots otherwise.
Oh no, it must be Ruth with the second red dot!
Would this mean the colony would self-implode?
That makes sense. What about the other commenter, who said something like “Alice has a blue dot.”
Wouldn’t that not lead to everyone’s death?
I feel like some timing procedures need to be defined.
Whether someone is "slower at solving logic problems" goes into IQ etc, and is not relevant to the logic problem (the same way "what if someone refuses to kill themselves over something so superficial" is -- one should assume they can all do the math it takes equally well, else we would have been told of that.
The flaw in the proof is that it assumes that townsfolk only learn their dot color based on counting arguments. If the stranger's "anything non-trivial" statement includes information beyond just a raw count, then a townsfolk may learn their dot-color prematurely (e.g. by being told in the statement) and the proof fails.
If it was the latter, a one person town would always die.