[thebrainkid]

I agree. If the stranger says something along the lines of, "The number of blue dots is greater than 50." on one day, and on some subsequent day says, "The number of blue dots is not an odd number less than 45." or "The number if blue dots is not a number less than 40 which is divisible by 3.", then no new information will have been conveyed by these latter example statements. I imagine that the stranger could keep stringing them along like this for quite some time, and if multiple statements referring to the same subset were allowed (ex: "The number of blues is not a number which is divisible by 37 which is less than 45." and "The number of blues is not 37.") then the stranger could continue this indefinitely.

[fenomas]

The puzzle doesn't involve the stranger saying multiple things. He just shows up, says one thing that everyone already knows to be true (e.g. "At least one of you has blue eyes"), and then leaves forever. And that's enough to cause everyone to (eventually) commit suicide.

The fact that this happens even though it doesn't sound like new information is what makes it an interesting puzzle!