[Hoagy]

I thought this initially as well: if there are many of each colour, and the only information is that there is at least one blue dot, how could this be new information to trigger the suicides?

But this isn't correct. Let's say n = 6, a-c are blue, d-f are red, and the information is that there is at least one blue dot. a knows there are at least two, but thinks b may believe there is only one blue dot. Moreover, a believes b may believe that c may believe that there are no blue dots.

So if a was red, the information would mean that b would commit suicide if c did not initially commit suicide, but since neither has happened, a must have a blue dot and therefore must commit suicide.

A convoluted process to be sure but does it make sense how the information transmits by ruling out hypotheticals?